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I “EDI-i

LIBRARY

Michigan State
University

 

This is to certify that the

thesis entitled
THE EFFECT OF BARGAINING SEQUENCE AND

TYPE OF PAYOFF UPON COALITION STRUCTURE
AND STABILITY IN THE TRIAD

presented by

David Kline

has been accepted towards fulfillment
of the requirements for

 

_Ph_-D_-_degree in PSVCh0102V

 

{/ 1/

Major professor
Date 2//,/ é 8/

0-169

ABSTRACT

THE EFFECT OF BARGAINING SEQUENCE AND
TYPE OF PAYOFF UPON COALITION STRUCTURE
AND STABILITY IN THE TRIAD

By David Kline

Coalition formation theories make predictions about the two person
alliances that will form in three person groups, and the manner in which
the payoff will be divided between alliance partners. The predictions
are based on the initial resources possessed by each participant in a
given situation. The situation investigated the most often is that in
which 1) all participants have different initial resources, 2) no
participant has a majority of the resources, and 3) the combination
of the resources of any two persons yields a majority control of the
resources. This situation is called the Type 5 coalition situation.

The research studies investigating the Type 5 situation have pre-
sented evidence for two different coalition processes: 1) the two weak
players unite against the strong player and divide the payoff in pro-
portion to their relevant resources; and 2) the three possible types
of coalitions occur equally often and the payoff is divided equally.

An examination of these research studies revealed that their results

could have been produced by three extraneous factors.

 

—--

David Kline

The three extraneous factors were: 1) unequal status—-the player

 

with the largest resource value had greater status than the other two
players because he could win by himself if no coalition formed; 2) time
pressure-~since the first two players to make an agreement on dividing
the payoff were the winning coalition, there was a pressure to form a

quick coalition regardless of its terms; and 3) experimental demand char-

 

acteristics-—since the game's payoff was of little value to the partic-
ipants, the subjects played the game in order to obtain the experimenter's
approval and not the game's reward. It was hypothesized that the removal

of these extraneous influences would produce a more equal distribution of

 

initial contacts, initial coalitions, and payoff splits than previously
obtained, and result in coalitions more resistant to dissolution (i.e.,
coalitions that are more stable).

Unequal status was eliminated by employing a coalition—bargaining
game in which only a two—person coalition could win. The time pressure
was alleviated by requiring each player to have preliminary negotiations
with each of his two opponents prior to attempting to form a winning
coalition. The experimental demand characteristics were obviated by
creating a game payoff of significant value to the subjects, i.e., $9
in real money.

The results indicated that preliminary negotiations resulted in
payoffs being divided more equally than when no preliminary negotiations
were allowed. Real money payoffs, as opposed to play money payoffs,
resulted in a more equal distribution of initial contacts, and initial
coalitions, as well as payoff splits. In addition, real money increased

the stability of the coalitions. However, real money payoffs did produce

David Kline

distributions of contacts and coalitions that were significantly different
from chance. The only condition in which these distributions were not
significantly different from chance was the condition combining real money
payoffs and preliminary negotiations. It was concluded that while real
money payoffs contributed the most influence in producing equal coalition
outcomes in the Type 5 coalition situation, equal status and preliminary
negotiations were also necessary conditions for producing outcomes more
in line with chance distributions.

Additional results indicated that real money payoffs and preliminary
negotiations resulted in the players taking less time to reach an agree-

ment.

THE EFFECT OF BARGAINING SEQUENCE AND TYPE OF PAYOFF UPON

COALITION STRUCTURE AND STABILITY IN THE TRIAD

By

David‘Kline

A THESIS

Submitted to the College of Social Science
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Psychology

1968

 

Acknowledgements

The author expresses his gratitude to Dr. James L. Phillips, Dr.
Santo F. Camilleri, Dr. Alfred G. Dietze, and Dr. Jeanne E. Gullahorn
for their guidance in the planning and completion of this dissertation.
Special thanks are given to Dr. James L. Phillips for his assistance
and friendship through all phases of this dissertation. The author also

thanks his wife, Marilyn, for her devotion to the completion of his

degree.

 

 

TABLE OF CONTENTS

Page
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF ILLUSTRATIONS. . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF APPENDIX A TABLES. . . . . . . . . . . . . . . . . . . . . ix
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . l
PROBLEM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .I 12
METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
RESULTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

 

Table

LIST OF TABLES

Page

Caplow and Gamson's predicted coalitions in triads of
varying initial resources . . . . . . . . . . . . . . . . 2

2 X 2 factorial design of the experiment. . . . . . . . . 25

Exact probability test for independence between the

initial coalition distribution in the single stage/

play money condition and the initial coalition distri-

bution in Vinacke and Arkoff's experiment . . . . . . . . 39

Exact probability test for independence between the

payoff distribution in the single stage/play money

condition and the payoff distribution in Vinacke and

Arkoff's experiment . . . . . . . . . . . . . . . . . . . 40

Exact probability test for independence between the

initial contact distribution in the single stage/

play money condition and the initial contact distri—

bution in Chertkoff's experiment. . . . . . . . . . . . . 41

Exact probability test for independence between the

initial coalition distribution in the single stage/

play money condition and the initial coalition

distribution in Chertkoff's experiment. . . . . . . . . . 42

Frequency with which each player contacted the Opponent
with the greater number of votes or the opponent with
the fewer number of votes . . . . . . . . . . . . . . . . 44

Factorial design exact probabilities of contacting
the Opponent with the greater number of votes or the
Opponent with the fewer number of votes . . . . . . . . . 45

Exact probability test for independence between the

initial contact distribution in the multi—stage/

real money condition and the initial contact distri-

bution in the single stage/play money and the multi-

stage/play money condition. . . . . . . . . . . . . . . . 47

iv

 

 

Table

10

ll

12

13

14

15

16

17

18

19

20

21

22

23

Frequency of formation of initial coalitions in the
experimental design conditions. . . . . . . . . . .

Factorial design exact probabilities of formation
of initial coalitions in the experimental design
conditions 0 O O O O O O O O O O O O O O O O O O O O

Exact probability test for independence between
the initial coalition distribution in the multi—
stage/play money condition and the initial coali—
tion distribution in the multi-stage/real money
condition . . . . . . . . . . . . . . . . . . . . .

Means, standard deviations, and Ns for amount of
money won by player with greatest number of votes
in initial coalition. . . . . . . . . . . . . . . .

Analysis of variance of amount of money won by
player with the greatest number Of votes in ini-
tial Coalition. 0 O O O O O O I O O O O O C O O O 0

Multiple comparison t values for all pairs of means
of amount of money won by player with greatest
votes in initial coalition. . . . . . . . . . . . .

Means, standard deviations, and N3 of the amount
Of money in final agreement . . . . . . . . . . . .

Analysis of variance of the amount of money in
final agreement . . . . . . . . . . . . . . . . . .

Multiple comparison C values for all pairs of means
of amount of money in final agreement . . . . . . .

Means, standard deviations, and Ns of the average
number Of rejections per agreement. . . . . . . . .

Analysis of variance of the average number Of
rejections per agreement. . . . . . . . . . . . . .

Multiple comparison t values for all pairs of means
Of average number of rejections per agreement . . .

Means, standard deviations, and N5 of time taken
to make first agreement . . . . . . . . . . . . . .

Analysis of variance of time taken to make first
agreement 0 O O O O C O O O O C .. O O O O O C O O O

Page

48

49

49

52

53

53

55

55

56

56

57

57

59

59

 

 

Table Page

24 Multiple comparison t values for all pairs of means

of time taken to make first agreement . . . . . . . . . . 6O
25 Correlation of time taken to make first agreement

with amount of money in final agreement and aver—

age number Of rejections per agreement. . . . . . . . . . 6O
26 t test of difference in the amount of money won by

player with the greatest number of votes between
single stage/real money groups and repeat/single
stage/real money groups . . . . . . . . . . . . . . . . . 62

27 t test of difference in the amount of money in
final agreement between l—hour/multi—stage/play
money condition and 2—hour/multi—stage/play money
condition . . . . . . . . . . . . . . . . . . . . . . . . 62

28 Exact probability test for independence between
the initial contact distribution in the single
stage/real money condition and the initial
contact distribution in the single stage/
real money/divider condition. . . . . . . . . . . . . . . 63

29 Exact probability test for independence between
the initial coalition distribution in the single
stage/real money condition and the initial
coalition distribution in the single stage/real

money/divider condition . . . . . . . . . . . . . . . . . 63
30 Confirmation Of experimental hypotheses one
through three . . . . . . . . . . . . . . . . . . . . . . 7O

 

 

LIST OF ILLUSTRATIONS

Figure Page

1 Table divider (tOp View). . . . . . . . . . . . . . . . . 26

vii

LIST OF APPENDICES

Appendix Page
A Ancillary results . . . . . . . . . . . . . . . . . . . 78
B Coalition—bargaining game instructions. . . . . . . . . 116
C Coalition—bargaining game forms . . . . . . . . . . . . 128

1. Player's record sheet
2. Initial contact form
3. Agreement contract
4. Record of agreement
5. Communication form
D Player's rule cards . . . . . . . . . . . . . . . . . . 133
E Postmgamc questionnaire . . . . . . . . . . . . . . . . 135
1. Play money form
2. Real money form
F Experimenter's record sheet . . . . . . . . . . . . . . 141

viii

LIST OF APPENDIX A_TABLES

 

Table Page
1 Means, standard deviations, and N5 of interest and in-
volvement in the game . . . . . . . . . . . . . . . . . . 8O
2 Analysis of variance of interest and involvement in the
game. . . . . . . . . . . . . . . . . . . . . . . . . . . 8O
3 Means, standard deviations, and Ns for amount of trust
in initial coalition. . . . . . . . . . . . . . . . . . . 82
4 Analysis of variance of amount Of trust in initial
coalition . . . . . . . . . . . . . . . . . . . . . . . . 82
5 Multiple comparison t values for all pairs of means Of
amount of trust in initial coalition. . . . . . . . . . . 83
6 Means, standard deviations, and N3 of how hard subjects
tried to win game's payoff. . . . . . . . . . . . . . . . 84
7 Analysis of variance of how hard subjects tried to win
game's payoff . . . . . . . . . . . . . . . . . . . . . . 84
8 Frequency of premature suspicion that initial coalition
could be broken . . . . . . . . . . . . . . . . . . . . . 87
9 Factorial design exact probabilities for subject's pre-
mature suspicion that initial coalition could be broken . 88
10 Frequency of subjects in real money condition who be—
lieved they would receive payoff in real money. . . . . . 89
ll Factorial design exact probabilities for subjects in
real money condition who believed they would receive
payoff in real money. . . . . . . . . . . . . . . . . . . 89
12 Exact probability test for independence between the ini-

tial contact distribution in the single stage/real money
groups and the initial contact distribution in the re-
peat/single stage/real money groups . . . . . . . . . . . 9O

ix

Table

13

14

15

16

17

18

19

20

21

22

23

24

25

26

 

Exact probability test for independence between the'
initial coalition distribution in the single stage/

real money groups and the initial coalition distribu-
tion in the repeat/single stage/real money groups . . . .

Frequency with which each player contacted the player
on his left or the player on his right. . . . . .

Factorial design exact probabilities Of each player's
contacts of the player on his left or the player on his
right . . . . . . . . . . . . . . . . . . . .

Frequency Of initial coalitions by position .

Factorial design exact probabilities of initial coali—
tions by position . . . . . . . . . . . . . . . . .

Frequency with which players facing each other contacted
each other.

Factorial design exact probabilities for choosing player
facing you. O O O O O O I O O O 0 O O O I O O O O O O 0

Distribution of votes by position around the game table
and the probability Of Observing the distribution obtain—
ed in the single stage/real money condition . . . . . .

Distribution Of pairs of votes by position around the
game table and the probability of observing the distri—
bution obtained in the single stage/real money condition.

Frequency with which Ss in multi-stage condition con-
tacted the first or second opponent bargained with in
the preliminary round . . . . . . . . . . . . . . . . .

Factorial design exact probabilities of contacting
first or second opponent bargained with in preliminary
round of multi-stage condition. . . . . . . . . .

Frequency Of initial coalitions in multi-stage condition
according to preliminary bargaining order . . . . . . .

Factorial design exact probabilities of forming initial
coalition according to preliminary bargaining order in
mUlti-Stage condition 0 o o o o o 0 o o o o o o o O a

Means, standard deviations, and N8 of how Often subjects
played competitive games. . . . . . . . . . . . . . .

Page

90

92

93

94

94

96

97

99

99

101

102

103

103

104

 

Table Page

27 Analysis of variance of how often subjects played com-
petitive games. . . . . . . . . . . . . . . . . . . . . . 104

28 t test of mean difference between single stage/real
money condition and multi-stage/real money condition
in value of $9.00 . . . . . . . . . . . . . . . . . . . . 106

29 t test of mean difference between single stage/real
money condition and multi-stage/real money condition
in need for $9.00 . . . . . . . . . . . . . . . . . . . . 106

30 Means, standard deviations, and Ns for the average
number of messages sent between coalition partners per
agreement 0 O I O O O O O O O O O O O 0 O O O O C O O I O 107

31 Analysis Of variance of average number of messages sent
between coalition partners per agreement. . . . . . . . . 107

 

32 Correlation of average number of messages sent between
coalition partners with stability . . . . . . . . . . . . 109

33 Frequency with which player who spoke first in initial
coalition negotiations received the largest share of
the payoff. . . . . . . . . . . . . . . . . . . . . . . . 110

34 Factorial design exact probabilities of whether player
who spoke first in initial coalition negotiations
received the largest share of the payoff. . . . . . . . . 111

35 Frequency with which individual players broke initial
coalition . . . . . . . . . . . . . . . . . . . . . . . . 112

36 Factorial design exact probabilities for players who
broke initial coalition . . . . . . . . . . . . . . . . . 113

37 Frequency with which individual players broke the initial
coalition according to the proportion of the payoff they
received (data only for initial coalitions that were
broken) . . . . . . . . . . . . . . . . . . . . . . . . . 114

38 Factorial design exact probabilities for individual
players who broke the initial coalition according to
the proportion of the payoff they received (data only
for coalitions that were broken). . . . . . . . . . . . . 114

xi

 

Any time two or more persons enter into a relationship in which each
person is dependent on the other person(s) in order to attain his own
goals, that relationship can be characterized as a mutual dependence re-
lation. Many social psychological eXperiments have investigated mutual
dependence behavior. These experiments have examined behavior ranging
from simple reciprocal behavior between two persons, to more complex two
person bargaining behavior, to the extreme in mutual dependence behavior—-
coalition formation. In coalition formation a common-fate alliance is
formed between two or more persons, and from that point on the alliance
acts as a single unit. Theories to explain the coalition formation process
have been proposed by Caplow (1956) and Gamson (1961a). These theories
make predictions about the manner in which triads will divide into a two-
unit coalition and an isolate. The following assumptions about the coali-
tion situation are made by either one or both of these theories: (1) it
is a mixed-motive situation (i.e., a person is reward for both competitive
and cooperative behavior); (2) each person's goal is to maximize his
outcome (payoff); (3) no person has dictator power (i.e., can control the
outcome by himself); (4) Gamson, but not Caplow, makes the assumption
that no person has veto power (i.e., is required to be a member of a coali-
tion in order for it to win); (5) all participants have equal information

about the situation; and (6) the payoff to all coalitions is constant.

 

 

 

The predictions Of the theories are expressed in terms of the relevant
resources initially possessed by each participant in a given situation.
The theories assume that each participant's expectations and demands in a
situation are determined by the proportion of relevant resources he con-
trols in the situation. For this reason, the theories of Caplow and Gamson
will be referred to as ”Resource” theory (RT) in this paper. Caplow's
and Gamson's predictions as to which coalition will form, given a certain
resource distribution, are presented in Table 1.

Table 1. Caplow and Gamson's predicted coalitions in triads
Of varying initial resources

 

 

 

 

Type Distribution of Resources Example Predicted Coalition
No. Caplow Gamson

1 A=B=C 1-1-1 any any

2 A>B, B=C; A<(B+C) 3-2—2 BC BC

3 A<B, B=C 1-2-2 AB, AC AB, AC

4 A>(B+C); B=C 3-1—1 none none

5 A>B>C; A<(B+C) 4-3-2 AC, BC BC

6 A>B>C; A>(B+C) 4—2-1 none none

7 A>B>C; A=(B+C) 3—2—1 AB, AC inapplicable
8 A=(B+C); B=C 2-1—1 AB, AC inapplicable

 

The eight resource distributions can be divided into two classifications:
(1) those in which any two—party coalition can control a majority of the
resources (Types 1, 2, 3, and 5); and (2) those in which one participant

has either dictator or veto power (Types 4, 6, 7, and 8). Since dictator

 

and veto situations are of little research interest, most of the research
has focused on Types 1, 2, 3, and 5. Of these four distributions, the
only distribution for which the theories of Caplow and Gamson make variant
predictions is Type 5 (4-3—2). For this reason, and also because of the
veridicality of the all—different distribution, most of the research test-
ing resource theory has focused on the Type 5 distribution.

The general nature of the prediction as to which coalition will form
in a Type 5 situation can be summarized in the statement that the greater
the combined resources of two players, the less likely it is for those two
players to form a coalition (i.e., 3 and 2 will ally most Often, and 4 and
2 will ally more often than 4 and 3). This effect is oftendescribed as
the ”strength is weakness" (STE) effect. Most of the coalition research
to date that has used the conventional research paradigm, in which the first
two-person coalition that forms is the winner and all coalitions have
the same probability of future success, has reported obtaining the STE,
effect (Vinacke and Arkoff, 1957; Vinacke, 1959; Gamson, 1961b; Bond and
Vinacke, 1961; Chertkoff, 1966; and Phillips and Nitz, 1968).

An additional prediction of RT is that the division of the payoff bet—
ween the coalition partners will be proportional to the amount of relevant
resources contributed to the coalition by each partner. The research
evidence obtained for the division of the payoff does not support the pre-
diction of RT very strongly. Most of the coalition experiments have yielded
an ambiguous and inconclusive pattern of results for the division of the
'payoff.

A second theoretical approach to coalition formation is akin to the

”game theory” concepts of von Neumann and Morgenstern (1944), and Shapeley

 

 

and Shubik (1954). No formal definition of this theoretical position has
been presented, but the basic tenets of this approach to coalition forma-
tion have been presented in a number of various research publications
(Vinacke and Arkoff, 1957; Kelley and Arrowood, 1960; and Vinacke, Crowell,
Dien, and Young, 1966). This explanation for coalition formation is based
on the assumption that each person acts in a purely rational and objective
manner in the coalition situation. For the purposes of this paper this
explanation of coalition formation will be called the rational—objective
theorem (R-O—T). The R—O—T states that in a three—person competitive game
each player is able to determine at the outset Of the game the optimal
strategy of each of his opponents, and thus select that strategy for him—
self that will maximize his outcome in the game. A rational-objective
analysis of the conventional coalition situation reveals that since any
two—party coalition can control a majority of the game's resources, the
differences between the participant's initial resource values bear no
real significance in determining which coalition will form and how the pay-
off will be divided. In actuality, each player has the same amount of
pivotal power (Shapeley and Shubik, 1954), or pivotal resources (i.e.,
each player can make a coalition a winning coalition as Often as any other
player). Therefore, the three possible two—party coalitions should occur
with equal frequency, and the payoff should be divided equally between
the two coalition partners.

The primary Objective of three of the more important coalition studies
(Vinacke and Arkoff, 1957; Kelley and Arrowood, 1960; and Vinacke, Crowell,
Dien, and Young, 1966) has been to determine whether RT or the R—O-T Offers

the best explanation of what goes on in a three—person social situation in

 

which any two—person coalition can win.
The experimental game used in these three experiments was a modified
parchesi game and is described below by Kelley and Arrowood (1960).

Three subjects play a game in which each moves his counter along
the spaces Of a game board. The first one to reach the goal
receives a prize of 100 points. On successive trials, the ex—
perimenter rolls a single die and each player advances a number
of spaces determined by the product of two numbers: (a) the
number of pips turned up on the die and (b) a "weight", ranging
from 2 to 4, which was randomly assigned him at the beginning of
the game. For example, in one game Player A may have weight 4,
Player B, weight 3, and Player C, weight 2. Since all players
start at the same point on the board and move each time the die
is cast, the person assigned the largest weight automatically
wins. A further rule, however, enables any pair of players to
form a coalition by combining their weights at any time during
the game. When they do so, they are given a single counter
placed at a position equal to the sum of the distances the two
have attained at that time. On subsequent rolls, they advance
according to the sum of their two weights. The formation of a
coalition is acknowledged by the eXperimenter only when the two
players have agreed upon how they will divide the 100 point prize,
should they receive it; and, once formed, a coalition is indis-
soluable for the remainder of that game. Thus, the individual
or coalition that can mobilize the largest weight automatically
wins that game and there is really no need for going through the
motions of rolling the die [p. 231].

The three research studies, previously mentioned, that used the above

described experimental paradigm confined their investigation to male subjects.
Vinacke and Arkoff (1957) were the first to use the parchesi paradigm

in testing RT versus R—O—T. These experimenters had each of thirty triads

play the modified parchesi game 18 times, each of the six different types

of initial resource distributions being used three times. Each set of

six games that had different initial resource distributions was played in

a Latin square order to offset order effects. Before each game, each player

drew a counter which determined the weight he would have for that game.

The order of draw was counter—balanced so that each player drew first,

second, and third an equal number of times.

 

The coalition results confirmed the §2fl_hypothesis. In the Type
5 situation 67% of the coalitions were 3—2 coalitions. The results for
the division Of the payoff, on the other hand, offered very little support
for RT predictions. Vinacke and Arkoff reported that the players in the
Type 5 situation split the payoff equally about 47% of the time, and Split
the payoff unequally about 53% Of the time. One problem with this data is
that it is not presented according to the prOportion of the payoff obtained
by each player in the coalition. Instead, the data was collapsed across
all players and games, and categorized according to 50/50 and non-50/50
splits. This procedure assumes that any deviation from an exact 50/50
split is an indication that the subjects divided the payoff in proportion
to their initial resource values. Such an assumption is probably too
stringent since it does not allow for any deviation from an equal split
as a result of error, chance, or compromise.

Kelley and Arrowood (1960) discount the Vinacke and Arkoff findings
as spurious results. According to Kelley and Arrowood, subjects in the
Vinacke and Arkoff experiment became confused about how to play the game
because the resource distributions were changed between each of the 18
games. Consequently, the subjects never had ample Opportunity to perceive
the Objective character of the situation, and they erroneously equated the
initial power weights with each subject's actual power in the situation.
Kelley and Arrowood offered the hypothesis

that with a simpler procedure, subjects will acquire an adequate

understanding of the true power relations and act more in accord

with a rational analysis Of the situation than the Vinacke and

Arkoff data would suggest. (1960, p. 233)

Kelley and Arrowood tested this hypothesis by having 30 triads play the

parchesi game using only the Type 5 (4-3-2) resource distribution. The

number of games played by each triad varied from 10 to 70 and averaged
approximately 24 games. Each player kept the same weight throughout the
series of games his triad played. The implication of this statement,

even though Kelley and Arrowood do not specifically say so, is that each
subject played against the same two Opponents in all the games he played.
Kelley and Arrowood also gave their subjects extensive formal instructions
and an orientation for each subject to maximize his payoff without regard
to the other players in his group.

The results obtained by Kelley and Arrowood revealed a distribution
of coalitions for the first three games that was significantly closer to
a chance distribution than that Obtained by Vinacke and Arkoff in their
three games. Kelley and Arrowood's coalition distribution for the first
three games, however, was significantly different from a chance distribution
(.Ol<p<.02). On the other hand, the coalition distribution for the last
three games each triad played was not significantly different from chance
(.20<p<.30). As Kelley and Arrowood indicate, however, the chi-square
tests used to Obtain these significance values are not legitimate since
each triad played a series of games and the Observations are, therefore,
not independent. NO data was presented by Kelley and Arrowood about the
manner in which the payoff was divided.

Kelley and Arrowood conclude that simplifying and clarifying the
experimental procedure will result in the subjects perceiving the situation
more objectively and forming coalitions more in accord with a chance
distribution.

Vinacke, Crowell, Dien, and Young (1966) reject the conclusions of

Kelley and Arrowood for the following reasons:

1. allowing each player to have the same resource value for all
games caused subjects to become bored, and, consequently to
mix up their alliances to alleviate the boredom.

2. playing against the same players with the same resource values
for a series of games is highly similar to the experimental
procedure used by Vinacke (1959) and Emerson (1964) in their
cumulative score games. The cumulative score experiments re-
vealed that keeping a cumulative score tends to result in a
coalition process where the persons with the smallest scores
are the most likely to get into the next coalition. This means
that if the weak players initially ally against the strong, at
some point they will surpass the strong member in cumulative
score and then the strong member will be the most likely player
to get into a coalition, and so forth. This process would
eventually equalize the frequency of occurrence of each possible
coalition, which is the result claimed by Kelley and Arrowood
to be due to clarifying the experimental procedure.

Vinacke e£_gl. conducted an experiment that was intended to test Kelley
and Arrowood's hypothesis under experimental conditions not subject to the
above criticisms. These researchers conducted a study in which triads were
directly informed of the rational—objective approach to coalition formation
and of the conventional resource theory approach, and were then allowed to
choose which Of the strategies they wanted to use in the experimental game.
This experiment used the same paradigm as the Vinacke and Arkoff (1957)
experiment except that: 1) each triad played 48 games, 12 games of each of
four types of resource distributions; 2) the 48 games were divided into two
phases:

a) Phgggwl - the first 24 games (six games of each of the four types

of distributions) were played under the conventional
paradigm instructions and rules.

IN
I

either one, two, or all three players in a triad were
randomly selected and received the special information
describing the two strategies that could be used to
play the game. Each triad then played another series
of 24 games (six games of each of the four types of
distributions).

b) Phase

3) all six games of each distribution type were played consecutively; 4)
the order in which the four resource distributions were played was randomized;

and 5) data was reported for only two resource distributions (Types 2 and 5).

Vinacke, ££_fll., interpret their results as supporting RT and not
the RrO—T. It should be pointed out, however, that because of the manner
in which the results are reported, it is difficult to verify Vinacke,
_§£_§l.'s interpretation of the data. For example, the coalition data was
presented for the combined 3—2-2 (Type 2) and 4—3—2 (Type 5) distributions,
summed across all games. This procedure confounds the interpretation of the
4-3—2 data. For example, in two previous experiments that employed all six
types of resourCe distributions (Vinacke and Arkoff, 1957; Vinacke, 1959),
the distribution that yielded the highest frequency of STE coalitions was

the 3-2-2. This is probably a result of the fact that in addition to being

 

the two weakest players, 2—2 are also equal in power and may be more attracted
to each other as a result of some similarity bias. Therefore, collapsing
the 3-2-2 distribution with the 4—3-2 distribution most likely inflates the
.gyg result. In addition, the coalition data is not reported in terms of the
number or percentage of weak coalitions that were formed but, instead, in
terms of the number of triads that formed weak coalitions more often than
chance or less Often plus equal to chance across all games. This method Of
presenting the results destroys most Of the comparability between this
experiment and the Vinacke and Arkoff and Kelley and Arrowood experiments.

A comparison of the first three games in the Vinacke, et a1. experiment
with the last three games revealed an exception to the §1E_effect. Triads
in which all three members were informed of the two strategies available to
them formed significantly fewer weak alliances in the last three games than
they did in the first three games. Vinacke, et a1., reject the interpretation
Of the above result that greater experience in playing the games or greater

understanding of the game situation led to a rational strategy of game playing.

10

Instead, Vinacke, et a1., Offer an alternate explanation.

In the post-game questionnaire each player was asked if he "tried to
win", and he was also asked three questions to measure his understanding
of the special strategy information. The percentage Of subjects that
received the special strategy information, who said they tried to win,
was much greater for the subjects who showed they had a partial or good
understanding of the strategy information than for the subjects revealing
a poor understanding of the information. Vinacke, et a1., concluded that

this means then, that the procedure whereby one or more members

of the group were provided with special information led to an

expression of stronger motivation to win, as well as accomplish-

ing our original aim to instruct players in the two alternative

strategies. (1966, p. 187)

In addition, Vinacke, et a1., report finding, but without the use of a
significance test, that as the number of triad members who had a desire to
win increases, the incidence of weak coalitions decreases. From all of
this information, these authors conclude that "the formation of weak
alliances (as an aspect of strategy) is a function not of understanding
the true character of the power situation but Of desire to win." (1966,
p. 187).

It is difficult for this writer to determine by what scientific process
Vinacke, et a1., arrived at this conclusion. It seems just as easy to
argue, and more likely to be true, that the subjects who came into the game
with a greater desire to win were motivated to learn more from the special
strategy information, and, as a result, understood the situation better. This
sequence of events could have produced fewer weak coalitions. Vinacke, et a1.,
present no evidence to indicate the causal order Of events that produced the

obtained results, and, therefore, they have no legitimate basis for suggesting

that higher motivation leads to fewer weak alliances, instead of better under-

11

standing leading to fewer weak alliances.

Current state of resource theory and rational—Objective theorem controversy

 

What conclusions can be stated about the evidence that has been
presented to date to explain the coalition process in the Type 5 situation?

1. Both resource theory and the rational—objective theorem have
received partial support from the empirical data that has
been reported. None of the evidence that has been reported
validates either one of the theoretical positions.

2. The data on the division of the payoff is inconclusive as to
whether it supports resource theory or the rational-Objective
theorem.

3. The coalition experiments that have examined resource theory
and the rational—Objective theorem are all Open to criticism
for inadequately controlling their experimental design and
procedure.

 

4. The experimental game that has been used to investigate
coalition formation is too complicated for effective
scientific investigation. A new game is needed that play-
ers can comprehend in one trial.

5. The empirical support for the rational—objective theorem
has been attributed to both a greater understanding of the
experimental situation and to a greater motivation to win.

 

 

PROBLEM

The critical question facing coalition theory at the present time
is this: Is the coalition process Operating in the Type 5 situation
based on the belief that the participant's initial resources are actually
different (RT), or, instead, is it based on the belief that the three
players have equal resources (R—O-T)? The problem with the present state
of coalition research is that there is evidence for affirmative responses
to both parts of this question. It must be concluded, therefore, that
either there are two coalition processes in operation and the contra-
dictory evidence is the result of these dual processes, or the evidence
supporting one or both theories is artifactual. This investigator be-
lieves that the latter is the correct explanation for the contradictory
results.

It was the fundamental tenet of this study that the coalition-bar-
gaining games used in most of the previous coalition experiments created
a pseudo-coalition situation in which the most likely outcome was that
predicted by resource theory. The two main coalition—bargaining games
used were 1) Vinacke and Arkoff's (1957) modified parchesi game and 2)
Gamson's (1961b) political convention game. The characteristics of both
of these games that contributed to the creation of this pseudo-coalition

situation were:

12

13

l) the initial resource values were randomly assigned;
2) the first two players to reach an agreement were declared the
winning coalition;

3) the payoff for the game was of little value to the participants.
In addition, the modified parchesi game has a rule that the player with the
largest resource value will win the game by himself if no coalition is form-
ed. A game with this rule is called a non—forced coalition game. The non-
forced coalition paradigm also contributed to the artifactual RT outcomes.
The Gamson political convention game is called a forced coalition game since
only a two—person coalition can win, that is, £22; can not win by himself.
In spite of this difference between these two games the forced coalition
game produced the STE effect. (Gamson, 1961b; and Chertkoff, 1966)

In order to substantiate the above criticisms and conclusions about
previous coalition research, the following three questions were examined

and answered:

 

1It has been the assumption of all previous research studies on
coalition formation that the random assignment of initial resource values
would not significantly alter the character of the coalition process.
There is no empirical evidence to suggest that this is a correct assump-
tion. In fact, it is very likely that random assignment could suggest
to the player a lack of difference in initial resources that would produce
a more equal distribution of coalitions and payoffs. On the other hand,
random assignment could suggest to the subjects a lack of reality in the
game resulting in the subjects playing the game with little earnestness
or desire to win. This loss of motivation and reality could cause the
subjects to play the game the easiest or most plausible way just to get
it over with. The most plausible way to play the game is to use the ini-
tial resources to decide whom to choose for a coalition partner, otherwise
why even assign them. Further discussion of this problem is presented in
later parts of the Problem section. In order to compare the experiment
described in this paper with previous experiments, this experiment will
also assume that random assignment of initial resource values makes no
difference to the coalition process.

 

l4

1) What were the prevailing conditions in the conventional
research paradigm that produced the Resource theory out-
comes? Were these conditions extraneous factors in the
experimental paradigm?

2) If so, can the experimental conditions be altered so that
the coalition process is not affected by these extraneous
factors and is instead the result of a more veridical
process that is experimentally controlled?

3) If so, what will be the coalition process outcomes in
such a situation?

Conditions producing Resource theory outcomes

 

There are three factors in the conventional research paradigm that

contributed to the RT outcomes. The first factor is the demand character—

 

istics_g£ the experimental situation. Since the conventional game's pay-

 

off was of little value to the players, the main reward in the situation was
demonstrating to the observers of the game (i.e., other players and the
experimenter) how well one could play the game. Good performance in an
experimental competitive game demonstrates two types of competence: 1)
ability to perceive the experimenter's purpose in conducting the study and
2) skill in competitive game playing. In a psychology experiment the

first of these expressions of competence is usually the most important to
the participants. In order for a player to be able to demonstrate that

he has perceived the true purpose of the study, he must play the game the
way it is supposed to be played. In order for the player to prove that he
has played the game correctly, he must determine what it is the experimenter
wants him to do in the experiment, and then Obtain the experimenter's posi-
tive evaluation of his performance. In the coalition-bargaining game the
subject usually decided the experimenter wanted him to use the initial re—

source values in deciding whom to choose as a coalition partner. The player

 

15

reasoned that if this were not the case, the experimenter would not have
assigned these values. In addition, the experimenter must have wanted the
subject to take into account the difference in value of the resources of
each participant, otherwise every subject would have been given the same
value. The subject further reasoned that the experimenter, therefore,
must have wanted to see if the participants perceived that they could
maximize their winnings by choosing the player with lesser votes, instead
of the player with greater votes. Also, since the players chose on the
basis of initial resource values, they divided the payoff according to
initial resources. "Such strategy resulted in RT outcomes.

Another possible result of the conventional game's payoff being of
little value was for the participants not to care how they performed in
the game. In this case, the players looked for the easiest and most
plausible way to complete the game. According to the rationale just
described, that would have been to play the game the way it Obviously
should be played. Therefore, this set of circumstances also caused the
players to use the initial resource values to determine their choice of
partners and payoff division. As stated above, using the initial resource
values resulted in the outcomes predicted by RT.

The second factor producing RT outcomes was time pressure. The winning

 

coalition in the conventional research paradigm was defined as the first
two players who reached an agreement on dividing the payoff. This defini-
tion pressured players into forming a coalition with the person who would
make the quickest deal, instead of seeking a coalition with the player who
would make the best deal. Data from previous experiments (Chertkoff, 1966;

and Gamson, 1961b) supported this conclusion since most winning coalitions

16

were formed by the first two players to choose each other. This time
pressure reinforced the subject's existing tendency, which was a result

of the demand characteristics in the situation, to choose the weaker of

the two opponents. Since the player had to make a quick deal, he did not
have time to probe the other two players about possible terms for an agree-
ment, and then make the choice of his preferred partner. Instead, the
player had to choose, the first chance he got, the opponent most likely

to choose him. Each player reasoned that the other players must also
perceive the situation in this way. Since the time pressure did not allow
the subjects an opportunity to develop a new strategy, the players select-
ed the most obvious strategy for determining which Opponent to choose. This
strategy was to choose a partner on the basis of the initial resource
values. Therefore, each subject chose the Opponent with the smallest re-
sources. In addition, the two players who chose each other did not want
to risk failing to reach an agreement and losing the coalition. As a
result, they divided the payoff the most Obvious way--according to initial
resource values. Such strategy resulted in RT outcomes.

The third factor contributing to RT outcomes was unequal status

 

among the participants. Unequal status occurred only in the non-forced
coalition situation. By allowing the player with a resource value of
four to win the-game if no coalition forms, four was elevated to a position

of greater status than the other two players. This status difference

engendered an 'underdog' feeling between three and two, and increased the
chances of these two players forming the winning coalition. Such an out-
come was the same as that predicted by resource theory. At the same time,

this "underdog" feeling created an equality between three and two. This

 

 

l7

equality may have accounted, in part, for the subject's tendency, in pre-
vious experiments, to split the payoff equally more often than predicted
by RT.

An examination of the initial partner choices that each subject is
likely to make in the conventional game situation may further clarify these
points. If each player's goal is to maximize his share of the game's pay-
off and each player uses the initial resources to determine his optimum
payoff, the following partner choices will be made-:EggE_will choose Egg,
three will choose Egg, and Egg will choose three. However, maximization,
in this situation, does not only mean obtaining the largest absolute share
of the payoff one can possibly get; it also means being a member of the
winning coalition at any price so that one obtains something rather than
nothing. Each subject, therefore, must take this time pressure into account
and make sure he selects the subject who selects him. In this regard, Eggg
is sure three will choose Egg, and EggE_thinks it may be possible that Egg
will choose EggE; therefore, EggE Chooses Egg. Three is quite sure EggE
will not choose him but feels that Egg will most likely choose three.
Therefore, three chooses EXP: Egg figures that both EggE and three will
probably choose him. If Egg_desires to maximize his payoff on the basis
of initial resource values, he will choose three, but if Egg is anti—
competitive or wants to form the largest and most certain majority, he will
choose EggE, In the modified parchesi game there is another factor that
will influence two's decision. Since EggE can win if no coalition forms,
Egg; is "top—dog" and three and Egg are "underdogs"; therefore, Egg usually
chooses EBEEE: The above rationale accounts for the §Efl effect that has

been Obtained in previous studies. As can be seen, almost everything in

18

the conventional experimental situation was structured in favor Of pro-
ducing RT outcomes. Therefore, RT outcomes were not a result of the
player's strategy decisions being based on a belief in the viability of the
initial resource values. Instead, they were the result Of each player's
belief that the experimenter wanted him to use the initial resource values
in choosing his coalition partner, and of the fact that using the resource
values to determine one's strategy was the most obvious way to play the
game. A more adequate test of coalition theories would be to examine
coalition behavior in a situation in which the player's decisions would

be free of the effects Of artifacts.

If the preceding assumptions and rationale are correct, then the
experiments of Vinacke and Arkoff (1957) and Vinacke, et a1. (1966) were
not adequate tests of resource theory. Since Kelley and Arrowood used the
modified parchesi game to collect their data, neither was their experiment
a valid test of the rational—objective theorem.

The object of this experiment, therefore, was to demonstrate that
the rationale presented above was an accurate description of what takes
place in coalition experiments using the conventional research paradigm.
The best way to test the validity of this description was to remove the
undesirable extraneous influences in the conventional research paradigm and
then observe the resultant coalition behavior.

The general hypothesis of this experiment was that the elimination
of these extraneous influences would result in.the coalition formation out-

comes predicted by the rational-objective theorem.

 

19

Elimination Of extraneous influences and the resultant hypotheses

Unequal status. The influence of four's greater status, because he
could win the game alone, was eliminated by constructing a new forced
coalition experimental game. In this new game the only means of winning
was to form a two—person coalition. This change by itself, however, could
not eliminate the RT outcomes (Chertkoff, 1966; and Gamson, 1961b).

Time pressure. The time pressure exerted on the players to be a
member of the first possible coalition regardless of desirability was
alleviated by altering the bargaining and negotiation method. Each play—
er was allowed preliminary bargaining contact with each of his opponents
prior to making his selection of a coalition partner. An S should have
been more satisfied with his coalition agreement, using this negotiation
method, than he was in the conventional coalition research situation. A
measure used to ascertain the subjects' satisfaction with an agreement was
to examine the stability Of coalitions. Coalition stability was investi-
gated by permitting coalitions to dissolve, if they wanted to, and new
coalitions to take their place.

H1: Players allowed preliminary bargaining contact with each

other before choosing their preferred partner will tend

to form 4-3, 4-2, and 3—2 coalitions with more equal fre-
quency, split the payoff more equally, and form coalitions
that are more stable, than players that have no preliminary
bargaining contact.

Demand characteristics of situation. The demand characteristics of
the situation were obviated by making the game's payoff of significant
value to the subjects. Under this condition, each subject should have

played the game for its reward, and not to impress the other players or

the experimenter. The game's payoff was made of high value to the sub—

 

20

jects by rewarding the subjects who formed the winning coalition with real
money. Subjects winning real money in the coalition-bargaining game should
be more careful about the agreements they make and also be more reluctant

to take any risks that would jeopardize their winnings. As a result, coali—
tions formed in the real money condition should be more stable than coali-
tions formed in the play money condition.

H2: Player's receiving their payoff in real money will tend

to form 4—3, 4—2, and 3-2 coalitions with more equal
frequency, split the payoff more equally, and form coali-
tions that are more stable than players who play the

game for play money.

H z The effects of bargaining sequence and incentive will

combine so that the greatest equality in the formation

of 4-3, 4-2, and 3-2 coalitions, the most equal payoff

splits, and the most stable agreements will occur under
the preliminary contact-real money condition.

A variable, heretofore unexamined in coalition research, that is quite
likely related to some of the independent and dependent variables used in
coalition research is the amount of time required to reach the agreement
for forming the first coalition. Preliminary contact should lessen the
time required to reach an agreement for forming the first coalition since
the players will have already discussed possible agreement terms.

H4: Players allowed preliminary bargaining contact will take

less time to reach an agreement than players that have no
preliminary contact.
Real money should increase the incentive of the players to reach an agree-
ment and, thus, shorten the time required to make an agreement.
H5: Players receiving their payoff in real money will take less
time to reach an agreement than player's receiving their
payoff in play money.

H : Bargaining sequence and incentive will combine so that the

preliminary contact—-real money groups will take the least
time to reach a first agreement.

21

Time required to reach the first agreement should also be related to
the stability of agreements. The more time required to reach an agree—
ment, the more conflict and disagreement that probably occurs in reaching
that agreement. Coalitions are probably less stable the more that conflict
and disagreement occur in the process of reaching an agreement.

H : The less time taken to reach an agreement in each experi-
mental condition, the more stable the agreement.

Alternate hypotheses. Kelley and Arrowood (1960) suggested that sim—
plifying the experimental game and having subjects play only one type of
resource distribution would result in the outcomes predicted by the rational-
Objective theorem. The game used in this experiment was very simple and
the subjects played the game only once. If understanding of the situation,
per se, would produce the R—O-T results it should have produced them under
these conditions. In order to test Kelley and Arrowood's hypothesis, the
no preliminary negotiation-play money condition was examined to determine
if simplifying the game would produce R-O-T results.

ALT-H1: Simplifying the coalition bargaining game and the

experimental procedure will result in equally fre-
quent coalitions, equally Split agreements, and
stable coalitions.

A control condition was used in which triads played the coalition—
bargaining game a second time. The second game was played against different
opponents. If experience or learning could produce a more equally frequent
distribution of coalitions, agreements that were more equally split, and

agreements that were more stable, the effect should have been observable

in this condition.

 

22

ALT-H : Playing the coalition-bargaining game twice will

result in a more equal frequency of 4-3, 4-2, and
3—2 coalitions, payoffs that are more equally
divided, and agreements that are more stable.

In a second control condition, subjects signed up for a two-hour
experiment to ensure that the pressure of time would not be a factor in
producing the stability of coalitions.

ALT-H3: When the time limit Of the experiment is not

approached during the playing of the game, the

coalitions will be less stable than when the

time limit is approached, reached, or exceeded.
Additional problems

Previous coalition research has used the symbols A, B, and C as
names for players during the experiment. Since these symbols also re-
present value judgments about how well students are performing in college,
there is good reason to believe that college students have some preconceived
preferences for one or more of these symbols. These preferences probably
add extraneous "noise" to the data collected in coalition research. In
the study proposed in this paper, nonsense symbols were used in place Of
the letters A, B, or C.

In order to collect as much information as possible about the coali-
tion bargaining process, detailed records were kept of the offers,
acceptances, and rejections Of the players during negotiations. The new
coalition-bargaining game used in this study allowed much more informa-
tion about the bargaining process to be collected.

In order to reduce the effect of such extraneous factors as cheating,
passing information to Opponents without the experimenter knowing it, a

feeling that the experimenter was one of the players in the game, position

of subjects in relation to each other, etc., a physical divider was used

23

during the game. This divider would not allow subjects to see what the
other players were doing, but the subjects were able to see each other's
face.

A post-game questionnaire was administered to each subject in order
to ascertain each player's perception of the experiment and to collect

information about the subjects' social and economic backgrounds.

METHOD

Subjects

Subjects were 312 male students enrolled in introductory psychology
classes at Michigan State University. Subjects participated in the experi-
ment in groups of three players. Eighty-four triads comprised the experi-
mental conditions and 18 triads made up the control conditions. Two
triads that signed up for the experiment were not used because some of
the members knew each other.
Design

A 2 X 2 factorial design was used. The two factors that were experi—
mentally varied are (l) bargaining sequence and (2) type of payoff (Table 2).

Bargaining sequence. One level of bargaining sequence was the pre-
viously described conventional bargaining method in which the subjects were
not allowed bargaining contacts prior to indicating their preferred coali-

tion partner. This level was referred to as the single stage (SS) condi-

 

tion. The second level of bargaining sequence was that in which each play-
er participated in a preliminary negotiation session with each of his
opponents prior to selecting his preferred partner. This level was referred

to as the multi-stage (MS) condition.

 

Type of payoff. One level of the payoff factor was that in which the
payoff was expressed in terms of play money (PM). The payoff in this condi-
tion was $900 in play money. The second level of the type of payoff factor
was a real money (RM) payoff. The payoff in this condition was $9 in real

money.

24

 

25

Table 2. 2 X 2 factorial design of the experiment

 

 

Bargaining sequence Single stage Multi-stage

 

Type Of payoff Play money Real money Play money Real money

 

Number of
Observations 24 triads l8 triads 24 triads 18 triads

 

 

 

 

 

 

Apparatus

Coalition—bargaining game table divider. The three players and the
experimenter sat around a 2 1/2' X 5' table in a 6' X 9' room. On top
of the table was a divider that separated all three subjects from each
other and from the experimenter. The portion of the divider that sepa-
rated all three subjects from each other and from the experimenter. The
portion of the divider that separated the subjects from the experimenter
‘was 6” higher than the divider between the subjects in order to make a
more acute separation of the experimenter from the game. During the first
part of the game the subjects could see each other over their dividers
but no subject could see what the other players were doing. During the
second part of the experiment, 10" extensions were put on tOp of the
dividers separating the subjects so that the subjects could not see each
other. There was a slot at the bottom of the experimenter's divider for
each subject's compartment, through which all communications were passed.

A diagram of the divider is given in Figure 1.

 

 

 

 

 

 

 

 

a E f
t I
r'-1 """
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Figure 1. Table divider (top view)
Procedure

Coalition—bargaining game. Subjects signed up voluntarily for a

 

one—hour experiment on sign-up sheets posted in their psychology classes.
The SS in the real money condition were not informed that real money
could be won in the experiment until they arrived to participate in the
experiment. Each subject received one-hour's research credit for his
participation, which was used as extra credit in his psychology class.
When the subjects arrived for the experiment, they took their places
around the playing table and were told that they were going to partici-
pate in a competitive game. The subjects were also informed that if the
game did not take the full hour, they would play a second, non-competi-
tive game, separately, to fill out the one hour's credit (see Appendix B
for a record of the instructions). Each subject was then assigned a

nonsense symbol (VAF, YOV, or ZEJ)2 which was used as a means of referring

to each player during the game. Each symbol name was assigned approximately

the same number of times to each of the three positions around the table.

 

These nonsense syllables were selected from the list comprised by
Glaze (1928). The association value of all three syllables was zero.

27

The experimenter then presented three envelopes to the subjects and asked
each subject to draw one envelope. The order in which the subjects drew
the envelOpes was randomized and the envelopes were shuffled prior to
each game. In the envelopes were cards with either "4 votes," "3 votes,"
or "2 votes" typed on them. The card a subject drew indicated the number
of votes he would have in the game. Each subject then wrote his own
symbol name and his number of votes, and his opponents symbol names and
their numbers of votes, on a record sheet (see Appendix C, part 1). The
object of the game was to obtain control of a majority of the votes and
thereby win the payoff (either $900 in play money or $9 in real money).
The players were informed that presently none of them had a majority of
the votes but that if any two players would pool their votes and form an
alliance, that pair would be the winner of the game. The only condition for
declaring that a winning alliance had been formed was that two players
mutually agree on how to divide the payoff. In addition, subjects were
informed that the amount of money won by each player would be compared
with the amount of money won by all previous players of the game who began
the game with the same number of votes as they did.

The procedure for determining which two players would form an
alliance varied according to condition. In the single stage bargaining
condition the subjects secretly wrote on a special form (see Appendix C,
part 2) the symbol name of the player they would prefer to form an
alliance with, and passed the form to the experimenter. In the multi-
EEggg bargaining condition each of the three pairs of players was
given two minutes for preliminary verbal negotiations. The order in
which the three pairs bargained was counter—balanced. No final agreement

could be reached during the preliminary negotiations, but offers and

 

28

counter-offers could be made by each player. Preliminary agreements,

if any were made, did not have to be honored later in the game. Following
the preliminary negotiations the multi—stage subjects secretly filled

in the forms indicating their partner preferences. From that point on

the two conditions were identical.

The first two players to choose each other were given three minutes
to verbally negotiate the terms of an agreement. Subjects were told that
if no reciprocation occurred during the course of the game, there would be
no winner. Whenever two players were negotiating (either in the single
stage or multi-stage condition) the third player left the room and the
two remaining players negotiated at the game table. The experimenter
remained in the game room, but he could not be seen by the negotiators
nor did he enter into the negotiations. If the pair of players negotia-
ting reached an agreement, they had to record the terms of the agreement
on a contract form. Both subjects were required to sign the form (see
Appendix C, part 3). If the signed form was not passed to the experi-
menter within three minutes, the agreement was not valid. If a pair of
players did not reach an agreement in three minutes, the third player
returned and the process of balloting and negotiating was repeated. When
an agreement was reached, the third player was brought back into the room
.and the terms of the agreement were announced by the experimenter. Each
player then wrote the terms of the agreement on a record sheet (see Appendix
C, part 4). At this time, the experimenter put the divider extensions
in place so that the subjects could not see each other. The player who
was not a member of the coalition was then allowed to offer the coalition

partners terms for a new coalition agreement. The excluded player was

29

permitted to make a maximum of two written offers, one at a time, to each
coalition partner. The offers could be sent in any order to the two coali-
tion partners. If either of the alliance partners accepted an offer, the
existing coalition was dissolved and a new coalition was formed. However,
if a coalition broke a penalty of $100 in play money (or $1 in real money)
was assessed against the game's payoff. When a coalition broke, the members
lost all of their winnings in the game. The player left out of the new
coalition, however, was allowed to make offers to each coalition partner
for forming another coalition. If a coalition partner accepted, a new
coalition was formed and the new partners split the payoff, less the amount
of the penalty. This process continued until either all of the money was
gone or the two partners in a given alliance each rejected the two offers
received from the excluded player.

No talking was allowed during the second part of the game. All offers
during this part of the game were written on special forms (see Appendix
C, part 5). The forms were passed to the experimenter, who checked them
for legality and delivered them to the player to whom they were addressed.
A maximum of two mintues was permitted for each Offer and reply. An
alliance partner receiving an offer from the excluded player could make
a counter—Offer or comment in responding to the offer from the excluded
player, but he could not initiate an offer to the excluded player. The
alliance partners were allowed to send messages to each other, as many
as they wanted, and whenever they wanted. The only restriction was that
the partners could not change the terms of their present agreement. These
rules were summarized and given to the subjects on typed 4” X 6" cards

(see Appendix D).

30

The bargaining sessions were tape recorded for most of the groups.
Most of the subjects were unaware that the sessions were being tape re—
corded. At the end of the game the subjects filled out a questionnaire
(see Appendix E) and if their winnings were in real money, the money was
given to them. Finally, all subjects were asked to say nothing about the
experiment to anyone.

Control groups

 

Groups playing game a second time (Repeat/SS/RM). A record was
kept of the names and phone numbers of the 54 subjects in the 18 SS/RM
groups. From these 54 subjects, 27 subjects were randomly selected to
form 9 triads that participated in the identical experiment a second
time. No subject played the game a second time with either of the two
subjects with whom he participated in the first experiment.

Two-hour/multi—stage[p1ay money grogps (2—houijS/PM). Thirty

 

subjects (10 triads) signed up for a two-hour experiment. The extended
time limit was used to determine whether subjects stOpped breaking coali-
tions in the 1—hour experiment because 1) they wanted to conclude the
experiment as quickly as possible or 2) the one hour time limit had
almost expired or had been exceeded. The experimental procedure was iden-
tical to the MS/PM Condition.
It was decided prior to running the play money conditions that if
no differences were found between the l—hour and 2—hour groups, they would
be combined. This procedure is legitimate since the only difference in
the two conditions is the length of time for which subjects signed up.
Single stage/real money groups with extended divider (SS/RMLDIV.).
After observing the behavior Of the subjects in the SS/RM groups, the

experimenter ran 9 triads in which the subjects could not see each other

 

31

prior to indicating their partner preference. In addition, the subjects
were informed only of how many votes went with each nonsense syllable
name; they did not know which of the other two players had which name
until after two subjects had chosen each other as their preferred partner.
The remainder of the eXperiment was identical to the SS/RM condition.
Operational definition Of dependent variables.

The experimental hypotheses, previously stated, referred to four
dependent variables--the formation of coalitions, the division of the
payoff, the stability of the coalitions, and the time required to reach
an agreement for forming the initial coalition. An Operational speci-
fication of the type of data that was collected for each of these
dependent variable processes is presented below.

Coalition process. Data on the coalition process was collected in

 

two forms: 1) contact data and 2) coalition data. Contact data is.

a specification for each player of the Opponent with whom each subject
indicated he would prefer to form a coalition. This data was collected,
trial by trial,3 until two players chose each other. For the purposes

of this study, contact choices on the initial trial were the only data
analyzed. Coalition data is a specification of which two players formed
the initial coalition in each game. Initial contact choices are probably
a more sensitive measure of the actual perceptions and strategies of the
subjects than coalition data. Coalition data may be confounded by extra-
neous factors, such as personality conflicts during bargaining, need for a
specified amount of money, and other interferences created in a face—

to-face bargaining situation that would prevent the first reciprocal

 

 

 

3A trial is defined as the simultaneous specification by each player
()f his preferred coalition partner.

 

32

pair from forming a coalition.

Division of the payoff. For each coalition, another measure of the

 

subject's interdependent expectations and strategies is how the two
coalition partners divided the payoff. Since there is only one degree

of freedom in specifying the amount of money won by two coalition members,
it is only necessary to record the amount of money won by one Of the
coalition partners. However, the partner whose winnings are recorded
must be the same partner, in reference to some unit of analysis, across
all observations. In this study, the payoff winnings were recorded for
the partner with the greatest number of votes in the coalition. The
amount of money won by the subject with the greatest number of votes was
compared not only among experimental conditions but also with a mean of
$450 ($4.50 in the real money condition) to see how it differed from an
equal division of the payoff. Another item of data relevant to testing
the hypotheses about the division of the payoff is whether or not the
person with the greater number of votes in the initial coalition received
an amount of money equal to or greater than his partner. If the payoff
is divided according to the initial resource values then there should not
be any payoff reversals (i.e., the person with more votes should not re—
ceive less money). If the votes are not important to how the payoff is
divided, there should be a number of payoff reversals.

Stability of the coalitions. Two independent measures of coalition

 

stability were used. The first measure was the amount of money in the
final agreement (the more money, the greater the stability). This measure
includes information about initial coalition breakage, as well as about
the number of coalitions broken subsequent to the initial coalition break-

ing. This measure is the most sensitive measure of coalition stability.

33

The average number of offers to break a coalition and form a new alliance

that are rejected, per agreement, is a second measure of coalition stability
(the more offers rejected, the greater the stability).

Time for first agreement. The amount of time taken to make the first

agreement was recorded in minutes and hundredths of seconds.

 

RESULTS

Uncommon statistical procedures

Eggct probability tests. Since the unit of analysis for much of
the coalition process is a three—person group, the number of independent
observations in this study was fairly small. The type of data collected
about the coalition process was, for the most part, a tabulation of the
frequency with which a given event occurred (e.g., type of coalition
formed). The significance test most commonly used to test for differences
between the experimental conditions in this type of data is the Chi-
square statistic. The Chi-square statistic is also used to test for
the goodness—of-fit of one distribution to another (e.g., the fit of
the distribution of type of coalitions to the uniform chance distribution).
However, there are certain instances in which the continuous Chi—square
distribution is not a good approximation to the discrete distribution of
the Chi-square statistic. The most important instance is that when the
expected values in the Chi-square formula are less than five, the
approximation is unreliable. There were a number of instances in this
experiment in which the expected values were less than five. Therefore,
the Chi—square statistic was not an appropriate statistical test for much
of the data in this experiment.

The alternative to Chi-square is to calculate the empirical probability
(exact probability) of obtaining a given response distribution for some
In order to do this, each possible response distribution for the

event.

34

35

event must be enumerated and the number of ways calculated in which each
response distribution could be formed. The sum across all possible
response distributions of the number of ways each response distribution
could be formed equals the numbers of ways the event could have occurred.
The probability of Obtaining the observed response distribution is equal
to the sum of the number of ways the observed response distribution
could be formed plus the sum of all response distributions less likely
to occur, divided by the total number of ways the event could occur.4
As is apparent, calculating these permutations requires the use of a
computer. In order to calculate exact probabilities for all effects
of interest in this experiment, a set of computer programs was assembled
(Kline, Anderson, Lawton, and Phillips, in preparation). The set of
programs was comprised of three parts. First, for the purpose of
performing a goodness-Of~fit test, a computer program was written
that calculates according to the method previously described, the
probability of obtaining a one—dimensional distribution.5 Second, as
a means of performing a test of independence on two-dimensional dis—
tributions, a program was obtained that calculates the exact probabilities
for two-dimensional tables in which each dimension may have two or more
levels. This computer program is based on a method devised by Freeman
and Halton (1951), which is an extension of Fisher's exact test for the

2 X 2 contingency table.6 Third, a computer program was written that

 

4
This procedure is based on the method devised by Fisher for calcula—
ting the exact probability Of a 2 X 2 table of distributions.

5

This program was written for the computer by John Morris, a member
Of the staff of the Computer Institute for Social Science Research, Michigan
State University.

6
This program was written for the computer by Joseph L. Zinnes of
the Department of Psychology, Indiana University.

36

calculates the exact probability of distributions with three or more
dimensions.7 This program was based on a method devised by Myers (1958),
which was an extension of the Freeman and Halton concept.

Sutcliffe (1957) has described a method for partitioning Chi-
square in order to obtain independent Significance tests for each effect
in a factorial design. This same result can be accomplished in terms
of exact probability by combining the three programs previously described.
Some of the effects in the factorial design may be fixed and, therefore,
would not be calculated. In addition, since each effect is calculated
independently, there would be no need to calculate effects irrelevant to
the hypothesis tested. However, any effects in a factorial design
that one desires to statistically investigate by means of exact probability
can be calculated by these programs.
Interpretation of Significance values

In this paper Significance values between .055 and .104 will be
interpreted as indicating that it was unlikely for the Obtained statistical
value to have occurred by chance only. In other words, in addition to
chance some other process was operating to produce the obtained differ-
ence between the observed factors. These statistical values will be
denoted by one asterisk. Significance values between .015 and .054 will
be interpreted as indicating that it was very unlikely for the Obtained
statistic to have occurred by chance. In other words, the chance process
contributed a very small part, if any, in creating the Observed differences

in the dependent variables. These statistical values will be denoted

 

7This computer program was written by John Anderson and David Kline
of the Human Learning Research Institute, Michigan State University.

 

37

by two asterisks. Significance values less than .015 will be interpreted

as indicating that it was extremely unlikely for the Obtained value Of

 

the statistic to have occurred by chance. In other words, any observed

differences in the dependent variables were due to some process other

than chance. These statistical values will be denoted by three asterisks.
Whenever a specific decision is to be made on the basis of significance

values the critical significance value used will be .05.

Two—hour experiment

 

No significant differences were found between the one—hour and two—
hour MS/PM groups in any of the dependent variables. The significance
values of the statistical tests for differences between the two groups
ranged from .25 to 1.0. Since none of the significance values even
approached the .05 significance level, the two conditions were collapsed,
yielded 24 groups.

Comparison with pEevious coalition results

 

The condition in this experiment most similar to the conventional
coalition formation paradigm (e.g., Vinacke and Arkoff, 1957; and
Chertkoff, 1966) was the SS/PM condition. The primary difference between
the SS/PM condition and the conventional parchesi game paradigm was that
no player could win unless he was a member of a two person coalition.
Other differences, of lesser importance, between the SS/PM condition and
the parchesi paradigm and/or the political convention paradigm were 1)
the commodity used as resources, 2) the seating position of the subjects
in the game, 3) the type of coalition-bargaining game used, 4) the
method of bargaining, and 5) permitting the coalitions to break. In order

to determine if these changes would produce results not supporting

38

RT, the SS/PM condition was compared with two previous coalition studies.
that supported RT predictions. First, a comparison was made with the
Vinacke and Arkoff (1957) experiment (non-forced coalition paradigm).
Second, results obtained by Chertkoff (1966) in his forced coalition
experiment were compared with the SS/PM results.

Comparison with Vinacke and Arkoff experiment. The two types of
data common to both Vinacke and Arkoff's experiment and this experiment
were coalitions formed and, to some extent, the division Of the payoff.
Table 3 reveals that there was no significant difference in the distribu-
tion of initial coalitions for the two experiments. The data on the divis—
ion Of the payoff in the initial coalition was not reported in the same
form in the Vinacke and Arkoff experiment as in the experiment being
analyzed here. In order to compare the results of this experiment with
Vinacke and Arkoff's results, the data in this experiment were retabulated
and analyzed according to Vinacke and Arkoff's system. The data in Table
4 Show that the payoff was divided 50/50 Significantly more often in
Vinacke and Arkoff's experiment than in this experiment.

Copparison with Chertkoff's experiment. Since Chertkoff used a forced

 

coalition paradigm, his experiment is more comparable to the experiment
being analyzed here than Vinacke and Arkoff's study. Chertkoff presents
comparable data for contacts and initial coalitions. Tables 5 and 6 reveal
no significant differences between the two experiments in either initial
contacts or initial coalitions.

Restatement of experimental hypotheses

The seven experimental hypotheses tested in this experiment were:

39

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43

H : Players allowed preliminary bargaining contact with each
other before choosing their preferred partner will tend to
form 4—3, 4~2, and 3~2 coalitions with more equal frequency,
split the payoff more equally, and form coalitions that are
more stable, than players that have no preliminary bargain-
ing contact.

H : Player's receiving their payoff in real money will tend to
form 4—3, 4-2, and 3—2 coalitions with more equal frequency,
split the payoff more equally, and form coalitions that
are more stable than players who play the game for play
money.

H ' The effects of bargaining sequence and incentive will com-
bine so that the greatest equality in the formation of 4-3,
4—2, and 3—2 coalitions, the most equal payoff splits, and
the most stable agreements will occur under the preliminary
contact-real money condition.

H : Players allowed preliminary bargaining contact will take
less time to reach an agreement than players that have no
preliminary contact.

H : Players receiving their payoff in real money will take less
time to reach an agreement than player's receiving their
payoff in play money.

H : Bargaining sequence and incentive will combine so that the
preliminary contact——real money groups will take the least

time to reach a first agreement.

H : The less time taken to reach an agreement in each experiment—
al condition, the more stable the agreement.

Analysis of eXperimental hypotheses.

 

The data collected to test the seven experimental hypotheses will be
presented according to dependent variable in the following order: 1)
coalition data; 2) division of payoff data; 3) stability data; and 4)
time for first agreement data.

Coalition data. Data collected to analyze the coalition process

 

consists of two types—-initial contact frequencies and initial coalition
frequencies.
The contact data is presented in Table 7. The exact probabilities

for the faccorial analysis of contacts are presented in Table 8. An examina—

44

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45

 

 

 

Table 8. Factorial design exact probabilities of contacting the
opponent with the greater number of votes or the opponent
with the fewer number of votes

Effect Exact probability

Bargaining sequence (A) fixed effect

Type of payoff (B) fixed effect

Subject's votes (C) fixed effect

DV - contacts (D) <.0001***

A x B fixed effect

A x C fixed effect

A x D .7510

B x C fixed effect

B x D .0163**

C x D .0792*

A x B x C fixed effect

A x B x D .7781

A x C x D .1072

B x C x D .7165

A x B x C x D 1.0000

 

*unlikely distribution
**very unlikely distribution
*W*extremely unlikely distribution

46

tion of Table 8 reveals that in the entire experiment players chose the
weaker Opponent significantly more Often than the stronger Opponent.
There was not a significant difference between the bargaining sequence
conditions and, therefore, Hypothesis 1 for the contact data was not sup-
ported. Players in the real money condition chose the Stronger opponent
significantly more often than did players in the play money condition.
This result confirmed Hypothesis 2 for the contact data. However, further
analysis revealed that the players in the real money condition chose the
weaker opponent significantly (p = .0050) more often than they chose the
stronger opponent. The almost significant interaction between contact
choice and number of votes suggests there was a tendency for the player
with two votes to contact the opponent with the greater number of votes
more often than do the players with three or four votes. In order to
test the validity of Hypothesis 3 for the contact data, simple effects
in the A x B x D interaction were analyzed. Table 9 reveals that the
subjects in the MS/RM condition chose the opponent with the greater number
of votes significantly more often than did the subjects in either the 88/
PM or MS/PM condition. However, the difference between the MS/RM and 88/
RM conditions was not significant (p = .6889) for this dependent variable.
Therefore, Hypothesis 3 was not confirmed for the contact data. Some sup—
port for Hypothesis 3 was revealed in the fact that the MS/RM condition was
the only condition in which the distribution of contact choices was not
significantly different from chance.

The pattern of results for the coalition data is much the same as that
obtained for the contact data. An inspection of Table 10 and 11 reveals

a significant main effect for the type of coalition formed and a Significant

 

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48

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w a H H N Mia
msOHuHHmOO
HmHuHcH
mHQDOH Nedoe Hmmm hence >mHm xodos Hmom memos NmHm mmo%mm
mo OQ%H
owmumanHsz meuw onnHm monosvom wcHnHmwumm

 

 

 

 

 

mcoHuncoo cmeop HmunoEHnomxo ego
CH mcoHuHHmoo HmHuHsH mo OOHumEnow mo modoswoum

.OH OHQmH

49

Table 11. Factorial design exact probabilities of formation of
initial coalitions in the experimental design conditions

 

 

Effect Exact probability

 

 

Bargaining sequence (A) fixed effect
Type of payoff (B) fixed effect

DV - Initial coalitions (C) .0000004***
A x B fixed effect

A x C .7694

B x C .0418**
A x B x C .4238

 

** very unlikely distribution
*** extremely unlikely distribution

Table 12. Exact probability test for independence between the initial
coalition distribution in the multi-Stage/play money condition
and the initial coalition distribution in the multi-stage/real
money condition

 

 

 

 

Condition
Initial Multi—stage/ Multi-stage/ Totals Exact
coalition play money . real money probability
4-3 1 4 5
4-2 7 7 14 .1094
3-2 16 7 23
Tocals 24 18 42

 

 

 

 

 

50

interaction between type of payoff and initial coalition type. The main
effect difference for the type of coalition formed indicates that the three
types of possible coalitions (4—3, 4-2, and 3-2) were not formed with equal
frequency. Instead, the overall design confirms the §Efl hypotheses that
the 3-2 coalition occurs most often, the 4—2 coalition next most often, and
the 4—3 coalition least often. The significant interaction between type

of payoff and type of coalition formed indicates that more strong coali-
tions (4-3 and 4—2) were formed in the real money condition than in the
play money condition. This result confirmed Hypothesis 2 for the coali—
tion data. However, the real money subjects did not form the three types
of coalitions with equal frequency (p = .0292). Hypothesis 1 was not
confirmed for the coalition data since no difference was found in the
distribution of coalitions between the two levels of the bargaining se-
quence factor. In order to test Hypothesis 3 it was necessary to examine
the simple effects in the A x B x C interaction table. The two most dis-
crepant distributions of initial coalitions are presented in Table 12.

Even though the difference between the two distributions was in the hy—
pothesized direction, it was not a statistically significant difference.
Therefore, Hypothesis 3 was not confirmed for the coalition data. It
should also be noted that the only distribution of initial coalitions in
the four experimental conditions that was not significantly different

from chance was the distribution in the multi—stage real money condition.

Division of the payoff. The amount of money won by the player with

 

the most votes in the initial coalition was used to determine whether there
were any differences between experimental conditions in the way the payoff

was divided. The closer to 4.50 the amount of money won by this player,

51

the more equally divided the payoff. The means and standard deviations
are presented in Table 13. The analysis of variance8 (AOV) presented in
Table 14 Shows a significant main effect for bargaining sequence and
type of payoff. The difference between the single-stage and multi—stage
bargaining conditions was in the hypothesized direction and confirmed
Hypothesis 1 for the payoff data. The difference between the play money
conditions and real money conditions was also in the hypothesized direc—
tion and confirmed Hypothesis 2 for the payoff data. In order to test
Hypothesis 3 for the payoff data multiple comparison t tests were made
between all pairs of means in the 2 X 2 design.9 Table 13 reveals that
the mean payoff value for the player with the most votes in the initial
coalition was the closest to the point of equality (4.50) in the MS/RM
condition. However, this mean payoff was significantly different from
the mean payoff of only the SS/PM condition (Table 15). This result did
not confirm Hypothesis 3 for the payoff data. The mean payoffs in all
conditions were significantly different from the equal split mean of 4.50.
Payoff reversals (i.e., where the player with more votes in the initial
coalition receives the lesser amount of money) were observed in only the

_______.__.__,_- __._—-. --_---..———_

Because there was not an equal number of replications in each cell
of the 2 X 2 factorial design, a least squares method was used for all
analyses of variance. The computer program used was made available by
the Agricultural EXperiment Station at Michigan State University (Ruble,
1966). The method of analysis was that described by Winer (1962). Since
in an unequal N design the factors are correlated, the mean square for
any given effect is not the same when analyzed with different sets of
factors; it fluctuates according to its correlation with the factors

that are included in the design. For this reason any factor, other than
the two basic factors in the experimental design, that yielded no signi—
iicant main effect or interactions was discarded from the analysis of a

given dependent variable, and the analysis was recalculated on N-l
factors.

Scheffe 5 test (Edwards, 1967)

52

CH paw COHDHOGOO %Ocos Nme OSO

.COHuncoo zones Hmou Ofiu :H manHop

CH wanHop mo newness; pH powwouaxo mH hence mo bosoEm exam

 

 

 

 

 

 

No. Va manna Ho. Va manna Ho. Va Naume Ho. Va amuse om.a gone smug cesaoo
quw.N Nmow.m mMNw.m NmmN.w mo oodmuomep now amen o
wH «N mH qN z
mqu. onm. wNNq. oqu. .>op .pom
mwwN.q omom.¢ comm.¢ woNN.m cmoz
mOHumHumom
Nocos Hmem Noses NmHm Noses Hmom zecos NmHm mmwoxma
mo omzH
mwmumuHanz meum onch mosesvom wchHmemm

 

 

 

 

COHOHHmOO HmHuHcH CH mmuo> mo noeasc pneumonm zuHB uokam

%@ nos Noses mo unsoEm now mz paw .mGOHumH>Op pnmwomum amcwoz .MH oHan

53

Table 14. Analysis of variance of amount of money won by player with
the greatest number of votes in initial coalition

 

 

 

Source of variance SS df Mean square F Significance
value

Bargaining sequence (A) .8126 1 .8126 4.399 .04**

Type of payoff (B) 1.1187 1 1.1187 6.056 .02**

A x B .0670 1 .0670 .363 .55

Error 14.7772 80 .1847

Total 16.8620 83

 

g
I

P
7very unlikely F value

Table 15. Multiple comparison t values for all pairs of
means of amount of money won by player with
greatest votes in initial coalition

 

 

 

Means SS/PM SS/RM MS/PM critical ratio
Means
SS/RM 2.1754
MS/PM 2.0746 .2578 1 2.8566
MS/RM 3.2376* .9922 1.3200 p =.OS

 

 

 

 

 

7'cSignificant beyond .05 level

54

MS/RM condition. Two 3—2 coalitions in the MS/RM condition made an agree—
ment in which the 2—vote player received the larger proportion of the pay—
off. These payoff reversals give support to Hypothesis 3 for the payoff
data.

§Egpi1ity. Two independent measures of stability were used: 1)
amount of money in the final agreement and 2) the average number of Offers
to form a new coalition rejected per agreement.

The means and standard deviations for the amount of money in the
final agreement are given in Table 16. The differences in the means of
the various experimental conditions were in the predicted direction.

Table 17 reveals that there was a significant difference between the real
and play money groups for this dependent variable. This result confirmed
Hypothesis 2 for the amount of money in the final agreement. Hypothesis

1 was not confirmed. In order to test Hypothesis 3 multiple comparison t
tests were made between all pairs of means. Table 18 reveals that the
MS/RM mean was significantly different from the means of only the SS/PM

and the MS/PM conditions. This result did not confirm Hypothesis 3 for the
level of final agreement. An analysis of this dependent variable by type
of initial coalition revealed no significant differences in the level of
final agreement between types of initial coalitions.

An examination of the average number of rejections per agreement
(Table 19) reveals differences between the experimental conditions in the
hypothesized direction. Table 20 shows a significant difference in the
average number of rejections per agreement between the real and play money
SrOUPS. This result confirmed Hypothesis 2 for the average number of

rEjections per agreement. Hypothesis 1 was not confirmed. As predicted,

55

Table 16. Means, standard deviations, and NS of the
amount of money in final agreement

 

 

 

 

 

 

 

 

 

 

 

 

Bargaining sequence Single stage Multi-stage
Type of .
ayoff Play money Real money Play money Real money
Statistics
Mean 5.9583 8.2222 6.7917 8.7222
Std. dev. 2.6289 1.3528 2.2259 .5745
N 24 18 24 18
Table 17. Analysis of variance of the amount
of money in final agreement
Source of variance SS df Mean square F Significance
value
Bargaining sequence (A) 9.1428 1 9.1428 2.362 .13
Type of payoff (B) 90.4802 1 90.4802 23.377 <.0005***
A x B .5714 l .5714 .148
Error 309.6389 80 3.8705
Total 410.7024 83

 

9‘: 7'.- 7':

extremely unlikely F value

56

 

 

 

 

 

 

 

 

Table 18. Multiple comparison t values for all pairs of
means of amount of money in final agreement
Means J . . .
SS/PM SS/RM MS/PM cr1tlca1 ratio

Means

SS/RM 3.6871* 2.8566

MS/PM 1.4672 2.3298 p =.05

MS/RM 4.5014* .7625 3.1441*

7(Significant beyond .05 level
Table 19. Means, standard deviations, and N3 of the average

number

of rejections per agreement

 

 

 

  

 

Bargaining sequence Single stage Multi-stage
Type of
payoff Play money Real money Play money Real money
Statistics
Mean 2.0625 3.4000 2.4667 3.6667
Std. dev. 1.1162 1.0748 1.2075 .6642
N 24 18 24 18

 

 

 

 

 

57

Table 20. Analysis of variance of the average number of

rejections per agreement

 

 

 

Source of variance SS df Mean square F Significance
value

Bargaining sequence (A) 2.3144 1 2.3144 2.073 .15

Type of payoff (B) 33.1144 1 33.1144 29.656 <.0005***

A x B .0972 1 .0972 .087 .77

Error 89.3296 80 1.1166

Total 125.0442 83

 

‘k 7'

extremely unlikely P value

Table 21. Multiple comparison t values

for all pairs of means of

average number of rejections per agreement

 

 

 

Means . ' .
Means SS/PM SS/RM MS/PM critical ratio
SS/RM 4.06047? 2.8566
MS/PM 1.3252 2.8333 p =.05
MS/RM 4.8703‘k .7572 3.64299.

 

 

 

 

 

7"Significant beyond .05 level

58

the largest average rejections occurred in the MS/RM condition. A com—
parison of means of the four experimental conditions showed a significant
difference between the MS/RM mean and the SS/PM and MS/PM means (Table 21).
This result did not confirm Hypothesis 3 for the average number of re—
jections per agreement. An investigation of the effect Of initial coali—
tion type upon the average number of rejections revealed no significant
differences in rejections between type of initial coalition.

Time for first agreement. Tables 22 and 23 reveal that it took the

 

real money groups significantly less time to reach an agreement than the
play money group. This result confirmed Hypothesis 5. Hypothesis 4 was
not confirmed. An inspection of Table 22 shows that it took the least
time to reach an agreement in the MS/RM condition. A comparison Of the
MS/RM mean with the means in the other conditions revealed it was signi—
ficantly different from the SS/PM mean, but not from either of the other
two means (Table 24). Therefore, Hypothesis 6 was not supported.

Hypothesis 7 received no support from either the amount of money in
the final agreement or the average number of rejections per agreement
(Table 25). An examination of Table 25 reveals the same general type of
correlations in all conditions except the SS/RM condition. Z transforma-
tion tests for differences between the correlations in the MS/RM and SS/RM
conditions yielded significance values of .41 for the amount of money in
the final agreement, and .23 for the average number of rejections. There—
fore, there were no significant differences between experimental conditions
in the correlation of time with stability.

Alternate hypotheses

 

Alternate hypothesis 1: simplifying coalition—bargaining game. As

nreviously reported, the SS/PM condition yielded SIW contact and coalition

 

 

Table 22.

59

taken to make first agreement

Means, standard deviations, and NS of time

 

 

 

  

 

 

 

 

 

 

Bargaining sequence Single stage Multi-stage
Type of
payoff Play money Real money Play money Real money

Statistics

Mean 1.9904 1.6444 1.7717 1.2161

Std. dev. .7179 1.0121 .8208 .7346

N 24 18 24 18
Table 23. Analysis of variance of time taken to make first agreement

 

 

Significance

Source of variance SS df Mean square F

 

value
Bargaining sequence (A) 2.1534 1 2.1534 3.195 .08*
Type of payoff (B) 4.1799 1 4.1799 6.202 .02**
A x B .2259 1 .2259 .335 .56
Error 53.9163 80 .6740
Total 60.3216 83

 

7I'unlikely P value

7'“kvery unlikely F value

 

60

 

 

 

Table 24. Multiple comparison t values for all pairs
of means Of time taken to make first agreement
Means . , .
Means SS/PM SS/RM MS/PM critical ratio
SS/RM 1.3531 2.8566
MS/PM .9243 .4978 p =.05
MS/RM 3.0281* 1.5659 2.1728

 

 

 

 

 

7cSignificant beyond .05 level

Table 25.

Correlation of time taken to make first agreement with amount

of money in final agreement and average number of rejections
per agreementa

 

 

 

     

 

 

Bargaining sequence Single stage Multi-stage
Play money Real money Play money Real money
Stability
Money in final
agreement -.144 .092 -.155 -.205
Average rejections -.O69 .068 -.143 -.369
N 24 18 24 18

 

 

 

 

 

None of the correlations were significantly different from a zero

correlation at the .05 significance level.

61

results almost identical to the previously reported research. In addition,
the coalitions were very unstable. For these reasons alternate hypothesis
1 was ngt_confirmed.

Alternate hypothesis 2: experience and learning effect. A comparison
between the SS/RM groups and the repeat/SS/RM groups revealed a signi-
ficiant difference between the two conditions on only one dependent vari-
able. The subjects divided the payoff more equally the second time they
played the game than they did the first time (Table 26). Alternate
hypothesis 2 was, therefore, partially confirmed. Additional data support—

ing the conclusions about the repeat/SS/RM group is presented in Appendix

Alternate hypothesis 3: amount of time for experiment. An analysis
of the amount of money in the final agreement in the 2—hour condition and
the l—hour condition revealed no significant difference between the two
conditions (Table 27). Therefore, alternate hypothesis 3 was Egg confirmed.
Additional factors that could influence dependent variables. An exam—
ination of the initial contacts and coalitions by subject's position at
the game table revealed a tendency for subjects at the ends of the game
trfiyle in the SS/RM condition to choose each other. In order to determine
if this tact could have altered the pattern of contacts and coalitions
in the SS/PM condition a control group was run. In the control group,
subjects could not see each other until after two players had selected
each other as their preferred partner. In addition, the players did not
knOW'which of the other two persons in the experiment had which number of
votes until after a reciprocal partner selection. Otherwise, the game was
identical to the SS/PM condition. Tables 28 and 29 reveal that the tendency

to choose the player facing one did not significantly alter the coalition

 

 

62

Table 26. t test of difference in the amount of money won by
player with the greatest number of votes between
single stage/real money groups and repeat/single
stage/real money groups

 

 

 

Condition Repeat/
single stage/ Single stage/ t value
Statistics real money real money
Mean 4.6111 4.9306 2.4117**
Std. dev. .1816 .4778 df = 26
N 9 18 .02<p< .05

 

 

 

 

7‘: '2'c
very unlikely t value

Table 27. t test of difference in the amount of money in final
agreement between l-hour/multi-stage/play money
condition and 2-hour multi-stage/play money condition

 

 

 

Condition 1-hour/ 2-hour/
multi-stage/ multi-stage/ t value
Statistics play money play money
Mean 7.0000 6.5000 .4897
Std. dev. 2.0400 2.5500 df = 18

N 14 10 p >.50

 

 

 

 

 

Table 28.

63

Exact probability test for independence between the initial

contact distribution in the single stage/real money condition
and the initial contact distribution in the single stage/real
money/divider condition

 

 

 

 

 

Condition Single stage/ Single stage/ Exact
real money real money/ Totals probability
Contacts divider
Greater 18 13 31
.2486
Fewer votes 36 14 50
Totals 54 27 81
Exact probability test
for uniformity of .0198** 1.0000

column distribution

 

 

 

 

 

7': 7':

very unlikely distribution

 

 

 

 

 

column discribution

 

 

 

 

Table 29. Exact probability test for independence between the initial
coalition distribution in the single stage/real money condition
and the initial coalition distribution in the single stage/real
money/divider condition

Condition Single stage/ Single stage/ Exact
real money real money/ Totals probability

Coalitions divider

4-3 1 3 4
4-2 10 4 14 .2084
3—2 7 2 9
Totals 18 9 27
Exact probability test
for uniformity of .0193** .9146

 

wwvery unlikely distribution

 

64

process. Additional data to support this conclusion are reported in
Appendix A (p. 91).

An analysis of all the dependent variables failed to reveal any
significant differences as a result of the three symbol names assigned
to the subjects.

The order in which the subjects bargained in the preliminary negotia-
tion round of the multi-stage condition could have affected the coalition
process. If there was a primacy or recency effect from the bargaining
order, it would not be too surprising to have obtained a somewhat equally

distributed set of coalitions. An analysis of the effect of preliminary

 

bargaining order upon all of the dependent variables revealed no signi—
ficant effects. Data to support this conclusion are presented in Appendix
A (p. 110).

An analysis of information about subjects' prior knowledge of the
experiment revealed that three subjects had heard it was a bargaining
game and two subjects had heard money could be won. None of these five
subjects was discarded from the eXperiment.

Information collected about subjects' participation in other psycho-
logical experiments revealed that no subjects had participated in any
experiments that one would expect to bias a person's behavior in this
experiment.

If subjects had suspected that they would be allowed to break the
initial coalition at the time they were negotiating to form the coali—
tion, it would very likely have influenced their coalition behavior. The
subjects were asked on the post-game questionnaire whether or not they

had su5pected, prior to being informed by the experimenter, that they would

65

be allowed to break the first agreement. Forty—eight subjects responded
that they were not sure they would be allowed to break the first agree—
ment but that they did feel there would be more to the game than had been
described to them. In explaining this response to the experimenter after
the game was over, subjects said the game, as described, seemed too
simple and too short for there not to be more to it. An analysis of the,
reSponses to this question by experimental condition is presented in
Appendix A (p. 85).

A critical factor when offering real money as a payoff in a psycho—

logical experiment is convincing the subjects that they will actually

 

receive the money. Prior to being given the money, the subjects in the
real money condition were asked if they believed they would receive the
payoff in real money. Ninety—five of the 108 subjects responded affirma-
tively. An analysis of the responses to this question by experimental
condition is presented in Appendix A (p. 86).

An analysis of data collected on the post-game questionnaire revealed
that there were no differences between experimental conditions in l) the
subjects' experience in playing competitive games, or 2) the value of $9
to the real money subjects. Data to support these conclusions are pre—

sented in Appendix A (p. 100).

DISCUSSION
This experiment's fundamental tenet was that previous results sup-
porting resource theory predictions in the Type 5 coalition situation
were the product of three artifacts in the experimental design. These
artifacts were: 1) unequal status among the game participants; 2) time
pressure to make a quick coalition; and 3) demand characteristics

of the experimental situation. According to the general hypothesis, if

 

these artifacts were removed, the resource theory outcomes would be
eliminated and the coalition process would be that predicted by the
rational—objective theorem.

Effect of equalizing status and makingfiminor changes in game

 

A comparison of the forced coalition game used in this experiment
with the non-forced coalition game of Vinacke and Arkoff (1957) revealed
no difference in the distribution of initial coalitions. A comparison
of this experiment's results with Chertkoff's (1966) forced coalition
experiment revealed no differences in either initial contacts or coali-
tions. However, there was a significant difference between the experi—
ment reported in this paper and Vinacke and Arkoff's experiment in the
division of the payoff. In order to make this comparison, the payoff
splits in this experiment had to be retabulated to fit Vinacke and Arkoff's
arbitrary classification scheme. It is doubtful that Vinacke and Arkoff's
scheme is as appropriate a test of the payoff division hypothesis as would
be a mean difference test. In spite of this criticism, it is evident

that Vinacke and Arkoff's subjects split the payoff exactly 50/50

67

considerably more often than the players in this experiment. This
difference causes one to suspect that the coalition process in the two
experiments was different. An examination of the Vinacke and Arkoff
experimental procedure suggests a possible explanation for this apparent
difference in coalition processes. In the parchesi game the winner was
defined as the player, or players, first crossing the finish line. When
two players formed a coalition in this game their separate game markers
were replaced by one single marker representing the two—person coalition.
Since both players in the coalition would cross the finish line at the
same time (i.e., would be equal winners), this procedure implied an
equality between the two coalition partners. In addition, coalition
partners may have tended to perceive each other equally because Vinacke
and Arkoff did not give their subjects a strong orientation to maximize
their individual payoff within the coalition. These two equalizing
tendencies could very well account for the coalition partners splitting
the payoff 50/50 almost one—half of the time in Vinacke and Arkoff's
experiment. It should be pointed out that this same explanation could
account for the failure of the payoff data in the parchesi paradigm
experiments to support the predictions of resource theory.

In comparison with the parchesi game, the coalition game used in the
eXperiment reported here emphasized the inequality of the coalition partners.
Each coalition member was encouraged to maximize his individual winnings
in order to 1) be the first place winner in the game, and 2) surpass
all previous players of the game who began with the same number of votes.
Under these circumstances, a subject would be inclined to want more money

than his partner, even if it was only one dollar more. The difference

 

68

in orientation and rules between the two experiments could easily account
for the discrepancy in the payoff splits. In any case, payoff splits

in the experiment reported here are more in line with RT expectations
than are the Vinacke and Arkoff data.

It was concluded, therefore, that the coalition—bargaining game used
in the SS/PM condition of this experiment produced results strongly sup—
porting the predictions of RT. Consequently, any observance of outcomes
not supporting RT, obtained using this game, can not be accredited to
differences in structure between conventional paradigm games and the SS/PM
game.

Effect of alleviating time pressure

Hypothesis I predicted that by allowing all pairs of players to have
preliminary negotiations the coalition process outcomes would give greater
support to the predictions of the rational-objective theorem than ob—
tained without preliminary negotiations. Table 30 reveals that this
hypothesis was confirmed only for the division of the payoff. One possible
explanation for the failure of preliminary negotiations to eliminate
the §Ifl_effect for contacts and coalitions is as follows. The factor
about which the subjects are negotiating in the preliminary round is the
share of the payoff each coalition partner will receive. The bargaining
strategy used in the preliminary negotiations by the player with the most
inotes (relative to the opponent bargaining with) is usually that the pay-
off should be split in proportion to the number of votes each player
would contribute to the coalition. The player with less votes usually
wants to ignore the votes and bargain on the basis of equal power and,
therefore, an equal split of the payoff. Since each player wants to

ensure that he will be chosen by both of the other players, there is a

 

 

68

in orientation and rules between the two experiments could easily account
for the discrepancy in the payoff splits. In any case, payoff splits

in the experiment reported here are more in line with RT expectations
than are the Vinacke and Arkoff data.

It was concluded, therefore, that the coalition-bargaining game used
in the SS/PM condition of this experiment produced results strongly sup—
porting the predictions of RT. Consequently, any observance of outcomes
not supporting RT, obtained using this game, can not be accredited to
differences in structure between conventional paradigm games and the SS/PM
game.

Effect of alleviating time_pressure

 

Hypothesis 1 predicted that by allowing all pairs of players to have
preliminary negotiations the coalition process outcomes would give greater
support to the predictions of the rational—objective theorem than ob—
tained without preliminary negotiations. Table 30 reveals that this
hypothesis was confirmed only for the division of the payoff. One possible
explanation for the failure of preliminary negotiations to eliminate
the STE effect for contacts and coalitions is as follows. The factor
about which the subjects are negotiating in the preliminary round is the
share of the payoff each coalition partner will receive. The bargaining
strategy used in the preliminary negotiations by the player with the most
votes (relative to the opponent bargaining with) is usually that the pay—
off should be split in proportion to the number of votes each player
would contribute to the coalition. The player with less votes usually
wants to ignore the votes and bargain on the basis of equal power and,
“therefore, an equal split of the payoff. Since each player wants to

ensure that he will be chosen by both of the other players, there is a

69

tendency for each player to offer his opponents better terms in the pre—
liminary negotiations than he would actually agree to in a final negoti—
ation. This means that the player with more votes makes preliminary
agreements in which he receives less than his proportionate share of the
payoff,and the player with less votes makes preliminary agreements in
which he receives less than one-half of the payoff. Even though pre—
liminary negotiations are not binding there is a tendency for these pre—
liminary agreements to become the terms of final agreements. Choosing

a coalition partner on the basis of the most profitable preliminary
agreement results in three and Egg choosing each other. However, the
preliminary agreement results in a final agreement that divides the
payoff more equally than dividing it in proportion to initial resource
values.

It was concluded, therefore, that even though the preliminary negoti—
ations did not eliminate the gig effect for contacts and coalitions, they
alleviated the tendency for the time pressure to cause the payoffs to be
split according to the initial resource values.

Effect 2f obviating demand characteristics

 

It was hypothesized that subjects playing the game for real money
would form coalitions more in accord with the rational-objective theorem
predictions than subjects playing the game for play money (Hypothesis 2).
Table 30 shows that the data confirmed this hypothesis for every dependent
variable. It was concluded, therefore, that the most significant factor
in producing outcomes more in agreement with the R—O—T than with RT is
providing the players with a payoff for the game that is of significant

value. The assumption made in the experiment was that a payoff of signi-

7O

 

 

vwauflwfioo uoc poeufimcoo meHHmaoo uoc chHuomnwu wwwum>m An
msna coo uoc oEHH Goo oEuH Goo uod cofiufl moo ms“ :H
p .m p m p .m H H m
hmcoE mo ucsoEm Am
mmmooua %Uflaflnwum .m
poEuflmcoo no: casufimdoo woauflwcoo soflmfi>fip mwommm .N
moEuflmdoo uoc woapfimcoo woaufimnoo uoc mcowufiamoo An
woeuflwaoo won poEHflmdoo pmauflmaoo uo: muowucoo Am
mmooonm schofiamoo .H
moanmwsm>
cw some
m N H u p Q

 

 

 

memosuomxm

 

 

mouse swnounu mso mommsuomzn kucoafluomxm mo dehumauflcho .om wanes

 

71

ficant value obviates the subjects tendency to play the game 1) for the
experimenter's approval or 2) the easiest and fastest way. Instead, the
subject plays the game for its own reward.

Even though the contact, coalition, and payoff data were more equally
distributed in the real money condition, the distributions for all three
dependent variables were different from a chance distribution. Therefore,
the effect of the initial resource values was not completely eliminated by
real money payoffs.

Combination of preliminary negotiations and real money payoff

Hypothesis 3 stated that the greatest incidence of equal coalitions
and payoff splits, and the greatest coalition stability, would occur in
the preliminary negotiation~—real money condition. This hypothesis was
not statistically confirmed for any of the dependent variables. However,
there are three other types of information that give support to the validity
of this hypothesis. First, for every dependent variable, the condition
producing behavior most in agreement with the R—O—T was the MS/RM condition.
The consistency of this result suggests that there is more going on in
this condition than can be accounted for by the real money main effect.
Second, the only condition that reported payoff reversals was the MS/RM
condition. This is a significant event since it has never before been
reported that the person with the most votes in a coalition received less
money. The implication of a payoff reversal is that the votes are of little
significance in determining the division of the payoff. This result offered
further support for Hypothesis 3. Third, further evidence of the validity
of this hypothesis was revealed in the fact that the only condition in which
the contact and coalition distributions were not significantly different

from chance was the MS/RM condition. In other words, the MS/RM condition

72

is the only condition in which the STE effect was completely eliminated.
However, the payoff division in the MS/RM condition was significantly
different from a chance division.

It was concluded, therefore, that neither a forced coalition paradigm,
preliminary negotiations, nor real money payoff could by itself eliminate
the RT outcomes and produce R—O-T outcomes. However, if all three of these
factors were present in a coalition situation, the outcome would be more in
agreement with the predictions of the R-O—T than resource theory.

Time for first agreement

 

Another variable of interest in analyzing the coalition formation
process was the amount of time taken to reach the first agreement. The
data revealed that, as predicted, it took less time to reach an agree—
ment in the real money than the play money condition. This implies
that when persons are playing a game of real value to themselves, their
negotiations are concise and direct and they do not waste time bickering
over unimportant details. There was no difference in time taken for
the first agreement between the groups with preliminary negotiations and
those without preliminary negotiations. The prediction that when prelimi-
ary negotiations are combined with a real money payoff the negotiations
take the least time was not confirmed.

In addition, the amount of time required for the first agreement
was not significantly related to the stability of the coalitions. It was
concluded, therefore, that the amount of time taken to reach an agreement
was significantly related to only the main effect variables of bargaining

sequence and type of payoff.

73

Alternate hypotheses

 

A number of alternative explanations were offered for the results
obtained in this experiment, such as l) greater understanding of the
coalition situation as a result of simplifying the coalition—bargaining
game; 2) the one—hour time limit of the experiment inducing false
stability; 3) differential preference for players as a result of their
position around the table; 4) differential preference for players
symbol names; and 5) differential preference for players as a result
of preliminary negotiation bargaining order. An examination of all of
these factors revealed no significant effects upon the coalition formation
process.

The alternate explanation, that more experience in playing the game
would result in R—O-T outcomes, received some support from the payoff
data in the repeat/SS/RM group. The subjects in the SS/RM condition who
played the game a second time split the payoff more equally than the
subjects in the original SS/RM condition. The post—game interview with
the subjects repeating the experiment revealed the reason for the differ-
ence in payoff distributions between the two times they played the game.
Since the subjects in the repeat condition had already played the game,

they were aware that the initial coalition would be allowed to break.

 

10 . . .
If the behav1or observed in an experiment can be accounted for

by an alternate explanation as well as by the theoretical explanation
being studied then one cannot be sure which explanation is correct.

In order to substantiate the theoretical explanation being tested,

one must show that the only set of existing circumstances that could
have produced the observed effect was that set controlled by the experi-
ment. At the same time, one does not reject a theoretical explanation
that has been offered merely because some alternate set of circumstances
could have produced the observed effect. In order to reject the theoret-
ical explanation being tested, one must demonstrate that the alternate
set of circumstances did affect the dependent variable in the manner
predicted by the experimental hypotheses.

74

In anticipation of this the subjects made initial agreements that split
the payoff more equally in hopes that their partner would not be too
susceptible to offers to break the initial coalition. Of course, if the
initial coalition did not break there would be more money in the game.
Since, there was no difference between the SS/RM groups and the repeat/
SS/RM groups in initial contacts or coalitions, it was concluded that
experience, per se, could not account for the R-O—T results obtained in
this experiment.

The fact that three subjects had some prior knowledge of the experi-
mental game was not taken as a serious influence since the information
given these subjects was no more revealing than the information provided
on the experiment sign—up sheets. The two subjects who knew before
arriving for the experiment that the game was to be played for real
money said they had signed up for the experiment before learning about
the money. Therefore, no subjects were omitted from the analysis for
possessing prior knowledge of the experiment.

The 48 subjects who indicated that they prematurely thought the
first coalition would be allowed to break were not discarded from the
experiment. In post-experimental discussion, many of these subjects
confessed that this was only one of many possibilities that occurred to
them. In the case of others, it was apparent to the experimenter that
some subjects responded affirmatively to this question just because they
did not want to admit that they had not been able to foresee this
possibility. It appears that a post-game questionnaire is not a valid

means for obtaining data about this factor.

75

Conclusions and further research

The main conclusions of this experiment about the coalition process

in the Type 5 coalition situation are:

l)

2)

3)

4)

5)

The strength—is—weakness results that have been obtained in the
Type 5 coalition situation using the conventional research
paradigm are, at least partially, the product of artifacts in
the experimental situation.

The main factor contributing to the production of rational-
objective theorem outcomes is the use of real money to create
a payoff for the coalition-bargaining game that is of signi—
ficant value to the participants.

Real money payoffs are not sufficient to completely eliminate
the strength—is—weakness effect and produce rational-objective
theorem coalition outcomes; however, the combination of real
money payoffs with a forced coalition paradigm and preliminary
negotiations will tend to produce an equal distribution of
initial contacts and coalitions.

If the coalition process is examined in a realistic situation
for testing coalition formation theory, the results are more in
agreement with the rational-objective theorem than resource
theory.

Both preliminary negotiations and real money payoffs contribute
to participants taking less time to reach an agreement to form
a coalition.

These conclusions assume that the coalition process is not altered if the

initial resource values are randomly assigned. However, Anderson (1967)

suggests that the random assignment of initial resources is a prime factor

in producing equal outcome effects in coalition formation studies. In order

to test this hypothesis a follow-up study is being conducted in which the

subjects will earn their resources prior to playing the coalition-bargaining

game.

BIBLIOGRAPHY

Anderson, R. E. Status structures in coalition bargaining games.
Sociometry, 1967, 20, 394—403.

 

Bond, J. R., and Vinacke, W. E. Coalitions in the mixed~sex triad.
Sociometry, 1961, 23, 61-75.

 

Caplow, T. A theory of coalitions in the triad. American Sociological
Review, 1956, 22, 489—493.

 

Chertkoff, J. M. The effects of probability of future success on
coalition formation. Journal of Experimentgl Social Psychology,
1966,_2, 265—277.

Edwards, A. Statistical methods. Second edition. New York: Holt,
Rinehart, and Winston, 1967.

 

Emerson, R. M. Poweredependence relations: Two experiments. Sociometry,
1964,.22, 282—298.

Freeman, G. H., and Halton, J. H. Note on exact treatment of contingency,
goodness of fit, and other problems of significance. Biometrika,
1951, 28, 141-149.

 

Gamson, W. A. A theory of coalition formation. American Sociological
Review, 1961(a),.26, 373-382.

 

Gamson, W. A. An experimental test of a theory of coalition formation.
American Sociological Review, 1961, 26, 565—573.

 

Glaze, J. A. The association value of nonsense syllables. Journal of
Genetic Psychology, 1928, 22, 255-269.

 

 

Kelley, H. H., and Arrowood, A. J. Coalitions in the triad: Critique
and experiment. Sociometry, 1960, 22, 231—244.

 

Kline, D. K., Anderson, J., Lawton, D., and Phillips, J. L. A 3400/3600
Fortran program for computing chi—squares and exact probabilities of
all effects in a factorial design. Technical Report No.

Human Learning Research Institute, Michigan State University, in
preparation.

76

77

Myers, J. L. Exact probability treatments of factorial designs.
Psychological Bulletin, 1958, 5Q, 59-61. '

 

Phillips, J. L., and Nitz, L. H. Social contacts in a three-person
political convention situation. Journal of Conflict Resolution,
1968, 22, 206—214.

Ruble, W. L. Analysis of covariance and analysis of variance with unequal
frequencies permitted in the cells. STAT series description No. 18,
Agricultural Experiment Station, Michigan State University, 1966.

Shapeley, L. S., and Shubik, M. A method for evaluating the distribution
of power in a committee system. American Political Science
Review, 1954, 48, 787-792.

 

Sutcliffe, J. P. A general method of analysis of frequency data for
multiple classification designs. Psychological Bulletin, 1957, 54,
134-137.

Vinacke, W. E., and Arkoff, A. An experimental study of coalitions in the
triad. American Sociplogical Review, 1957, 22, 406-414.

 

Vinacke, W. E. Sex roles in a three-person game. Sociometry, 1959, 22,
343—360.

 

Vinacke, W. E. The effect of cumulative score on coalition formation in
triads with various patterns of internal power. American Psychologist,
1959, 23, 381.

 

Vinacke, W. E., Crowell, Doris, Dien, Dora, and Young, Vera. The effect
of information about strategy on a three-person game. Behavioral
Science, 1966, 22, 180-189.

 

von Neumann, J., and Morgenstern, 0. Theory of game and economic behavior.
Princeton: Princeton University Press, 1944.

 

Winer, B. J. Statistical principles in experimentalfidesign. New York:
McGraw—Hill, 1962.

 

APPENDIX A

ANCILLARY RESULTS

Two types of results are presented in this section. First,
results that support some of the conclusions stated in the Discussion
section. These results usually contain no significant effects, or
if the effects are significant, they are of no consequence to the
problem being examined. These results will be examined under two
different headings: 1) the subject's perception of the experimental
situation; and 2) alternate explanations for the results obtained to
verify the experimental hypotheses. The second type of results pre-
sented are those that were obtained from data not directly related to
the hypotheses being tested.

Subject's perception of the experimental situation

How interesting and involvipg was the_game? In order to determine

 

if the subjects played the game in earnest, the subjects were asked the
following question on the post game questionnaire--How interesting and
involving was the game? The possible responses were listed on a four—
point scale and ranged from not very interesting 9; involving (scale

value of one) to very interesting and involving (scale value of four).

 

The mean response for all subjects was 3.113 and the standard deviation
in responses was .738. Only two subjects responded that the game was

not vegyginterestigg and involving. The average response was that the

 

game was quite interesting and ipyolvigg. A least squares analysis of

 

variance revealed no significant differences between the experimental
conditions in the responses to this question. The means and standard

deviations and the AOV summary table are presented in Tables 1 and 2.

79

Table 1.

80

Means, standard deviations, and Ns of

interest and involvement in the game

 

 

 

 

 

 

 

 

 

 

 

 

 

Bargaining sequence Single stage Multi-stage
Type of
ayoff
Statistics Play money Real money Play money Real money Overall
Mean 3.139 3.056 3.072 3.204 3.113
Std. dev. .683 .763 .773 .711 .738
N 36 54 69 54 213
Table 2. Analysis of variance of interest and
involvement in the game
Source of variance SS df Mean square F Significance
level
Bargaining sequence (A) .0842 .0842 .154 .70
Type of payoff (B) .0289 .0289 .053 .82
A x B .5805 .5805 1.059 .30
Error 114.5358 209 .5480
Total 115.2958 2128

 

aThe discrepancy between the total N of 213 for this analysis and
the overall N of 252 for the experiment is due to the fact that the first
few groups that were run either did not receive a post-game questionnaire

or received one with some questions omitted.

This explanation accounts

for the discrepancy in N in all analyses on individual subjects that did

not have 252 subjects.

81

How much trust in coalition partner? It was suggested in the
problem section that the conventional coalition paradigm engendered
a feeling of distrust or dissatisfaction in the coalition partners.

It was predicted that this distrust would result in a tendency to

break coalitions. Table 3 reveals that the SS/PM subjects (condition
most like conventional research paradigm) indicated they had the

least trust in their coalition partners. The AOV presented in

Table 4, however, shows that the SS/PM condition does not have
significantly less trust than the MS/PM condition; even though the
difference between the two conditions is in the hypothesized direction
and is almost significant at the .05 level. The main effect for type

of payoff is significant, with the real money groups reporting greater
trust than the play money groups. However, the interaction between
bargaining sequence and type of payoff is also significant. An examina-
tion of the means reveals that the interaction is produced by real money
causing an asymptotic level of trust. When play money is used, multi-
stage bargaining increases trust, but trust is increased by real money
to an asymptotic level at which multi—stage bargaining results in no
additional trust between coalition partners. This interpretation is
supported by the multiple comparison t values in Table 5.

How hard try to win game's payoff? In the real money condition,
the assumption underlying offering the winning players $9 in real
money was that such a payoff would increase the player's motivation
to win the game's payoff. In order to obtain some measure of the
effect of type of payoff on the participant's motivation, the subjects
were asked how hard they tried to win the game's payoff. Tables 6

and 7 reveal that the results do not support the expectation. The

82

Table 3. Means, standard deviations, and Ns for

amount of trust in initial coalition

 

 

 

 

 

 

 

 

 

 

Bargaining sequence Single stage Multi-stage
Type of
ayoff Play money Real money Play money Real money Overall

Statistics

Mean 2.167 3.722 2.980 3.622 3.190

Std. dev. 1.167 1.085 1.286 1.114 1.289

N 24 36 50 36 146
Table 4 . Analysis of variance of amount of trust in initial coalition

 

 

 

Source of variance SS df Mean square F Significance
level
Bargaining sequence (A) 4.3615 1 4.3615 3.146 .08*
Type of payoff (B) 41.4487 1 41.4487 29.899 (.0005***
A x B 7.1715 1 7.1715 5.173 .02**
Error 198.2382 143 1.3863
Total 242.6667 146

 

u:unlikely F value
7(very unlikely F value

xiv-x

extremely unlikely P value

83

Table 5. Multiple comparison t values for all pairs of means of
amount of trust in initial coalition

 

 

 

Means SS/PM SS/RM MS/PM critical ratio
Means
SS/RM 5.0128* 2.8304
MS/PM 2.7823 2.8837* p =.05
MS/RM 4.6905* .3603 2.4951

 

 

 

 

 

tc
bSignificant beyond .05 level

84

Table 6. Means, standard deviations, and N8 of how
hard subjects tried to win game's payoff

 

 

 

 

Bargaining sequence Single stage Multi-stage
Type of
payoff
Statistics Play money Real money Play money Real money Overall
Means 3.028 2.630 2.652 2.481 2.667
Std. dev. .878 .958 .937 .926 .940
N 36 54 69 54 213

 

 

 

 

 

 

Table 7. Analysis of variance of how hard subjects
tried to win game's payoff

 

 

 

Source of variance SS df Mean square F Significance
level
Bargaining sequence (A) 3.4589 1 3.4589 4.001 .05**
Type of payoff (B) 4.0800 1 4.0800 4.719 .03**
A x B .6523 1 .6523 .754 .39
Error 180.6985 209 .8646
Total 187.3333 212

 

7hr .
very unlikely F value

85

The play money subjects indicated they tried harder to win the game's
payoff than the real money subjects. The responses to this question,
therefore, do not support the assumption that real money increases the
player's motivation to win the game's payoff. A closer analysis of the
data reveals a possible explanation for this anomalous result. An investi—
gation of the individual responses to this question revealed that the players
who won the least money in the coalition, or who won no money at all,
indicated they did not try very hard to win the game's payoff. It appears
that in order to reduce any dissonance arising from not winning as much
money as desired, the players indicated they did not try very hard.
Evidently, reliable responses to this question can not be obtained

on a post—game questionnaire.

Suppect break first aggeement. As explained in the method section,

 

subjects were not informed that they would be allowed to break the initial
coalition and form subsequent coalitions until after the initial coalition
had been formed. If subjects suspected they would be allowed to break

the initial coalition it would very likely influence the type of coalition
and type of agreement they would make. The subjects were asked on the
post—game questionnaire if they had suspected initial agreements could be
broken prior to being informed. Forty—eight of the 213 subjects responding
answered the question yg_, In talking with the subjects after the eXperi-
ment it became very evident that a post—game questionnaire was not a good
place to ask this question. Subjects do not like to be duped or misinformed
in an experiment and are very reluctant to publicly admit they were

unaware of the full purpose of the experiment. Some subjects were, there—

fore, very reluctant to answer this question "no”. In addition, post—game

86

interrogation of the players revealed a strong tendency for the question
to be misinterpreted among the first subjects to participate in the
experiment. The subjects interpreted the question to be asking them if
they understood, at the time they were informed by the experimenter,

that they could break the first coalition. The question was, therefore,
reworded, however, subjects continued to respond quite often in the
affirmative, though the frequency of ygg responses did decrease. The
frequencies of yg§_and.p2_reSponses by experimental conditions are given
in Table 8 and the exact probabilities for each effect in the factorial
design are given in Table 9. The statistical tests reveal no differences
between experimental conditions in the responses to this question. The
difference between the overall number of yg§_andqgg responses was signifi—
cant.

Believe receive real money. A critical factor when offering real
money as a payoff in an experiment is convincing the subjects that they
will actually receive the money. Prior to being given the money,
subjects in the real money condition were asked if they believed they
would receive the money. Ninety-five of the 108 subjects in the real
'money condition responded affirmatively. The difference in ygg and 39
responses is significant beyond the .001 level. Tables 10 and 11 reveal
no differences between experimental conditions in the type of response
to this question.

Alternate explanations for results supportipgfiegperimental hypotheses

 

Amount of experience in playipg»coalition—bargaining,ggme. The

 

subjects playing the game a second time produced a distribution of
initial contacts and coalitions not significantly different from the

first game they played (Tables 12 and 13).

87

 

 

 

 

 

 

 

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88

Table 9. Factorial design exact probabilities for subject's
premature suspicion that initial coalition could be broken

 

 

 

Effect Exact probability
Bargaining sequence (A) fixed effect
Type of payoff (B) fixed effect
Subject's votes (C) fixed effect
DV ‘ SuSpect break (D) <,0001***
A x B fixed effect
A x C fixed effect
A x D .1379
B x C ' fixed effect
B x D .1421
C x D .1820
A x B x C fixed effect
A x B x D .7340
A x C x D .9118
B x C x D .8355
A x B x C x D .4625

 

ti . . . .
7”(extremely unlikely distribution

89

Table 10. Frequency of subjects in real money condition who
believed they would receive payoff in real money

 

 

 

      
 

 

 

Bargaining sequence Single stage Multi-stage
Subjects
votes 4 3 2 4 3 2 Totals
DV
Yes 16 15 16 15 16 17 95
No 2 3 2 3 2 1 13
Totals 18 18 18 18 18 18 108

 

 

 

 

Table 11. Factorial design exact probabilities for subjects in real money
condition who believed they would receive payoff in real money

 

 

Effect

Exact probability

 

Bargaining sequence (A)

Subjects' votes (B)

DV - believe receive real money (C)
A x B

A x C

B x C

A x B x C

fixed effect

fixed effect

< , OOO 1**7‘c

fixed effect

1.0000

1.0000

1.0000

 

eke . . . .
7 extremely unlikely distribution

 

90

 

 

 

 

 

 

 

 

 

Table 12. Exact probability test for independence between the initial
contact distribution in the single stage/real money groups
and the initial contact distribution in the repeat/single
stage/real money groups
Condition Repeat/ Single stage/ Exact
single stage/ real money Totals probability
Contactee real money
Greatest votes 7 18 25
.6128
Least votes 20 36 56
Totals 27 54 81
Table 13. Exact probability test for independence between the initial

coalition distribution in the single stage/real money groups
and the initial coalition distribution in the repeat/single
stage/real money groups

 

 

 

 

Condition Repeat/ Single stage/ Exact
single stage/ real money Totals probability
Coalitions real money

4-3 1 1 2

.2378
4-2 2 10 12
3-2 6 7 13
Totals 9 18 27

 

 

 

 

 

91

Differential_preference for_position around the game table. In order

 

to examine the effect of position upon initial contacts, an analysis was
done of the frequency with which each player contacted the person on

his left or the person on his right. In terms of Figure 1 (p.25 ) S3 is
S is on the left of 82’ and S

on the left of S is on the left of S3.

1’ l 2

Tables 14 and 15 reveal a significant interaction between bargaining
sequence, type of payoff, and subject's position at the table in the
frequency with which each player contacted the player on his left or
right. The interaction effect is localized in the single—stage/real
money condition where the players on the left and right chose each other
a disPrOportionate number of times. The difference in the number of times
the player on the left chose the other two players was significant at the
.03 level.

Initial coalitions were analyzed for a position effect by comparing
the frequency of left-right, left-center, and center-right coalitions,
In terms of Figure 1 (p.25 ) S1 is in the left position, 82 is in the

center position, and S is in the right position. Tables 16 and 17 reveal

3
no significant position effects for initial coalitions. However, the test
for the uniformity of the coalition distribution in the single stage/real
money condition is almost significant at the .05 level.

Position effects for division of the payoff and coalition stability
are not reported since they would be difficult to interpret due to con-
founding with other variables. In any case, there is no evidence of a
position effect for these dependent variables. An analysis of a position

effect on time taken to reach the first agreement yielded no significant

effects.

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one pouomucoo ummed Home :oHHB HoHa Hocookum .qH @Home

93

Table 15. Factorial design exact probabilities of each player's
contacts of the player on his left or the player on

 

 

 

his right
Effect Exact probability

Bargaining sequence (A) fixed effect
Type of payoff (B) fixed effect
Subject's position (C) fixed effect
DV--Position of contactee (D) .5618
A x B fixed effect
A x C fixed effect
A x D .5116

B x C fixed effect
B x D .6761

C x D .7928
A x B x C fixed effect
A x B x D .7980

A x C x D .2119

B x C x D .1839

A x B x C x D .0335**

 

“very unlikely distribution

Table 16.

94

Frequency of initial coalitions by position

 

 

 

 

 

 

Bargaining sequence Single stage Multi-stage

T e of payoff Play Real Play Real

money money money money Totals

Position
Left-center 12 4 8 6 30
Center-right 5 3 8 8 24
Left-right 7 11 8 4 30
Totals 24 18 24 18 84
Exact probability test
for uniformity of
column distribution .2524 .0566* 1.0000 .5613

 

 

 

 

 

 

t
'unlikely distribution

Table 17.

coalitions by position

Factorial design exact probabilities of initial

 

 

Effect

Exact probability

 

Bargaining sequence (A)

Type of payoff (B)

DV--Initial coalition by position (C)

fixed effect

fixed effect
.6762

fixed effect
.1365
.4031

.2263

 

95

In order to obtain more information about the effect of the players'
position on the coalition process further analyses were performed. An
investigation of the significant position effect for contacts in Table
14 suggested that the two players sitting across from each other at the
game table were choosing each other more often than by chance. There-
fore, an analysis was performed of the frequency with which the players
seated across from each other initially contacted each other. Tables 18
and 19 reveal a significant difference between the four eXperimental
conditions in the frequency with which the subjects sitting at the end
of the table choose the player seated across from them. The main differ—
ence lies in the single—stage/real money condition as it did with the
contacts analyzed in Table 14. In the single—stage/real money condition
the players chose the opponent sitting across from them 72% of the time.
There were no significant differences in the frequency with which players
chose the opponent across from them or not across from them in any of the
other three experimental conditions.

It is not sufficient to merely demonstrate a significant effect in
order to accept an alternate hypothesis. It must be shown that the effect
influenced the dependent variable being measured in the direction hypoth—
esized. If the subjects at the ends of the table contacted a player solely
because of eye contact of personal features then the results in the single-
stage/real money condition are not valid. On the other hand, if the play-
ers at the end of the table are first choosing on the basis of experimentally
provided variables (votes, random, equal power, etc.) and then using eye
contact and personal features to try and prematurely confirm their decision,

the coalition process is probably not significantly altered. The reason

96

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.wH mHsme

 

 

97

Table 19. Factorial design exact probabilities for choosing player

 

 

 

facing you

Effect Exact probability
Bargaining sequence (A) fixed effect
Type of payoff (B) fixed effect
Subject's position (C) fixed effect
DV - Position of Opponent (D) .6998
A x B fixed effect
A x C fixed effect
A x D .1223
B x C fixed effect
B x D .2129
C x D .4456
A x B x C fixed effect
A x B x D .0129***
A x C x D .5347
B x C x D .7604
A x B x C x D .5177

 

*
extremely unlikely distribution

98

it is possible for there to be no significant position effect and yet not
observe an equal distribution of contacts and coalitions is that the votes
were not assigned to each table position an equal number of times in the
single-stage/real money condition. Table 20 reveals that the player with
four votes was in the center position 61% of the time, three votes was in
the center position 28% of the time, and two votes was in the center posi—
tion 11% of the time. Thus, three votes and two votes were in the end
positions for most of the games. The exact probability of obtaining this
distribution of votes across positions was .0289. Table 21 shows that

the and positions at the table (left—right) were occupied by the 3—2 vote
pair 61% of the time, and by the 4-2 vote pair 28% of the time. The exact~
probability of obtaining this distribution is .0289. Thus, if the players
are choosing on the basis of votes, the most likely vote combination is
facing each other 61% of the time.

In order to determine if facing each other significantly affected the
results obtained in the single—stage/real money condition a control group
was run. In this control group the subjects could not see each other nor
know which player had how many votes until after they had indicated their
coalition partner preference. A comparison of the initial contacts and
initial coalitions obtained in the control group with the SS/RM group re-
vealed no statistically significant differences. (This data is presented

in the Results section.)

 

Differgnpiglgpgggggence for player's symbol names. An analysis of all
of the dependent variables failed to reveal any significant differences, or
any differences that approached significance, as a result of the label

assigned to the subjects.

99

Table 20. Distribution of votes by position around the game table and
the probability of observing the distribution obtained in
the single stage/real money condition

 

 

 

 

Votes Exact
Position 4 3 2 Totals probability
Left 4 7 7 18
Center 11 5 2 18 .0289
Right 3 6 9 18
Totals 18 18 18 54

 

 

 

 

 

 

Table 21. Distribution of pairs of votes by position around the game
table and the probability of observing the distribution
obtained in the single stage/real money condition

 

 

 

 

 

 

 

 

Votes Exact
Position 4-3 4-2 3-2 Totals probability
Left - center 9 6 3 18
Center - right 7 7 4 18 .0289
Left - right 2 5 11 18
Totals 18 18 18 54

 

 

 

 

100

Differential preference as a result of preliminary bargaining order.
The three players in the coalition—bargaining game participated in a
preliminary contact round in the multi-stage condition. The six possible
orders in which the pairs of three players could bargain were counter-
balanced. If there was a primary or recency effect due to this prelim—
inary bargaining order then it would not be too surprising to obtain a
somewhat equally distributed set of coalitions. The initial contacts
made by the multi-stage subjects were analyzed according to a subject's
preference for the first or second opponent he bargained with. Tables 22
and 23 reveal no significant differences in initial contacts due to
preliminary bargaining order.

An analysis of initial coalitions formed according to position in the
bargaining order yielded no significant differences between the three
bargaining orders. (Tables 24 and 25).

The analyses of the effect of preliminary bargaining order upon
payoff division, stability, and time to reach first agreement yielded
no significant differences.

Difference in player's previous experience in playing competitive
games. If there were differences between the four experimental conditions
in the experience the subjects had in playing competitive games, it might
confound the interpretation of the results. Tables 26 and 27 reveal no
difference between the experimental conditions in the experience subjects
had in playing competitive games.

Agtgrnate hypothesis 9: value of 9. Two different measures were

 

used of the value of $9 to the real money subjects. One measure was the

economic value of $9 as indicated on a six point scale ranging from very

101

 

 

 

 

    
  

 

 

 

 

 

 

GOHuanuuch nESHoo mo
oooo.H meNH. mesa sou Ho muHEHomHas
wow quu huHHHowHoum oomxm
oNH o o o o o o o w w w m w w w w mHmuoH
HN e N N N m a H m m a N a m s N Hqu eweHmems
Homde vacuum
mm N m a m H N m m m a H a m s H euHs emeHamums
HohmHa umuHm
mononucoo
mHmHOH m e N m a m a N m e N m a m a mooo>
m.ooomnsm
. . . . . . :oHuHmoa
m N m H N H m N m H N H mchHmemn muoonnsm
1
memos Hmmm moses mmHm Hmommd Ho mama

 

 

 

 

pesos mumaHaHHoum use oH LHHe pmaHmmHmn unusedmo
pcooom no omHHH ego wouumusoo GOHqucoo owmumcHuHsa cH mm :oHse HUHe zoomsvoum .NN oHomH

102

Table 23. Factorial design exact probabilities of contacting
first or second Opponent bargained with in preliminary
round of multi-stage condition

 

 

 

Effect Exact probability
Type of payoff (A) fixed effect
Subjects bargaining position (B) fixed effect
Subject's votes (C) fixed effect
DV--Contactee by bargaining (D) .1812
A x B fixed effect
A x C fixed effect
A x D .4682
B x C fixed effect
B x D .7105
C x D .8543
A x B x C fixed effect
A x B x D .5918
A x C x D .2240
B x C x D .8094
A x B x C x D .0970*

 

7"'unlikely distribution

 

103

Table 24. Frequency of initial coalitions in multi-stage condition
according to preliminary bargaining order

 

 

 

 

 

 

 

Type of payoff Play money Real money
Bargaining
order 1 2 3 1 2 3 Totals
Coalitions
4-3 0 1 0 l 1 2 5
4u2 O 1 6 3 2 2 14
3-2 5 5 6 2 4 1 23
Totals 5 7 12 6 7 5 42
Exact probability test
for uniformity of
distribution of '2524 '9557
column sums

 

 

 

 

Table 25. Factorial design exact probabilities of forming initial
coalition according to preliminary bargaining order in
multi-stage condition

 

 

 

Effect Exact probability
Type of payoff (A) fixed effect
Bargaining order (B) .5462
DV - Initial coalition (C) not relevant
A x B .3582
A x C .1094
B x C .6289

A x B x C .2090

 

 

Table 26.

104 '

subjects played competitive games

Means, standard deviations, and Ns of how often

 

 

 

 

 

 

 

 

 

 

 

 

Bargaining sequence Single stage Multi-stage
Type of
payoff Play money Real money Play money Real money

Statistics

Mean 4.028 3.704 3.652 3.741

Std. dev. 1.920 1.598 1.705 1.417

N 36 54 69 54

Table 27. Analysis of variance of how often subjects
played competitive games
Source of variance SS df Mean square F Significance
value

Bargaining sequence (A) 1.4454 1 1.4454 .532 .47
Type of payoff (B) .6993 1 .6993 .257 .61
A x B 2.1470 1 2.1470 .790
Error 568.2540 209 2.7189
Total 571.8122 212

 

 

105

little money (scale value of one) to §_very lot pf_money (scale value of

 

six). The second scale was a measure of how much the subject needed all,
or part, of the $9 as of the day of the experiment. The subject's re-
sponse to this question recorded on a six point scale ranging from very

little need (scale value of one) to g_very lot of need (scale value of

 

six). Table 28 and 29 indicate that there were no significant differences
between the multi—stage/play money and multi—stage/real money conditions
for either of these measures of the value of $9 to the subjects. There

is a slight tendency for the multi—stage/real money subjects to indicate

a greater need for the money than the single~stage/real money subjects,
however, since there were no observed differences in the dependent variable
between these two conditions it is of little consequence.

Conjunctive results of interest.

 

Distgibution of final coalitions. There were no significant differences

 

between the experimental conditions in the distribution of final coali-
tions or in the division of the payoff in the final coalition.

éyerage npmber of messages sent between coalition pgrtners. In the

 

second phase of the coalition game the Ss communicated by means of written
messages. The player excluded from the coalition made written offers to

the coalition partners who either accepted or rejected the offers. In
addition, the coalition partners could send messages to each other encour—
aging their partner to either maintain or break their agreement. An
analysis of the average frequency with which these messages were sent per
agreement reveals a significant difference between the two bargaining
sequence levels as well as between the two payoff levels (Tables 30 and 31).

A greater number of messages were sent in the multi-stage condition than

 

106

Table 28. t test of mean difference between single stage/real
money condition and multi-stage/real money condition
in value of $9.00

 

 

     
 

 

Conditions Single stage/ Multi-stage/ t value
Statistics real money real money
Mean 3.2593 3.3148 .3248
Std. dev. .9749 .7727 df I 106
N 54 54 p >.50

 

 

 

 

 

Table 29. t test of mean difference between single stage/real
money condition and multi-stage/real money condition
in need for $9.00

 

 

 

Conditions Single stage/ Mhlti-stage/ t value
Statistics real money real money
Mean 2.5926 3.0185 1.9214*
Std. dev. .9421 1.3102 df = 106
N 54 54 .05<p<.10

 

 

 

 

*unlikely t value

107

Table 30. Means, standard deviations, and Ns for the average number

of messages sent between coalition partners per agreement

 

 

 

 

 

 

 

 

 

 

Bargaining sequence Single stage Multi-stage
Type of
payoff Play money Real money Play money Real money

Statistics

Means 2.2779 3.4178 2.9925 4.8706

Std. dev. 2.6917 1.9861 2.8557 2.1117

N 24 18 24 18
Table 31. Analysis of variance of average number of messages sent

between coalition partners per agreement

 

 

 

Source of variance SS df Mean square F Significance
value

Bargaining sequence (A) 24.1583 1 24.1583 3.888 .05**

Type of payoff (B) 46.8402 1 46.8402 7.539 .007***

A x B 2.8025 1 2.8025 .451 .50

Error 497.0718 80 6.2134

Total 569.0347 83

 

M‘very unlikely F value
*extremely unlikely F value

108

in single stage condition, and a greater number of messages were sent in
the real money condition than in the play money condition. Table 32 re-
veals that the number of messages sent between coalition partners was
significantly correlated with the amount of stability in the coalition
process.

Player who speaks first in the initial coalition round. Previous
research has suggested that the initiator of the negotiations has some
added advantage in the situation (Vinacke and Arkoff, 1957; and Chertkoff,
1966). One measure of this fact would be if the player who spoke first
in the initial coalition round received a larger share of the payoff more
often than the player who spoke second. Tables 33 and 34 reveal that even
though there is a slight tendency for the player speaking first to receive
the largest share of the payoff in the play money condition, it is not a
statistically significant difference (p - .1333).

Playgr_who breaks initial coalition. An investigation was made of
the relationship between the player who breaks the initial coalition and
l) the number of votes he possessed; and 2) the proportion of the pay-
off he received. Tables 35 and 36 show that there was a significant dif-
ference in the proportion of initial coalitions broken by the player with
4 votes, 3 votes, and 2 votes. The player with 2 votes broke his initial
coalition 72% of the time, and 3—vote player broke his 31% of the time,
and the 4—vote player broke his initial coalition 27% of the time.

It was also the case that the player with the lesser amount of money
in the initial coalition broke the coalition significantly more often
than the player with either an equal or greater amount of money than his

partner (Tables 37 and 38).

 

109

 

osHm> H hHoxHch huo>

when

 

 

em wH qN wH qN z
and. BON.: xxHNo. mmo.n «room. meHuoonou owmuo><
xamNm. oao.- easem. omo. aamwm. neosoauwm
HmcHH CH mono:
NHHHHHmHm
H HHmHo>o kudos Hmmm kudos mmHm hocoe Hmmm mecca zmHm Hwommm
we make

 

 

 

 

owmumnHuHaz

 

owmum meaHm

mocoswom maHuswumm

 

 

 

onHHowum HuHB muocuumm cOHuHHmoo
coozoon noon wowmmmos Ho Honesc mmmum>m mo cOHumHouuoo

.Nm uHHmH

110

 

 

 

 

 

A
meH m NH m wH oH wH HH qH HH HN q wH mHmooa
HN N o H o m NH 0 N m m N HH pcoomm
NN H o N NH m o m N 0 NH N N omHHm
umpuo
mHmHOH A n v A H v A u v A u v wcmemam
coHouoaoum
Hmommm
choe Hmom Nocoe NmHm Noeoe Hmom choe NmHm Hmozma Ho maze

 

 

 

 

mwmumuHanz

 

mmmum onch

 

oocmsvom wchHmmHmm

 

 

mmomma mHu Ho mumHm ommwumH oHu pm>HmooH mGOHomHoowoo
coHoHHmoo HwHoHeH cH omHHm oxoam 0:3 uonHa HUHLB LHHB Nosesvoum .mm mHHmH

111

Table 34. Factorial design exact probabilities of whether player
who spoke first in initial coalition negotiations
received the largest share of the payoff

 

 

 

 

Effect Exact probability
Bargaining sequence (A) fixed effect
Type of payoff (B) fixed effect
Subject's proportion of payoff (C) not relevant
DV - speaking order (D) 1.0000
A x B fixed effect
A x C not relevant
A x D not relevant
B x C not relevant
B x D not relevant
C x D .2739
A x B x C not relevant
A x B x D not relevant
A x C x D .9077
B X C x D .1333

A x B x C X D 1.0000

 

112

 

 

 

 

om e m H oH HH m m N m wH oH m Hmuoa
mq N H H m w m N H N m NH m amHouo ooz
me N N 0 HH m N m H H mH a H coxoum
:oHoHHmoo
wHwHoe N m a N m s N m a N m s mmuo> HmHUHaH
m.oomnnsm
Nmeoe Hmom Nocoe NmHm choe Hmom Nance NmHm Hmommm mo maze

 

 

 

 

owmumuHuHaz

 

owmum onch

 

mocmsvom wchHmwumm

 

 

coHuHHmoo HmHuHaH oxoun mHmNmHa HmspH>HpaH :oHs3 HHH3 Nocoovoum .mm oHHMH

 

113

Table 36. Factorial design exact probabilities for
players who broke initial coalition

 

 

Effect Exact probability
Bargaining sequence (A) fixed effect
Type of payoff (B) fixed effect
Subject's votes (C) fixed effect
DV - Initial coalition breakage (D) not relevant
A x B fixed effect
A x C fixed effect
A x D fixed effect
B x C fixed effect
B x D fixed effect
C x D ,0003***
A x B x C fixed effect
A x B x D 4 not relevant
A x C x D .5534
B x C x D .1616
A x B x C x D 1.0000

 

extremely unlikely distribution

114

Table 37. Frequency with which individual players broke the initial coalition
according to the prOportion of the payoff they received (data only
for initial coalitions that were broken)

 

 

Bargaining sequence

Single stage

Multi-stage

 

    

 

 

 

 

Play money Real money Play money, Real money Totals
proportion
Less than partner 14 3 9 3 29
Equal to partner 2 2 2 1 7
More than partner 4 0 5 0 9
Totals 20 5 16 4 W 45

 

 

 

 

 

 

Table 38. Factorial design exact probabilities for individual players who broke
the initial coalition according to the prOportion of the payoff they
received (data only for initial coalitions that were broken)

 

 

Effect

Exact probability

 

Bargaining sequence (A)

Type of payoff (B)

Proportion of initial payoff received (C)

A x B x C

fixed

fixed

fixed

effect

effect

. 000 19:9”?

effect

.9047

.1052

1.0000

 

7‘c 7'?) . . . .
cextremely unlikely distribution

 

115

Players in final coalition. An analysis of the players in the final

 

coalition revealed no significant relationship between being a member of

the initial coalition and being a member of the final coalition.

 

 

 

APPENDIX B

COALITION—BARGAINING GAME INSTRUCTIONS

[time]

You are here [today

. to artici ate in a com etitive ame. If
tonith p p p g

this game does not take the full hour, I have a second non-competitive
game, in which you each play by yourself and not against each other, to
fill out the hour. The first game is a test of your bargaining and game
playing skills. During this game each of you should endeavor to win as
much of the game's payoff as possible and let the other players take care

of themselves. In other words, it is every man for himself.

 

In order to prevent personal characteristics from affecting the game,
I am going to give each of you a nonsense symbol. I would like for you
to refer to each other throughout the game in terms of these nonsense

symbols instead of by name, position around the table, hair color, etc.

 

 

That is:
The player on my left will be - - -/ l.
The player in the center will be - - -/
The player on my right will be — — —/ .

 

In this game you will each begin with a certain number of votes. The
number of votes you begin with is determined by which of these envelopes
you draw. [Show them (3) envelopes.] There are various numbers of votes
in each envelope. Each of you draw an envelope (any S order). Take out
the card inside, and as I call on you announce out loud how many votes you

have in the game. At the same time, each of you record your own label

 

lBlank spaces were filled in with the symbol name of the appropriate
player.

117

 

 

118

and number of votes; and your Opponent's labels and numbers of votes on
this sheet. [Record sheet——E write on Summary Sheet-~Repeat numbers out
loud.] Now put the cards back in the envelOpes and give the envelopes

to me. [Put envelopes back on hook] As you can see, there is a total
of.9 votes in this game—~your job is to find a means for obtaining control

over a majority of these votes (i.e., 5 votes or more), and thereby win

the payoff which is [I9 in real money]

$900 in play money (Put up clip board with card

$9
that has [£90

all players have less than 1/2 the total votes in the game (i.e., no

é} on it). Presently, you are all in the same predicament——

player has a majority of the votes); therefore, no single player can win

 

the [E309] by himself. However, if any two of you would form an alliance

and pool your voting power, that pair would control a majority of the votes

in the game and would receive the [$309] . Therefore, the basic rule of

this game is that in order to win any money, some two of you must form an

. $9
alliance. Thelégo

proportion they like. However. the goal for each of you in this game is

é] may be split by the alliance partners in any way or

to obtain as much of the ‘é30é1 as possible. In order to achieve this
goal you must try to be a member of that alliance in which you can maximize

’$9
your share of the [$900

The only condition for declaring that an alliance has been formed

$90

and that it will receive the lfg é] is that some two players mutually agree
on how to split [%9 él . If no alliance forms you all lose.

$90

Any Questions?

 

Examples:
(1) three political candidates——no majority-—pool votes and control

nomination, thereby dividing rewards.

 

 

 

119

(2) three board members of a company voting their shares on the
issue of bonuses for board members. No majority—~two pool
their votes and control distribution of bonuses——splitting
as they like.
In other words, I am referring to a situation in which no single individual
has the power to control the outcome but two people by pooling their
resources can jointly determine the outcome.
Remember, your goal in this game is to be a member of that two party
alliance which will maximize your share of the $900.
You should strive to achieve this goal because the amount of money
each of you wins in this game will be compared with the amount of money
won by each previous player in this experiment who started out with the
same number of votes as you in order to see if you are the current CHAMPION
in your group. That is, (ZEJ, VAF, YOV) ————— .
In other words, you are competing with previous players who started
the game under the same condition as you, as well as competing against
each other in this game to see who will be the winner in this game.

Any Opestions?

 

You will use the following procedure in order to decide which two

players will form an alliance.

 

 

 

 

 

120

Multi-stage2

 

You will begin by each pair (: : :) of you participating in prelim—
inary negotiations for periods of two minutes each. These negotiations are
only for the purpose of discussing possible terms for splitting the $900
and no final agreement can be made during this time. During these negoti—
ations you may make preliminary offers and probe the other player about
his possible terms for agreement, but offers and statements made during
this period are not binding and do not have to be honored. This round
(of;preliminary bargaining is designed strictly for the purpose of allow-

ing each of you to assess the bargaining strategy, offers, and expectations

 

of your opponents, before deciding which player you would like to form
an alliance with.

After all pairs have finished preliminary negotiations you will each
indicate on a secret ballot the symbol name of the player you prefer to
form an alliance with an the two players who first select each other will
be allowed to negotiate the final terms for splitting $900. You can re—
cord information about your preliminary negotiations on the bottom half
of your record sheet. This record sheet is just for your convenience, and
you are not obligated by anything you record on it. Take your record
sheet with you when you leave the room. You may now proceed-—remember you
are to discuss how you will divide [$308] . [Third player leaves] Do not'
begin until I get back.

You have two minutes to verbally discuss possible terms for forming

$90

agreement. I will inform you when you have thirty seconds remaining.

an alliance and splitting the {?9 é] . Remember you can not make a final

-——————-—-—.-—-——_

This section is used for multi-stage bargaining conditions only.

121

[time]
[Pair 1]

Now if will change places with , the

 

next pair will have preliminary negotiations.
[Pair 2]
Repeat above statement.

[Pair 3]

 

122

‘3
Single stageJ

 

Each of you will write on this slip of paper [choice form] the symbol
of that player with whom you would like to form an alliance, without letting
the other players see your choice, and pass it through the slot in the
divider to me. This selection procedure will be continued until two of
you select each other, or in the event none of you ever select each other—-
until the hour is up. The first two of you to select each other will then
attempt to negotiate a final agreement on how to split the [$900] . If
no agreement is reached by the two players who first select each other,
the process of choosing and negotiating will be repeated until an agree-
ment is reached or the time is up. In the event an explicit agreement is
reached by some two players, I will declare an alliance formed by those
two players and distribute the money according to the terms of their

agreement.

Any Questions?

 

O.K. Write the symbol of that player whom you would like to form
an alliance with on the second line of this sheet of paper and pass it
to me through the slot in the divider in front of you. I will inform

you when two of you have selected each other.

 

3 . . . . . . . .
This section is used for Single—stage bargaining conditions and
multi-stage bargaining conditions.

123

[Negotiations]

& have selected each other and will

 

 

have up to three minutes to verbally negotiate the final terms of an
agreement. If they cannot come to an agreement in three minutes, the
process of selecting and negotiating will be repeated. If they reach a

mutually acceptable agreement within three minutes, the two of them will

win the total [$302] ; and it will be Split according to their agreement.

out into the hall

If Wlll go into the other room

negotiations will begin.

 

However, & , please wait for me to return
before you start negotiations.

[third player leaves]

[time]

In the event the two of you come to an agreement, I would like for
you to let me know by filling out this form [agreement contract] and
passing it to me through the slot in the divider. [Explain how to fill
it out] It makes no difference who fills it out, but both of you must
sign it with your symbols if you reach an agreement in order for the agree-
ment to be valid. You will have up to three minutes to negotiate verbally
with each other and get the signed contract to me if you reach an agree-
ment. If I have not received a signed contract when three minutes is
up, I will declare that no agreement was reached and the other player will
return and we will repeat the process of selecting and negotiating. I
will tell you if and when you have one minute left.

Apy Questions?

 

Begin! [Negotiate]

& reached an agreement.

 

 

 

gets $ and gets 3

 

 

 

124

Now I would like for each of you to write the terms of this agree—
ment in the first section of this form. [Agreement form]

[Put up divider]
genial

did not win any money in this game, but we are going

 

to give him a chance to win some money. will be allowed

 

to make two written counter-offers proposing a new alliance with himself

to each of the alliance partners-—( & ).

 

 

If can induce either or

 

 

 

to break their existing agreement, then a new alliance between

 

and his new partner would replace the present alliance. In this event the

existing agreement between & would be VOID,

 

 

and the money would be redistributed according to the new alliance agree-

 

 

 

ment. However, if either or breaks their
existing alliance, whey will cause a penaltv of [2100] on the game, leaving
only 1:309] . This means that any offers makes to one of
the alliance partners must be based on how much of [:30é} he will give

his new partner if he breaks his present agreement and forms a new alliance

with . If a new alliance is

 

formed, then the player from the previous alliance who is not a member of
the new alliance loses all of his money from the previous agreement; but
he is then allowed to make counter-offers to the new alliance partner.

$70

However, his offers must be based on how much of [?7 é] he will give to a
player to ally with him, since I will assess a penalty of [7

$100] each time

an alliance agreement is broken. Remember, if an alliance breaks the

alliance partners receive no money——there is no accumulation of money from

 

 

 

125

one alliance to the next.
The game is over when either:
(1) all of the money is gone, or
(2) two alliance partner both reject two offers made to them by
the excluded player

Any Qpestions?

 

Here are some rule cards for you to refer to during this part of the
game.

Rules of the Game

 

1. NO TALKING-—all messages or offers to each other or to the

 

 

experimenter are to be made in writing and passed through the
slots in the divider.

2. The excluded player may make two, and only two, offers to each
of the alliance partners, but he may not send another offer
until he had received a reply to his present offer. [This means
one offer at a time, but the offers can be made in any order
(1111, 121, 112, 211, etc.)]

3. The alliance partners may either accept or reject an offer from
the excluded player, and they may include counter—offers or
other comments in their reply. The alliance partners may not
initiate offers or messages to the excluded player.

4. The alliance partners may initiate messages to each other
but these messages may refer only to maintaining or breaking
their present agreement. The messages may not be offers to

change the terms of the present agreement.

 

 

126

5. All messages are to be sent on the appropriate forms. A reply
must be made on the same form it was received on.

6. You have a maximum of two minutes to send or reply to an offer.

This means you need to—-

1. Keep your messages short—-Money speaks louder than words
anyway. If you are taking too much time to send or reply
to an offer, I will send you a notice saying you have thirty
seconds to act. If you do not send or respond to an offer
within those thirty seconds, the offer is void and is consid-

ered to be rejected.

 

In addition--

2. Save all messages and offers

3. Illegal offers or messages will be marked illegal and re—
turned to you with an explanation.

Any Questions?

 

4. The excluded players should realize that the number of votes
is no longer the basis for making an offer to a player, in-
lstead, his offers should be related to the amount of money a
player has in his present agreement.

5. During this part of the game, you should all take into account
the fact that the noise of writing and passing messages gives
your opponents some information about the number of messages
sent.

Remember, the object of the game is to win as much money as possible.

The game is over when either:
(1) all the money is gone;
or (2) each of the alliance partners reject two messages from the

excluded player.

 

 

127

As I said previously,

has no money in the game so

 

he will be allowed to make offers to

and

 

 

based on how much of $800 he will give one of them to form a new alliance

with him. If and

 

maintain their agreement,

 

will have 3

 

and

will have $

 

You may all begin to send messages according to the rules of the game.

All messages will be sent on this form [offer form] and passed to me

through the slots in the bottom of the divider.

I will check the messages

to see that they are legal, and if they are O.K. I will deliver them to

the intended player.

[time]

Statement to be read if an agreement breaks

 

All right, we have a new agreement.

 

agreement on your agreement form. In
$__ , and get $
Now has no money

 

to make offers to and

 

of $ he will give one of them

If and

Will you write the terms of this

this agreement gets

 

in the game, so he will be allowed

based on how much

 

to form a new alliance with him.

maintain their agreement then the

 

 

game is over and will

 

will have $

have $ and

 

You may now send offers and messages again.

 

-.—

[Repeat above, if necessary, after each agreement breaks.]

 

 

 

APPENDIX C

COALITION-BARGAINING GAME FORMS

Player's Record Sheet

1.

2% Hmvmw Hm

 

wmoona mummn

 

 

Onrmwlwpmwmwm

rmvmw

 

 

meHHSHDmnw 2mm0nwmnwosm

szONHmeosm awn:

 

 

H rm<m m <0nmm.

 

20. OH <o~mm

 

 

 

 

ooaamsnm

Preliminary negotiation section omitted for single stage condition.

Note

129

130

2. Initial contact form

 

 

From:

 

I would like to form an alliance

with:

 

 

3. Agreement contract

 

 

Agreement contract

The $ will be

divided as follows:

 

 

 

 

 

 

$ for
$ for
Signed:

 

and

 

 

 

131

4. Record of agreements

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

My label is
Total Amount of Alliance Amount of Money Agreement Status
Money Divided Partners for each player Maintained Broken
$ $
and and
$
$ $
and and
$
$ $
and and
$___
$ $
and and
$
$ $
and and
$

 

 

 

 

U)
{I}

 

and and

 

 

 

—-o--—————-—-.——~-—o—--——_——~--_———-— —-——_— .—_—-—_—--———-——-———_—_-——_-—n-—--——-

132

5. Communication form

 

 

From:

 

To:

I will give you $

 

 

and keep $ for myself.

 

Comments:

Reject

Accept

 

 

 

APPENDIX D

PLAYER'S RULE CARDS

 

 

 

Rules of the Game

 

1.

NO TALKING--all messages or offers to each other or to the

 

experimenter are to be made in writing and passed through the
slots in the divider.

The excluded player may make two, and only two, offers to each
of the alliance partners, but he may not send another offer
until he had received a reply to his present offer. [This means
one offer at a time, but the offers can be made in any order
(1111, 121, 112, 211, etc.)]

The alliance partners may either accept or reject an offer from
the excluded player, and they may include counter-offers or
other comments in their reply. The alliance partners may not

'initiate offers or messages to the excluded player.

The alliance partners may initiate messages to each other but
these messages may refer only to maintaining or breaking their
present agreement. The messages may not be offers to change
the terms of the present agreement.

All messages are to be sent on the appropriate forms. A reply
must be made on the same form it was received on.

You have a maximum of two minutes to send or reply to an offer.

 

134

 

 

 

 

APPENDIX E

POST-GAME QUESTIONNAIRE

1. Play money form
POST GAME QUESTIONNAIRE
Did you know any of the other players in this experiment before
coming to the experiment? Yes No
Did you know anything about this experiment before you came here
today? Yes No

If yes, what?

Have you participated in any other experiments similar to this
experiment? Yes No

If yes, briefly describe the other experiment.

How hard did you try to win as much money as possible?

I_ l l 1 I

not very somewhat quite very
hard hard hard hard

How interesting and involving was the game?

.L 1 l J

not very somewhat quite very interesting
interesting and involving
and involving

How often have you played a card game, parlor game, game of chance,

etc., in the last six months?

1 J _ J l J

very quite seldom often quite very
seldom seldom often often

During the first part of the game, before the first agreement was
made did you expect that the first agreement would be allowed to break

and new alliances be allowed to form? Yes No

If yes, why did you think this?

136

 

137

8. When each of you indicated by "secret ballot” whom you would like to

form an alliance with, why did you choose the player you selected?

9. If you were one of the partners in the first alliance, how much trust
or confidence did you have in your partner that he would not break the

first agreement?

1. 1 L1 1 I

very little little some quite a very much
trust or bit trust or
confidence confidence

10. As a goal, how important was it to you that you have the highest
winnings in your category, when compared with previous players who began

the game under the same conditions as you?

L 1 J L l 1 I

very quite somefihat 'somewfiaf' quite very
unimportant unimportant unimportant important important important

11. As a goal, how important was it to you that you be the winner of this

game irregardless of how you compared with previous players?

L l l J L 1 i

very quite somewhat somewhat quite very
unimportant' unimportant unimportant important important important

12. If you were playing for real money, would you have played the game
differently? Yes No

If yes, in what way?

13. If you could play the game again, what strategy would you use in order
to win the most money?
14. If you have any further criticisms or evaluations of this experiment,

please write them below.

 

   

2. Real money form
POST GAME 'QUES’I‘IOI'CNAIRE
Did you know any of the other players in this experiment before
coming to the experiment? Yes _ No ____~‘_
Did you know anything about this experiment before you came here
today? Yes No

If yes, what?

Have you participated in any other eXperiments similar to this

experiment? Yes No

—— mum-’0

 

If yes, briefly describe the other experiment.

How hard did you try to win as much money as possible?

L_ J I _1

not very somewhat quite very
hard hard hard hard

How interesting and involving was the game?

L 1 I d J

not very somewhat quite very interesting
interesting and involving
and involving

How often have you played a card game, parlor game, game of chance,
etc., in the last six months?

1i__ i J 1 I

very quite seldom often quite very
seldom seldom often often

During the first part of the game, before the first agreement was

made did you expect that the first agreement would be allowed to break

and new allf uses be alloyed to form? Yes NO

If yes, why did you think this?

138

 

8. When each of you indicated my secret ballot" whom you would like to

form an alliance with, why did you choose the player you selected?

9. If you were one of the partners in the first alliance, how much trust
or confidence did you have in your partner that he would not break the

first agreement?

L l L L l i

very little little some quite a very much
trust or bit trust or
confidence confidence

10. As a goal, how important was it to you that you have the highest
winnings in your category, when compared with previous players who began

the game under the same conditions as you?

L 1 l L l I !

vefy quite somewhat 'sfimewfiat quite very
unimportant unimportant unimportant important important important

11. As a goal, how important was it to you that you be the winner of this

game irregardless of how you compared with previous players?

1_ I l l L 1-,-_____J

very quite somewhat somewhat quite very
unimportant unimportant unimportant important important important

 

12, During the game did you believe that you would be given the amount you
won in real money? Yes No

;If no, why not?

13. If you could play the game again, what strategy would you use in order
to win the most money?
14. If you have any further criticisms or evaluations of this experiment,

please write them below.

139

 

 

15.

16.

17.

What is the value to you of the total amount

of money in this game?

i l.

 

very little some quite a
little money money bit of
money money

As of today, how much did you need to win as

in this game:

a lot a very lot
of of money
money

much money as possible

 

very little some quite a a lot a very lot
little need need bit of of of need
need need

What is the approximate annual income of your parents?

What is your approximate annual income?

140

 

 

 

 

APPENDIX F

EXPERIMENTER'S RECORD SHEET

I42

 

 

 

 

 

 

 

 

 

Time:
Group
Date
Condition
Table Position:
Preliminary Round (Time: )
Pair Preliminary agreement Initiator Explicitness
l.
2.
3.
lggreement Round (Time: )
Choices Pair Agreement Time Initiator
l.
2.
3.
4.
5.

Stability (Time: )

 

Isolate Amount Amount Offer Amount Accept (A)

Kept

Pot

To

of Offer

Reject (R)

 

\9
0

10.

ll.

12.

I3.

14.

l43

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

lldillJllllljlllulllljlfllllHMIWIH

9