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This is to certify that the
dissertation entitled

WELFARE IMPACTS OF SPECTRUM GOVERNANCE
REGIMES: AN ECONOMIC-ENGINEERING STUDY

presented by

Yl-FENG CAROL TING

has been accepted towards fulfillment
of the requirements for the

PhD. degree in Media and Information Studies

 

 

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2/05 m/CITaC/omoomm-ms

WELFARE IMPACTS OF SPECTRUM GOVERNANCE
REGIMES: AN ECONOMIC-ENGINEERING STUDY

By.

Yi-Feng Carol Ting

A DISSERATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY

Department of Telecommunication, Information Studies and Media

2005

ABSTRACT

WELFARE IMPACTS OF SPECTRUM GOVERNANCE REGIMES: AN
ECONOMIC-ENGINEERIN G STUDY

By

Yi-Feng Carol Ting
In spite of the overwhelming victory of the market system around the world, the
administrative licensing regime has been the dominant paradigm for spectrum
governance until now. Behind this seeming anachronism is the belief that mutual
interference can only be mitigated by means of administrative licensing and tight control.
However, this once dominant perspective has faced increasing challenges recently.
Mounting evidence of the inefficiencies under the administrative licensing regime has
received much attention and a consensus for reform has formed among industry players,

policymakers and scholars.

Notwithstanding the consensus for reform, proponents of spectrum policy reform are
divided over two approaches: spectrum property rights and spectrum commons. Property
rights proponents advocate the free market approach and call for privatization of
spectrum. To the contrary, commons supporters argue against spectrum ownership and
private control of the airwaves, championing the idea of open access to spectrum for the
public. Although the intense policy debate between proponents for spectrum property
rights and spectrum commons has been ongoing since the late 1990’s, the arguments
from both sides have been highly abstract and speculative. Through economic modeling
of the characteristics of different governance regimes and network structures, this study

provides a side-by-side comparisons of welfare outcomes under different regulatory and

technological settings. Such comparisons allow us to more systematically evaluate the

merits of competing regimes.

This study identifies three key policy instruments for spectrum governance regimes: entry
conditions, transmission power and interference robustness stipulations. Based on these
key policy instruments, the study builds a general model of demand for wireless services
that reflects the engineering properties of wireless communications and the impact of
these policy instruments. Since regimes differ in the configuration of policy. instruments,
the model allows us to analyze the decisions of firms and consequent welfare outcomes

under various regimes.

The analysis of welfare outcomes produces the following findings. First, government
regulation on robustness is undesirable. Second, the potential benefit of power
restrictions increases with the number of firms in the market. Third, when set
inadequately, all three policy instruments can cause significant welfare loss. Moreover,
comparison of a prototype property rights regime and a prototype commons regime
suggests, given the same power restrictions, the property rights regime tends to
outperform the commons regime as long as the number of firms is not significantly
smaller (in relative terms) than the optimal number of firms, which itself is a small
fraction of the open commons equilibrium number of firms. These observations on the
effect of fundamental policy instruments and the theoretical framework are the major

contribution of this study.

ACKNOWLEDGMENTS

I am tremendously indebted to my advisor, Professor Steven Wildman. Steve has been a
wonderful teacher and good friend and has enriched my life in many ways. Without his
support, understanding and patience, this dissertation would not be possible. The work
with this dissertation has been trying, and Steve has always been there to listen and give
advice. His clear thinking and commitment to scholarship are inspiring. It’s a great
privilege to have such a good teacher and good friend.

I am also very grateful to my co-advisor, Professor Johannes Bauer for his guidance. I
have benefited enormously from his broad knowledge and intellectual perspectives.
Working with Johannes has been a great learning experience for me. I have learned a lot
from his systematic approach and creative thinking. His friendship and support are much
appreciated.

Besides my advisors, I want to thank my committee members, Professors Barry Litman
and Stephen Lacy for their helpful comments and advice.

Finally, I want to thank my family for their support. A special thanks goes to my
nephew, Sidney, who can make me burst out laughing no matter what a bad day I had. I
appreciate his company during my last month working on the dissertation. In spite of
those dishes piled up in the sink and the trail of broken things he left behind, this has

been a wonderful experience.

iv

TABLE OF CONTENTS

 

 

LIST OF FIGURES ........................................................................................................... vii
LIST OF TABLES ............................................................................................................ viii
CHAPTER 1 INTRODUCTION - - 1
1.1 BACKGROUND ........................................................................................................ 1
1.2 RESEARCH QUESTIONS .......................................................................................... 3
1.3 RESEARCH METHOD .............................................................................................. 3
1.4 RESEARCH SCOPE .................................................................................................. 4
1.5 OUTLINE ................................................................................................................ 5
CHAPTER 2 A REVIEW OF THE SPECTRUM POLICY DEBATE 6
2.1 RESEARCH ON INSTITUTIONAL DESIGN OF SPECTRUM GOVERNANCE REGIMES ..... 7
2.2 EMPIRICAL AND COMPARATIVE STUDIES ON PERFORMANCE OF SPECTRUM
GOVERNANCE REGIMES ......................................................................................... 12
2.3 ENGINEERING STUDIES .......................................................................................... 13

CHAPTER 3 SPECTRUM GOVERNANCE REGIMES AND POLICY

 

INSTRUMENTS 15
3.1 MAJOR POLICY INSTRUMENTS AND THE THEIR ROLES ........................................... 15
3.2 SPECTRUM GOVERNANCE REGIMES AS CONFIGURATIONS OF POLICY INSTRUMENTS
............................................................................................................................... 18
CHAPTER 4 TECHNICAL ASPECTS OF SPECTRUM MANAGEMENT .......... 21
4.1 INTERFERENCE ....................................................................................................... 21
4.2 FACTORS DETERMINING THE EFFECT OF INTERFERENCE ON UTILITY .................... 24
4. 2.] Factors Determining Signal Strength: Transmission Power and Spatial

Separation ..................................................................................................... 25
4.2.2 Factors Determining Strength of Effective Interference ............................... 26
4.3 THE ROLE OF NETWORK ARCHITECTURE ............................................................... 29
4.4 OTHER TECHNICAL ISSUES .................................................................................... 32
CHAPTER 5 NATURE OF DEMAND FOR WIRELESS SERVICES .................... 35
CHAPTER 6 MODELS OF MARKETS FOR WIRELESS SERVICES ................. 40
6.1 MATHEMATICAL REPRESENTATIONS FOR INTERFERENCE AND SIR ....................... 41
6. 1.] Signal strength .............................................................................................. 44
6.1.1.1 Direct Two-way P2P Networks ............................................................ 45
6.1.1.2 Cellular-Type Networks ........................................................................ 45
6. I .2 Strength of Effective Interference ................................................................. 48
6.1.2.1 Direct Two-way P2P Network .............................................................. 48

6.1.2.2 Cellular-Type Services .......................................................................... 51

 

 

6.2 SPECIFICATION OF THE DEMAND FUNCTIONS ......................................................... 55
6. 2.1 Direct Two-way P2P Network ...................................................................... 55
6.2.2 Cellular-Type Network .................................................................................. 57
6.3 TRANSMITTER COST, FIXED COST AND THE PROFIT FUNCTION ............................. 59
6.4 DERIVATION OF EQUILIBRIA AND WELFARE OUTCOMES ....................................... 61
CHAPTER 7 WELFARE ANALYSIS 65
7.] PARAMETER VALUES USED IN THE BASELINE ANALYSES ...................................... 65
7.2 EFFECTS OF THE POLICY INSTRUMENTS ................................................................. 69
7.2.1 Welfare Comparison of Governance Regimes .............................................. 69
7.2.2 Effects of Poor Policy Choices ..................................................................... 78
7.3 OWNERSHIP VS. COMMONS .................................................................................... 82
7.4 PARAMETER VALUES AND SENSITIVITY ................................................................. 84
CHAPT ER 8 CONCLUSIONS - - 94
8. I SUMMARY OF THE DISSERTATION .......................................................................... 94
8.2 FUTURE RESEARCH ................................................................................................ 95
APPENDIX I IMPLEMENTING CALCULATIONS FOR EQUILIBRIA .............. 97
REFERENCES ................................................................................................................. 10]

vi

LIST OF FIGURES

Figure 3.1 Classification of Spectrum Governance Regimes ........................................... 20
Figure 4.1 An Illustration of Interference ......................................................................... 22
Figure 4.2 Factors Determining Interference Level and Utility ....................................... 29
Figure 4.3 Two Different Network Architectures ............................................................. 30
Figure 5.1 An individual firm’s perspective on demand for its service ............................ 39
Figure 6.] Factors Determining Interference Level and Utility ....................................... 42
Figure 6.2 s(TP) vs. T P ..................................................................................................... 47
Figure 6.3 Expected Signal Strength as a Function of Transmission Power .................... 47
Figure 6.4 Frequency Allocation in an FDD System ........................................................ 52
Figure 6.5 Mutual interference between devices in a cellular-type network .................... 53
Figure 6.6 Equilibrium Consumer Surplus ....................................................................... 64
Figure 7.1 Classification of Spectrum Governance Regimes ........................................... 70

Figure 7.2 Welfare Optima under Eight Regimes (Two-way point-to—point network) 71

Figure 7.3 Welfare-Maximizing cR and c7 as a function of n ........................................... 74
Figure 7.4 Welfare-Maximizing ck and Profit-Maximizing cT as a function of n ............ 74
Figure 7.5 Welfare Optima for Eight Regimes (Cellular-Type Network) ........................ 76

Figure 7.6 Welfare-Maximizing CR and c7 as a function of n (Cellular-Type Network) .. 77

Figure 7.7 Welfare-Maximizing cR and Profit-Maximizing c1 as a function of n (Cellular-

Type Network) .......................................................................................................... 77
Figure 7.8 Welfare as a Function of cR and c1 for n =6 under Regime l .......................... 79
Figure 7.9 Welfare as a Function of n and c1 under Regime 2 ......................................... 81
Figure 7.10 Welfare as a Function of n and CR under Regime 3 ....................................... 82
Figure 7.l 1 Spectrum Ownership VS. Open Commons .................................................... 84

vii

LIST OF TABLES

Table 6.1 Comparisons of a Direct Two-way P2P Network and a Cellular-Type Network
................................................................................................................................... 43
Table 6.2 Regimes and Equilibrium Conditions ............................................................... 62

Table 7.1 Parameter Values for Baseline Case in a Two-way Point-to—Point Network 66

Table 7.2 Parameter Values for Baseline Case in a Cellular Type Network .................... 68
Table 7.3 Result of Sensitivity Analysis (two-way point-to-point type network) ............ 90
Table 7.4 Result of Sensitivity Analysis (Cellular-Type network) ................................... 92

viii

Chapter 1 Introduction

1.1 Background

Fifty years from now people may have very different ideas about access to the airwaves
(spectrum) than today. At present Spectrum is viewed as a public asset, and (somewhat
ironically) government agencies serve as guardians in determining how and who among
the “public” can access the airwaves. Those who are awarded rights to provide services
using this public asset receive strong protections but also undergo intensive scrutiny
under administrative laws. All this is likely to change due to accelerating momentum

toward spectrum reform.

The current spectrum governance regime was established in the 1920’s, in the name of
preserving the value of Spectrum and protecting users from harmful interference.l Under
this regime, governments play the role of a central planner and set forward detailed rules
governing all aspects of spectrum usage. Although tight government controls over
spectrum allocation and uses have provided certainty for wireless businesses and services
over the decades, increasing wireless applications and contention for spectrum in recent
years have made efficiency concerns a frontline issue. Citing mounting evidence of
inefficiencies resulting from regulatory delays and distortions introduced by political
maneuvering, calls for replacing the administrative licensing regime with market

mechanisms have become stronger and louder. Abandoning the approach of tight

 

' Soon after radio became a commercial success in the 1920’s, a power fight between broadcasters broke
out in major markets, where broadcasters tried to overwhelm each others signals by transmitting at higher
power and mutual interference rendered the spectrum resource unusable. This prompted government
intervention and the Federal Radio Commission was established in 1927 to oversee spectrum management
issues.

government control, which was unthinkable some forty years ago, is now the mainstream

opinion.

However, in spite of the consensus on reform, the action plan for reform is a subject of
much debate. In essence, the market is the agreed upon mechanism to replace regulatory
fiat, but there is strong disagreement over whether technology protocols and etiquettes
alone are enough to prevent mutual interference or whether exclusive property rights
assignments are necessary. The division between technology-focused and property-
rights-focused approaches to spectrum management is commonly referred to as the
commons versus property rights debate because those with faith in technological
solutions would make spectrum a common resource. Given that there are almost no real-
world examples of these alternative regimes, anticipating issues and coming up with
solutions is a challenging task. As a result, the proposals are still Sketchy and the debate

has been mostly philosophical and abstract.

AS an attempt to more objectively evaluate alternative spectrum governance regimes, this
Study models the demand for wireless services, taking the engineering properties of
wireless services into account, and incorporates the demand model in models of markets
for wireless services. The models tie three key policy instruments (entry restrictions,
transmission power and receiver quality regulations) together, providing a framework for
systematic examination of the effects of the policy instruments and comparison of

regimes in terms of welfare performance.

1.2 Research Questions

Given the complex interplay between regulations, technology and market forces, any
attempt to answer the question “should we choose spectrum property rights or spectrum
commons?” will inevitably entail a great number of assumptions, whether made explicit
or not. One’s answer to this question necessarily depends on such assumptions, which
often are debatable. To meaningfully compare governance proposals while allowing
objective examination of the assumptions used in the analysis, this study focuses on
fundamental building blocks and asks the following more narrowly defined research

questions:

0 What are the most important policy instruments affecting welfare under different

governance regimes?

0 What are the welfare effects of variation in the policy instruments for different

governance regimes?

0 Based on the answers to these questions, what can we say about the relative

merits of the proposed regimes?

A careful examination of these questions helps identify factors critical to spectrum
management and provides more analytical rigor to the debate. This is the major

contribution of this Study.

1.3 Research Method

This study seeks to evaluate alternative spectrum governance regimes by comparing the
predicted outcomes of economic models built to reflect the nature of wireless services

and the characteristics of different governance regimes. In principle, this study employs

the standard economic approach for welfare analysis, but due to the complicated
functional forms required, the results are derived computationally instead of solving

systems of equations algebraically.

As a starting point, this study focuses on a one-period economic model. Demand for
wireless service in a homogeneous service market with identical service providers is
modeled. This modeling effort factors in technical issues affecting demand: transmission
power, robustness and network structure. Two types of services based on different
network structures are modeled. For the first type users communicate directly with each
other via terminal devices without a backbone relay; for the second users are connected
via base stations and backbone relay. Given the models, the three key policy instruments
are varied and the corresponding equilibrium welfare outcomes are computed and

analyzed.

1.4 Research Scope

The models used to study welfare under different regimes are one-period models, which
to some extent limit our ability to examine dynamic aspects of efficiency, such as the
welfare impact of consolidation of Spectrum ownership under a property rights regime
and whether a commons regime leads to more innovation versus an ownership regime. In
addition, since the study focuses on a homogeneous product market, the efficiency
properties of permitting a given block to be allocated among different services are

beyond the scope of the study.

This study focuses on the effects of interference and related technological factors

(transmission power and receiver quality) on welfare created in a wireless market. Other

factors, most importantly network effects and scale economies, are not addressed in the

present study.

1.5 Outline

The manuscript is organized as follows. Chapter 2 reviews the scholarly debate over
spectrum reform and spectrum governance regimes. Chapter 3 identifies key policy
instruments for Spectrum management and defines the governance regimes of primary
interest in terms of the configuration of the policy instruments. Chapter 4 provides
background information on relevant engineering properties of wireless services. Chapter
5 discusses how interference affects demand for wireless services. Chapters 4 and 5
provide foundation for the models of spectrum markets presented in Chapter 6. Findings
of a welfare analysis based on these models are presented in Chapter 7. Chapter 8

summarizes and concludes the study.

Chapter 2 A Review of the Spectrum Policy Debate

At the center of the debate over Spectrum policy is the issue of choosing the best
spectrum governance regime. A spectrum governance regime establishes a configuration
of rights to spectrum; it coordinates all activities involved in the appropriation of
spectrum through assigning these rights to various stakeholders. Currently spectrum is
governed by the principle of administrative licensing, with which the government serves
as a central planner and is heavily involved in the coordination between spectrum users
and uses. As central planning has been proven unproductive in most industries, the
administrative licensing regime governing spectrum usage for the past 80 years has been
the subject of increasing scrutiny and criticism. Two regimes have been proposed to
replace the administrative licensing approach: a property rights regime and a spectrum
commons regime. Currently these proposals do not offer much detail about how exactly
rights should be defined and implemented; however, the fundamental principles behind
them are in stark contrast: while a property rights regime creates ownership of spectrum
and uses the market to coordinate the spectrum owners and potential users, most
proposed commons regimes would rely on technical protocols to coordinate spectrum

USCS.

Most research on spectrum governance falls into one of the following categories: (1)
institutional design of spectrum governance regimes and cost-benefit analysis; (2)
empirical and comparative studies on efficiency under different spectrum governance
approaches; (3) engineering studies on mechanisms that facilitate coordination among

devices, improve spectrum utilization and increase capacity. The following sections

briefly summarize research in these areas, with emphasis on the first category, which is

the category this dissertation falls into.

2.1 Research on Institutional Design of Spectrum Governance
Regimes

Scholarly work on alternatives to administrative licensing as Spectrum policy can be
traced at least back to 1951, when Leo Herzel first proposed to replace the administrative
licensing regime with a spectrum market, which he argues would be much more efficient
in determining the best uses for spectrum resource. Herzel’s viewpoint was echoed in
Nobel laureate Ronald Coase’s seminal 1959 article “The Federal Communications
Commission,” which argues from a property rights and transaction cost perspective that
spectrum is no different from other scarce resources. Coase explains how the problem of
interference can be dealt with by defining spectrum property rights that can be traded in a
market and provided a detailed analysis about how such a market would work similarly to

markets for other goods.

The idea of allocating spectrum through a market system slowly gain acceptance among
scholars in the three decades after Coase’s “The Federal Communications Commission.”
DeVany et a1. (1969) proposed a system in which the government defines initial property
rights by dividing spectrum into packages along time, area and frequency dimensions and
allows firms to trade these packages and redefine the property rights based on a market
mechanism. Their proposal also provides an analysis on the engineering and legal issues
that can potentially arise under their proposed system. In similar vein, Minasian (1975),
Levin (1971) and Webbink (1987) provided similar analysis of property definitions that

would promote efficiency.

As wireless technologies progress and wireless applications became an increasingly
important part of people’s daily lives, contention for spectrum began to surface. The
rising value of spectrum prompted questions about the efficiency and merit of the
administrative licensing regime, and the property rights approach emerged as a strong
candidate for replacing it. Proposed property rights regimes share the fundamental
principle that spectrum ownership Should be established with exclusive and full property
rights. With exclusive and full property rights to Spectrum, owners can alter the use of
their spectrum, sell, combine, partition or disaggregate the spectrum they own (Kwerel
and Williams, 2002; Faulhaber & Farber, 2003). Such flexibility would guarantee
liquidity for a spectrum market where spectrum owners can work with one another to
deal with harmful interference. Following the traditional rationale for a market economy,
property rights proponents argue that spectrum owners’ information (about costs and
benefits of wireless services) and incentives to profit-maximize will lead to the most
efficient allocation and use of spectrum (Hazlett, 2001 ; White, 2000; DeVany, 1998;

Spiller and Cardilli, 1998).

A premise of a property rights system is that rights are enforceable; therefore, the
definition of spectrum property rights and protection against interference is of critical
concern. In general, property rights proponents advocate defining spectrum property
rights in terms of specified Signal strength at property boundaries. For example, Kwerel

and Williams propose:

To provide licenses maximum technical and service flexibility, spectrum
emissions rights between licenses should be defined in terms of power
limits at the boundaries between spectrum blocks and geographic areas

together with maximum in-band power limits. Subject to these output
limits, each licensee should be free to deploy transmitters within its
licensed spectrum block and area without coordination with licensees in
adjoining blocks and areas. Conversely, each licensee must design its
own receiving system to tolerate permissible levels of interfering power
from adjoining licensees.

By allowing an owner to make tradeoffs among inputs (for instance, antenna height and
transmission power), this approach promotes efficient use of resources. Moreover,
predefined power limits at the boundaries also bestow on property owners more certainty

and protection, thereby preserving investment incentives.

The increased appeal of the property rights regime is reflected in FCC policy in many
ways. Viewed as the first step towards establishing spectrum ownership, auctions were
introduced in 1993 as a mechanism for spectrum assignment and have been widely used
in many countries to expedite spectrum assignment and generate revenue for
governments. Although in some European countries 3G license auctions have led to
financial problems for successful bidders, overall the efficiency of Spectrum auctions is
widely hailed and considered to be a successful first Step towards spectrum privatization.
Changes happened on other fronts, too. Shelanski and Huber (1998) provide a detailed
analysis on a series of changes in the FCC’S licensing rules and argue convincingly that
such changes have essentially extended the rights of licensees. These developments

signaled a Steady shift towards the property rights regime through the 1990’s.

Just as the property rights proposal was gaining ground, tremendous progress was made
in wireless technology and the Internet, leading to proposals for a totally different
approach to spectrum management. In sharp contrast to privatization, the new approach

suggests a commons model in which Stakeholders (such as service providers and

equipment manufacturers) collectively govern the spectrum and users can access the
airwaves as they do public parks and roads (Lessig, 2001; Benkler, 2003; Werbach,

2004).

The philosophy behind the commons approach is drastically different from the property
rights concept, as Benkler explains:
...instead of creating and enforcing a market in property rights in
spectrum blocks, we could rely on a market. . .that would allow people to
communicate without anyone having to control “the Spectrum.” Just as
no one “owns the Internet,” but intelligent computers communicate with
each other using widely accepted sharing protocols, so too could
computationally intensive radios. . .[A] “spectrum commons”
approach. . .[regards] bandwidth as a common resource that all equipment
can call on, subject to sharing protocols, rather than as a controlled

resource that is always under the control of someone, be it a property
owner, a government agency, or both.

In this View, the optimization object is communication capacity rather than the resource
“spectrum,” and the goal of technical restrictions is to ensure coexistence rather than
protection of individual properties. To serve these goals, commons proponents in
general agree that some rules or etiquettes governing communication in a commons may
be necessary. Based on the influential work of Elinor Ostrom on commons governance
(1990), Buck (2002) analyzes institutional designs that may facilitate coordination

within a spectrum commons.

The significant differences between the two approaches have, not surprisingly, led to
heated debates. Proponents of the different regimes have found themselves deeply
divided over fundamental issues. For example, commons proponents argue that advances
in cooperative and adaptive technologies will eradicate spectrum scarcity. They contend

that by dividing spectrum into blocks and granting monopoly rights to license holders (or

10

spectrum owners in the property rights regime), administrative licensing and property
rights regimes create an artificial scarcity in spectrum and dead weight loss due to the
monopolization of spectrum. The additional capacity brought about by the new
technologies and the ability to utilize currently unused Spectrum2 will increase the
amount of usable spectrum tremendously and allow everyone to use it freely and orderly.
They also claim that in an open commons regime, more firms and inventors will have
access to spectrum; thus price and product competition will increase and lead to greater
innovation and welfare for the society (Benkler, 2003; Werbach, 2004). Noam (1998)
also shares these beliefs, although he takes a different approach towards open commons.
In his proposal, users dynamically bid for access to spectrum so that pricing is still used

to assign access when scarcity is an issue.

On the other hand, the property rights proponents predict tragedies under the commons
regime, arguing that exclusive rights to Spectrum are required to ensure market efficiency
and long run viability. Whereas Faulhaber and Farber (2003) and Hazlett (2001)
acknowledge that a commons regime might work as long as Spectrum is not scarce, they
also argue that demand growth will eventually lead to scarcity. Benjamin (2003)
contends that most of the technologies that would make possible the development of an
open commons can work just as well under a property rights regime given adequate
design of rights and their assignments; in most Situations, he claims a property rights
regime is more efficient. From the property rights perspective, the solution to this

resource allocation problem is institutional measures rather than technical.

 

2 New America Foundation and Shared Spectrum Company (2003), “Dupont Circle Spectrum Utilization
During Peak Hours”. This survey found most of the spectrum blocks are underutilized under the current
allocation. Available at http://www.newamerica.net/DownloaQJDOCngfs/Doc File 183 1.Ddf

ll

2.2 Empirical and Comparative Studies on Performance of Spectrum
Governance Regimes

Empirical studies of the inefficiencies created by the administrative licensing regime
have been an important catalyst for the movement towards Spectrum policy reform.
Hazlett is the most prolific and influential in this area He examined FCC regulation of
radio broadcasting and argued that the administrative licensing regime hinders innovation
because limiting firms’ ability to trade spectrum diminishes the incentive to innovate for
licensees (Hazlett and Sosa, 1997). Hazlett (1997, 1998) also provides detailed analysis
of how the incumbent licensees have successfully managed to establish entry barriers
under the administrative licensing regime and have enjoyed government protection at the

expense of the society.

On the other hand, empirical Studies on alternative spectrum governance regimes have
been scant. In Spite of the intense debate, literature on spectrum management to date has
been abstract and characterized by speculative arguments backed by anecdotal evidence.
Hazlett and Ibarguen (2002) cited the experience of the mobile phone markets in
Guatemala and El Salvador as examples of success in privatizing spectrum on a small
scale. Buck (2002) sees the successful Spectrum sharing agreement struck by the
Chicago Wireless Club (consisted of 100 amateur radio operators) and commercial radio

stations in 1910 as evidence that open commons will work.

To a great extent, proponents on both Sides simply talk past each other. While there have
been some attempts to provide comparative analysis of these different regimes, results are
rather sketchy because there have been few services governed by alternative regimes, and

even if they resemble these proposed regimes in some aspects, their administrative

12

licensing element often dictates the outcome (Ting, Bauer, & Wildman, 2003; Carter,

2004).

2.3 Engineering Studies

Advances in wireless technology that enable wireless devices to operate in an adaptive or
cooperative fashion have been an important stimulus for the commons approach. Four
types of technologies are most frequently cited as enablers of the commons regime:
Spread Spectrum, software-defined radio, mesh networks, and smart antennas.

Spread spectrum technology allows users to share the spectrum by transmitting at lower
power but using a wider bandwidth. Receivers using spread spectrum technologies can
decipher the low power signals based on Specific signal coding patterns. Those not
fitting the patterns will be rendered as random noise. In their in-depth engineering-legal
study on the policy implications of spread spectrum technology, Buck et al. (1998) claim
that this technology is a critical technical building block for open access. Software-
defined radios are adaptive radios with cognitive ability. These radios can gauge the
level of activity in the radio environment and adjust their operating frequencies to avoid
congested frequency bands. Merino (2002) examines their impact and concludes that
software-defined radios can potentially increase the intensity of spectrum sharing and
promote competition. Drawing on Shepard’s work on multi-hop spread spectrum
networks (1995), Reed (2002) contends that cooperative mesh networks, in which users
relay one another’s signals at low power, can increase system capacity and thereby
eradicate spectrum scarcity. Smart antennas take advantage of antenna arrays and the

locational information they can detect to distinguish desired signals from interference.

13

For a review of these technologies’ implications for the property vs. commons debate, see
Ting (2004).

On a more technical front, in recent years there have been many studies on designing
network protocols that improve coordination and network performance under various
settings and for different network architectures. Such studies model incentives for users
to “hoard” or “abuse” system resources and seek to establish design principles that
mitigate such incentives. Satapathy and Peha’s work (1996, 2000, 2002) on unlicensed
spectrum coordination mechanisms (including power limits and real-time Sharing) is
representative in this regard. They find that FCC stipulated etiquettes for unlicensed PCS
devices may not be sufficient for preventing overuse of spectrum and suggest alternative
design principles as remedies.

In summary, this chapter briefly reviewed literature on: (I) The institutional design of
spectrum governance regimes, (2) empirical studies on the performance of various
Spectrum governance regimes, and (3) engineering studies on the policy impact of new
technologies and design principles that can help coordinate devices and improve the
efficiency of spectrum usage. The review of institutional design summarizes the current
thinking of the alternative spectrum regimes and provides useful background information
for identifying the critical policy instruments for spectrum governance. Moreover, in
reviewing empirical and comparative studies we see that research to date has provided
little information on the relative merits of the proposed alternatives to administrative

licensing, a gap this dissertation can help fill.

I4

Chapter 3 Spectrum Governance Regimes and Policy
Instruments

AS mentioned in Chapter 2, under different spectrum governance regimes wireless
service industries may perform very differently in terms of policy measures such as
scarcity, welfare and technological innovations. An overall evaluation of the regimes
must take into account all factors that influence performance and their interplay and
focuses on differences in governance regimes and their performance in terms of control

over a set of key policy instruments.

The chapter starts by discussing the roles of three major policy instruments: entry
restrictions, transmission power and receiver robustness in Section 3.1. Building on
Section 3.1, Section 3.2 identifies eight governance regimes based on different
configurations of the policy instruments and discusses their relevance to the ongoing

policy debate.

3.1 Major Policy Instruments and the Their Roles

The debate over spectrum governance is often simplified to the choice between two
regimes: one, a spectrum commons, allows entry through acquiring devices that adhere to
certain usage rules and the other, spectrum ownership, allows entry through acquiring
spectrum ownership. This characterization might serve well as a quick-and-dirty guide to
spectrum policy, but without a closer look at how spectrum ownership is defined and how
the usage rules work under a spectrum commons, it is not possible for us to evaluate
different regimes. Worse yet, oftentimes people are arguing without realizing that they

have very different implicit assumptions about how a Spectrum commons or ownership

l5

regime works. To avoid such pitfalls, this section focuses on the role of the major policy
instruments under the proposed regimes, and the next section defines the regimes of

primary interest in terms of control of these policy instruments.

A spectrum property rights or ownership regime is still a fairly new idea,3 with most of
its details Still to be worked out. Nevertheless, as mentioned in Chapter 2, it is widely
anticipated that a property rights regime will have the following characteristic: (1) A
Spectrum band is sliced into blocks with exclusive usage rights. (2) Government
determines the initial number of blocks and their assignments to users through titles of
ownership or licenses. (3) Maximum acceptable interference levels that are initially
defined by the government and maintained through a combination of technical
specifications and Spectral separation between the signals of different service providers.
Under some proposed property rights regimes, the Spectrum owners can consolidate or
further divide spectrum blocks, and they may negotiate acceptable interference levels

with their neighbors. These possibilities are not considered in this study.

In general, what the commons proponents advocate is essentially an open access regime
subject to minimum requirements (Anyone who buys a certified device can access the
Spectrum resource.) Consistent with this interpretation, we use the term “open commons”
instead of simply “commons” to refer to the type of commons regime (there are others)
modeled in this dissertation. Open commons proposals generally have the following
characteristics: (1) Coordination (interference avoidance) is achieved through technical

restrictions (e. g., transmission power limits) and/or etiquettes (e.g., listen-before-talk)

built into devices. (2) Subject to compliance with the technical restrictions and etiquettes,

 

3 Strictly speaking, all regimes are property rights regimes. They differ only in the way the rights are
configured. Ownership is a more accurate term.

[6

there is no restriction on entry. (3) A collective agency (probably consisting of
equipment manufacturers and service providers) determines the technical specifications
required for coordination, such as a maximum power limit, communications protocols
(e. g. listen-before-talk), or a required level of interference robustness for devices such as

minimum signal-to-interference tolerance.

There are several types of both ownership and open commons regimes. Open commons
regimes are distinguished from ownership regimes by whether the government does or
does not control entry into the market. Different types of open commons and ownership
regimes are then determined by whether the government or the market determines

transmission power and/or receiver robustness.

Comparing these two sets of characteristics, we identify the following policy instruments
as the major components distinguishing the regimes. The welfare consequences of
different uses of these policy instruments restrictions (including not using them) will be

the focus of this study:

(1) Entry: while the open commons regime sets no limit on number of firms that can enter
a market, the number of firms granted access to the spectrum under the property rights
regime will be determined by the government through a rights assignment. This study
treats the number of firms as a policy instrument, recognizing this is equivalent to
analyzing spectrum usage rights directly on the initial assignment of rights with a

govemment-set number of firms, which can be treated as exogenous.

(2) Transmission power: restrictions on signal power can limit the potential incidents of

interference under both regimes. Firms’ signal powers may be determined by market

17

processes or limited by government in both regimes. For both regimes government

restrictions are limitations on usage rights.

(3) Device robustness: defined as a device’s ability to reduce the effect of interference
upon user perceived communication quality. While there are other ways to improve
robustness, in general more sophisticated mechanisms can be employed in receiver
designs to mitigate the degradation in service quality due to interference. Some have
argued that under an open commons regime firms will produce more sophisticated
devices to cope with an increasingly noisy radio environment (Shepard, 2002; Benkler,
2003), but firms might have similar incentives in an ownership regime as well. There
may or may not be a govemment-mandated minimum robustness level in both types of
regimes. By making device robustness a policy instrument in our models, we can

examine the plausibility of these arguments.

3.2 Spectrum Governance Regimes as Configurations of Policy
Instruments

Building on discussion over policy instruments in Section 3.1, this section defines the

regimes investigated in this study in terms of application of these policy instruments.

Figure 3.1 Shows eight different Spectrum governance regimes based on combinations of
entry conditions, transmission power restrictions and robustness requirements. A solid
line indicates that a policy instrument is set by the government, and a dotted line means
that instrument is left for the market to decide. The four branches on the upper half are
variations of ownership regimes because the number of firms is controlled. The four
branches on the lower half are commons regimes because the number of firms is

determined by market forces.

18

Among the eight regimes, Regimes l, 2, 5, 6, and 8 are of particular interest. Regimes 1
and 8 are two polar-opposite cases in that in Regime 1 government controls all three
policy instruments and Regime 8 is absolutely laissez-faire. When a government is
omniscient, it can always set the policy instruments correctly and do at least as well as
laissez-faire. Both can be used as benchmarks to evaluate the merits of other types of
regimes. Regime 2 (where both number of firms and transmission power are set by
government) is of interest because, reflecting literature review in Chapter 2, this
combination describes major proposed ownership regime(s). In contrast, Regime 6 (an
open commons regime with transmission power restrictions) corresponds to the regime
currently applied to unlicensed spectrum in the US. Regime 5 is a world where both
transmission power and entry are controlled by the government; whether adding the
robustness requirement can further improve welfare in a spectrum commons is worth

examining. Thus a comparison of Regime 5 to Regime 6 is instructive.

What policy instruments are controlled determines what is left for the firms to decide.
This affects their profit-maximizing output decisions. With a model of demand for a
wireless service, we can see how firms’ decisions change under different regimes and
how welfare changes by incorporating the demand model in a model of a wireless service

market. The next two chapters will develop a model of demand for a wireless service.

19

Figure 3.1 Classification of Spectrum Governance Regimes

 

G Regime 1

G: government (Optimal w/ omniscient govt.)

M: market . ..................

    

 

 

Regime 2
(Proposed ownership regime)

 

Regime 3
Regime 4

Regime 5

Regime 6
(Proposed commons regime)

 

Regime 7

Regime 8

(Unconstrained commons)
Who sets Who sets Who sets
number of transmission robustness?
firms? power?

20

Chapter 4 Technical Aspects of Spectrum Management

This chapter provides the technical information necessary for modeling the demand for
wireless services, which is the topic of the next chapter and a critical element of the
model in the chapter after that. We Start off by defining interference in Section 4.1;
Section 4.2 proceeds to identify the factors determining the actual effect of interference
on utility. In Section 4.3 we focus on the relationship between network architecture and
the demand and cost characteristics for wireless services, followed by a discussion of

some practical issues involved in the modeling of markets for wireless services in 4.4.

4.1 Interference

For the most part, in the policy debate over spectrum management regimes interference is
an abstract term commonly interpreted as unwanted signals that reduce the value of a
communication service to its users by reducing the rate of data transmission or the clarity
of a desired signal. To model the effects of interference on user valuation of a service, a

more formal and accurate description of how it works is necessary.

Figure 4.1 depicts what happens at a receiver when it experiences interference that affects
its reception of the desired signal. In these signal profile representations, the horizontal
axis is frequency and the vertical axis is the power density at given frequencies. If the
original signal is not altered during transmission, the receiver will be able to recover the
original signal within its design-specified passband, which is the band of frequencies that
passes through a filter with essentially no attenuation. AS a measure to suppress

distortion introduced during transmission, receivers are equipped with filters whose

21

 

function is to block unwanted signals.4 However, for a number of reasons such as
imperfect filtering and multi-path propagation, unwanted signals (the Shaded region of
the interfering signal in Figure 4.1) will always sneak into the passband of the receiver
and distort the desired signal profile, and the receiver will not be able to recover the
desired signal as it was originally generated. The practical question, then, is not whether
there is interference, but to what degree interference affects service quality and user
utility. From a user’s perspective, this is the question of to what extent her data
transmission slows down (for data communication) or the degree to which she has trouble
telling the conversation from noise (for voice communication) due to the operation of

other devices.

Figure 4.1 An Illustration of Interference

Interfering signal

 

 

 

 

 

 

 

 

 

 

Power . . .
density Received srgnal profile
A i
—— Frequency 1
Power
denshy
I 4’ i
Desired signal Passband frequency
JF—j\
Frequency

Passband

 

4 A filter in a receiver is designed to allow signals falling within the passband to go through unaltered but
suppress those falling outside of the passband.

22

For clarity of exposition, we need to distinguish two concepts, aggregate power from
unwanted signals (hereafter APF US) and effective interference, which are defined as
follows. APFUS is the sum of interfering signals’ power at a receiver’s location. But
what really determines the loss of utility due to the interfering signals is effective
interference, which is what remains of APFUS after the interfering signals are processed
by interference-countering mechanisms in the receiver. This difference is important in E

expressing the effect of interference on user utility.

The engineering concept of throughput, defined as the amount of data transmitted over a

 

specific period of time (usually measured in GbpS or Mbps), has been widely used as a
proxy for utility in engineering Studies of network resource management. In addition to
being easy to observe and measure, using throughput as a measure for utility has the
advantage that there are engineering models expressing throughput directly as a function
of effective interference.

The throughput model used in this study represents throughput, S, as:
S=G(r—e""S’R) (4.1)

where G is a constant reflecting traffic volume, k is a constant with a value determined by
the modulation scheme used, and SIR Stands for signal-to—interference ratio, which is the
received signal Strength divided by effective interference.5 Using throughput as a proxy
for utility allows us to directly link utility to interference. An important point about
Equation (4.1) is that it is a Signal’s power relative to the effective power of interfering
signals, rather than its absolute power, that determines utility. Factors determining SIR

will be discussed in 4.2.

 

5 The channel is assumed to be noiseless, otherwise interference Should include channel noise as well.

23

It should be noted that using throughput as a direct measure for utility has drawbacks,
too. In particular, the rate at which subjective utility (a user’s experience of personal
satisfaction) increases with throughput is likely to fall as throughput rises, just as utility is
typically expected to increase at a diminishing rate with the consumption of other goods.
In addition, throughput may not be as good a measure for voice communications as for
data communications. For data communications, higher throughput means faster
transmission and a larger amount of data sent in a specified amount of time, which is
likely to always increase subjective utility. Although the rate at which utility increases
with throughput will probably be diminishing in throughput, this can be easily dealt with
by assuming a non-linear relationship between utility and throughput. On the other hand,
for voice communication, as long as throughput is high enough to deliver the sound
quality beyond which human ears cannot sense further improvement, increases in
throughput will not affect utility. For example, most people probably agree that CD
quality sound is as good as they will ever experience. In other words, utility for voice
communications is likely to plateau at some point. A more realistic model of utility can
be created by assuming diminishing returns in utility to throughput and taking the nature
of different types of services into account, but this comes at the price of a more complex

model.

4.2 Factors Determining the Effect of Interference on Utility

For the throughput model described in Equation (4.1), both G and k can be exogenously
specified without loss of generality, but SIR depends on both signal and effective
interference strengths at the receiver, which are determined by several factors that are

affected by the choices made by suppliers. These factors include transmission power,

24

 

spatial distance between receivers and transmitters, number of devices in use, spectral

separation between systemsf’ and the robustness/quality of the receiver.

4.2.1 Factors Determining Signal Strength: Transmission Power and
Spatial Separation

Electromagnetic signals attenuate as they travel. As a result, Si gnal strength at the
receiver depends on both the original level of the transmission power at which the signal
is emitted and the distance between the sender and the receiver (referred to as spatial
separation hereafter). Given the same spatial separation, the greater the transmission
power the greater the signal strength at the receiver. On the other hand, as a receiver
moves away from a Signal source, received signal strength goes down because the Signal

attenuates the farther it travels.

Equation (4.2) states the free space path loss model, which describes how power from a
signal source attenuates with distance in a theoretical space devoid of all matter:

2
19,5423?) . (.2.

In Equatin (4.2), P, and PS are signal’s powers at the receiver and the sender,

respectively; 1. is wavelength of the signal and r is the Spatial separation. Both 1. and r are
measured in meters. Equation (4.2) says that power falls in inverse proportion to spatial
separation and signals attenuate faster at higher frequencies. Later on this model will be

used to derive cell Size and expected signal strength for different types of networks.

 

6 A system refers to all the devices provided by one service supplier.

25

_ _ l

4.2.2 Factors Determining Strength of Effective Interference
Transmission Power and Spatial Separation

The principles determining desired signal strength at the receiver also determine the
Strength of an unwanted signal at the receiver. Everything else being the same,
increasing transmission power or moving the source of an unwanted signal closer to the

receiver will produce greater interference.

Number of Interfering Devices

The powers of received signals are additive. AS the number of interfering devices in the
environment increases, APFU S (aggregate power from unwanted Si gnals) and the
interference the user experiences goes up as well. This is true even when we are talking
about devices transmitting at very low power—if the number of these devices becomes

very large they can cause significant interference to other devices.

Spectral Separation

Theoretically, communication systems should generate signals perfectly confined within
the designed band/channel, but in practice, due to imperfect devices, adjacent-channel
interference is commonplace. Conventionally, governments limit interference through
spectrum allocation, through which they separate the signal profiles of different systems

with buffer bands to prevent the scenario described in Figure 4.1.

Except for wireless network engineers or policymakers, today most people tend to take
the seemingly rare incidence of interference between adjacent systems as a rule of
physics, not realizing it is a product of rules implemented by a administrative licensing
regime that is under increasing criticism. To see the effect of relaxing such rules, our

models need to explicitly account for the effect of spectral separation, which is defined

26

 

in this study as the bandwidth between the operating frequencies of an unwanted signal

and the receiver it interferes with.

The relationship between spectral separation and APFUS and effective interference is
largely dependent on the signal profiles and filter properties of the systems in question.
Take Figure 4.1 as an example. Given the same spectral separation between the central
frequencies of the desired and the interfering Signals, if the power density of the
interfering signal is doubled at all frequencies, the effective interference will increase.
Similarly, if the interfering Signal still occupies the same bandwidth but now has constant
power density across the band it occupies, effective interference will also change
depending on its power density level. In spite of these complications, in general the
greater the spectral distance between two systems, the less the effective interference a

receiver user experiences.

Robustness/Quality of the Receiver

In Section 4.1 we emphasized the importance of the distinction between effective
interference and APFUS. The difference between the two is that effective interference is
the residual APFUS after interfering signals are processed by the interference-
suppressing mechanisms built into a receiver. In this study, the receiver’s ability to
suppress or distinguish the interfering signals from the desired signal is referred to as the

robustness or quality of the receiver.

Based on this definition, the relationship between effective interference and APFUS iS
determined by the robustness of a receiver. The more robust a receiver is, the less the
effective interference and the higher the throughput and user utility. The most direct way

to improve receiver robustness is to use filters that can more effectively reject signals

27

 

falling outside of the desired signal passband. In recent years, smart antennas have found
their way into many wireless access networks; these are basically antenna arrays that
collect Signals at different locations and take advantage of the additional location
information to separate the desired signal from unwanted ones. Of course, implementing
these additional measures increases the cost for the devices; hence, while more robust

devices can deliver better service quality, they also tend to be more costly.

In addition to these mechanisms that seek to directly pick out interfering Signals, indirect
interference-countering methods have also been widely used in communication systems.
These methods aim at reducing the negative impacts of the interfering signals the receiver
fails to intercept. Examples of indirect interference-countering mechanisms include
diversity (using multiple stations in a redundant configuration), interleaving (rearranging
data in a noncontiguous way to mitigate the effect of bursty interference) and error-
correction mechanisms (using computational algorithms to identify potential errors and

self-correct).

Figure 4.2 schematically represents the relationships described in Section 4.2. SIR and
throughput are increasing in the transmission power of the desired signal and the
robustness of the receiver but are decreasing in the number of interfering devices and
their transmission powers. SIR and throughput also increase with the spectral and spatial

separations between the receiver and the interfering devices.

28

Figure 4.2 Factors Determining Interference Level and Utility

 

 

Number of interfering sources

 

 

 

 

 

 

 

 

 

 

 

DeSIred Strength Of Power of the interfering sources
Signal effective .

strength interference Spectral separatlon
Spatial separation
Receiver robustness

SIR
Throughput
Utility

 

 

 

4.3 The Role of Network Architecture

Different types of networks are designed to provide different services and serve different
needs; therefore there often is a relationship between type of service and network

architecture, which determines the cost structure of the service.

For example, FRS (Family Radio Service) and CB radio are dynamically configured
networks with no backbone infrastructure to relay signals from one device to another.
Many unlicensed devices work similarly. We refer to this type of network as a direct
two-way point-to-point (P2P) network. In such a network, users may want to
communicate between any two points in the service area. With signal reach defined as

the distance a Si gnal can travel before its power drops below the level required for

29

satisfactory communication given the receiver technology, utility is a direct function of
Si gnal reach and transmission power, and individual users might be tempted to increase

power not only for higher throughput, but also for communicating over longer ranges.

Figure 4.3 Two Different Network Architectures

 

A direct 2-way point-to-point network A cellular-type network

On the other hand, in a cellular-type network where full coverage is guaranteed by
service providers, signal reach is not a concern for users and utility is connected to
transmission power only through throughput. Firms can guarantee full coverage by
covering the service area with cells within which the power level of received signals is
greater than the minimum level required to ensure acceptable communication quality. To
illustrate this, we set the guaranteed minimum power level of received signals within a
cell of cell size R (which is the radius of the cell) at 1 Watt. The original signal has
transmission power TP>l. Based on the free path loss model of Equation (4.2), to meet

such a minimum level requirement, T P must meet the following condition
2
nil] _>_ I .
472R

30

If this condition iS binding at the edge of the cell, then

2
4711?
TP=— . 4.3
[A] ( )

This implies that the transmission power required to cover a cell is proportional to the

area of the cell (or the square of the cell radius).

In a cellular-type network, firms can mitigate the contention for throughput by
substituting base stations for transmission power. That is, putting in more base stations
and letting each base station serve a smaller area (cell size). In this way, transmission
power can be reduced and each cell covers fewer users who may interfere with each
other. While this may increase user utility and overall demand for the service, reducing

cell Size has large cost impacts for service providers.

It is commonly known that cell Sites are the major cost component of a cellular-type
network (Loizillon et al., 2002). For complete coverage of a given area, reduction in cell
size must be compensated by an increased number of base stations. While on a per-cell
basis equipment required for covering larger cells is more costly, the costs of serving
smaller cells quickly add up. According to the study on the relation between base station
characteristics and cost structure by Johansson et al. (2004), as the traffic volume per unit
area increases, smaller cells and greater cell density become more economical.7 The
same study also points out that, depending on the capacity requirement per unit area, total
infrastructure cost (cost of cell sites, base stations and connecting the base stations) of

covering the entire area with larger cells may be either higher or lower than covering the

 

7 The observation that most wireless service providers start with larger cell size and split cells as demand
increases reflects this cost concern.

31

area with smaller cells. However, in general as the traffic volume per unit area goes
down, total infrastructure cost can be reduced by employing larger cells and higher
transmission power. The tradeoff between investment in infrastructure and interference

is built into the second model of a wireless market presented in Chapter 6.

In brief, this discussion illustrates how different network architectures can be associated
with different utility/demand and cost characteristics. A model of demand and supply of

wireless services must take such differences into account.

4.4 Other Technical Issues

Networks may differ in many ways in addition to architecture. This section discusses
two technology concepts incorporated in the models presented in Chapter 6: duplex

mechanisms and asymmetric transmission power in a cellular type network.

Duplex

Just like two people talking at the same time, if the two sides of a communication link
transmit at the same time using the same frequency, the incoming and outgoing signals
will interfere with each other. Duplex is the mechanism by which the signals coming into
a device and those it sends are coordinated. The two most commonly used duplex
techniques are time-division duplex (TDD) and frequency-division duplex (FDD). Their
pros and cons are beyond the scope of this study. Here we focus on why they Should be

modeled differently.

A good example of TDD is CB radio or traditional walkie-talkies, which require users to
turn over the channel to each other by saying “over!”. The incoming and outgoing

Si gnals share the same channel. In other words, they operate at the same frequency but

32

are separated into different time slots. Modern TDD systems are much more
sophisticated and the switch-over’s are done automatically in very quick succession so
users do not perceive any interruption. With a TDD service, each service provider
operates at its own unique central frequency. In modeling a TDD service we can assume
the device a user uses to send and receive signals and the device at the other end of the

communication do not contribute to the interference she perceives.

To the contrary, in a FDD system both the incoming and outgoing Si gnals are continuous
in time but are separated in the frequency domain. Most wireless telephony systems are
FDD systems. With FDD, each system occupies two sub-bands within the overall band
for the service, one for the uplink (mobile device to base station) and the other for the
downlink (base station to mobile device). In this case, each system operates at two
different frequencies, and for an individual user, the signals emitted by the destination

receiver and the intermediate base Station will add to the interference she receives.

Asymmetry in Uplinks and Downlinks in a Cellular-Type Network

Antenna arrays have been widely used in the base stations of modern wireless telephony
networks, allowing mobile devices to transmit at lower power, thereby prolonging users’
battery lives. The use of such technology results in an asymmetry in the power of uplink
and downlink transmissions and needs to be addressed explicitly in a model of a cellular-

type service.

Given the additive nature of power, an 8-element antenna array can combine inputs from
all eight antennas and increase the received signal strength by eight fold. Taking
advantage of the fact that Signals arriving at different locations will have different phases,

devices with such antenna arrays have higher sensitivity in detecting and deciphering

33

incoming Signals; this allows devices sending to them to transmit with lower power.
However, the usefulness of antenna arrays is severely limited by mobility and cost
concerns--in addition to high costs, an eight-element 900 MHz antenna would be about 4
feet wide and a 2 GHz eight element antenna would be about 2 feet wide (Lehne and
Pettersen, I999). The large physical size of antenna arrays makes them unsuitable for
mobile users, so they are mostly deployed at base stations. AS a result, the uplink power
in a cellular type network is typically only a fraction of the downlink power from the base
stations. This asymmetry in power of uplink and downlink signals may lead to different
throughput levels for uplinks and downlinks, and the overall utility of such services will

depend on users’ valuation of the uplink and downlink communication quality.

34

Chapter 5 Nature of Demand for Wireless Services

This chapter describes in general terms how interference affects the demand for wireless
services based on the discussion of interference in Chapter 4. This description of the
demand for wireless services serves as the foundation for the model of competitive

markets for wireless services that will be presented in Chapter 6.

Consider a market for a direct two-way P2P wireless service where there are n firms
competing for customers. Each firm occupies a unique operating frequency within the
band allocated to the service and each customer buys one unit of the service along with
the necessary access device. In this case, market demand is a schedule of consumers’
willingness-to-pay for the product. In the absence of interference (sans interference, SI),
customers View the firms’ services as homogeneous as long as their devices transmit at
the same power level (this restriction will be relaxed later). Assume that in the absence
of interference market demand for the service at a given fixed power level is
characterized by the linear downward-slopin g demand curve (or inverse demand
function)

P = a — bQ,
where P and Q represent the market price and quantity, respectively, and a and b are

positive constants. This will be referred to as the SI demand curve hereafter.

Adding interference to this picture makes it considerably more complicated. From a
customer’s viewpoint, services offered by different firms may no longer be homogeneous
when interference is taken into account. Chapter 4 points out that the interference a user

experiences increases with the number of interfering devices and their transmission

35

power (which is fixed at a common value for the time being for this discussion), but
decreases with the interfering devices’ spatial and spectral distance from the interfered
device. Depending on firms’ output levels and the location and operating frequencies of
their devices, some firms’ services may suffer from greater interference than others,
which translates to a greater loss in utility.8 The user makes her purchasing decision
based on which firm’s service provides her with the highest net surplus (the difference
between the interference-discounted utility and price charged). This Study assumes that
the utility loss associated with a given level of interference is independent of a user’s SI

valuation of the service.

We assume that each service provider knows the market demand function and the
interference that other firms’ users cause for its own customers. Moreover, firms’ beliefs
about rivals are assumed to be Nash in output levels and interference. That is, a firm
takes rivals’ output levels and the interference they cause as given and see them as
independent of its own choices. A representative firm’s perceived demand curve is
therefore the demand it anticipates for its service in response to its choices of

transmission power, device robustness and price given its Nash beliefs.
In Figure 5.1, Q_,- and q,- are total quantities sold by the rivals of representative firm i and

by firm i itself, respectively, and 1".,-and y(q,-) are the loss of utility for a representative i

customer caused by interference from its rivalS’ and its own devices. Since the utility

 

3 A user’s utility depends on the quality of both the signals she receives and those she sends; therefore her
overall utility should be a weighted sum of the utility levels associated with the quality of received signals
at both ends of her communication link. In this chapter we illustrate the nature of demand for wireless
services using a direct two-way P2P service. The utility levels associated with incoming and outgoing
signal quality are not distinguished because such service is symmetric in both incoming and outgoing
direction. Complications arising with asymmetry will be discussed in further detail in Chapter 6.

36

loss resulting from the interference associated with Q-,- is the same for all potential i

customers, the price firm ican charge for its first device will be a — bQ_,- — 12,-. If
mutual interference between firm i’s devices is ignored, firm i’s demand curve will be the

SI residual demand curve given Q-,~ Shifted down by 11,-, which is the innermost of the

three parallel lines in Figure 5.1. However, mutual interference between firm i’s devices
further reduces the price firm i can charge. The more devices firm i sells, the stronger the
mutual interference between them and the further the price drop due to interference.
Graphically, firm i’S perceived demand is the lower concave curve in Figure 5.1, which is

described by Equation (5.1).

Pi=a—b(qi+Q—i)_7i(qi)-r—i (5.1)

What this demand curve says is that the price firm i can charge for its service is
contingent on the aggregate loss of utility due to interference from devices sold by rivals

(11,-) and itself (y(q,-)), as well as total quantity sold in the market. A functional form for

the aggregate loss of utility due to interference (11,- + y(q,-)) will be Specified in the next
chapter.

As mentioned in Section 4.2, the loss of utility due to interference experienced by a user
depends not only on the strengths of interfering signals generated by other devices but
also on receiver quality. Firms can actively respond to interference by producing
receivers that reduce the effect of interference though various mechanisms, although
implementing these mechanisms is typically costly. More specifically, we assume that

firms can influence magnitude of the utility loss caused by interference through their

37

choices among alternative interference suppressing mechanisms that can be built into
their devices. Devices that do a better job of handling interference will be referred to as
more robust devices. Given that the effect of interference on utility is the same for all
users, so is the effect of robustness on utility. Therefore an increase in robustness can be

depicted as a parallel upward shift of the firm’s perceived demand curve.

If the assumption of fixed transmission power is relaxed so that firms can change their
transmission power, power may also be modeled as shifting a firm’s perceived demand
curve. For example, in a two—way point-to-point network, customers’ valuations of the
service potentially can increase with signal reach (Section 4.3). In this case, firms may
produce devices with higher transmission power and charge higher prices for these

devices.

38

Figure 5.1 An individual firm’s perspective on demand for its service

 

 

Price
ll
Utility loss due
to interference
from rivals N
devrces at Q_,-.
r—i

 

 

 

 

Market SI demand
curve assuming
quality associated
with interference
level at O_,-

 

 

 

   
  

39

 

rMarket SI demand curve 7

 

 

Market SI demand curve assuming
quality associated with interference
1 level at O_,-

 

 

 

 

Utility loss due to
interference from
rivals’ devices at

Q_,', [1"

 

 

 

Chapter 6 Models of Markets for Wireless Services

Building on the technical properties of wireless services described in Chapter 4 and the
description of demand for wireless services presented in Chapter 5, this chapter presents

two models of a market for a wireless service.

As stated in Section 4.3, cost structures and demand characteristics for different wireless
services may vary with applications and technology. Therefore, in modeling the market
for a wireless service, it is important to recognize differences in technologies that can
lead to different incentives and behavior. This study focuses on two types of wireless
networks: (I) a wireless network where all users directly communicate with others
without any type of backbone or relay (e. g. walkie-talkie); (2) a wireless network where
users’ signals are relayed to their destinations via base stations and backbone relay (e. g.
mobile telephony). While there is a range of technological alternatives, this Study
focuses on these two network configurations because they are representative of two major
types of mass market wireless services at the present time. The models presented in this
chapter reveal the tradeoffs involved in spectrum management and enable welfare
comparisons of various Spectrum governance regimes. They can also be modified to

study other types of network configurations.

Drawing on the technical properties discussed in Chapter 4, this chapter starts out by
specifying functional representations of interference and the signal-to-interference ratio
(SIR). Utilizing the specification of SIR, Section 6.2 fleshes out the demand models.

Section 6.3 specifies the cost structures for the services and describes firms’ profit and

40

welfare functions, which are derived from the demand function and the cost Structures.

Section 6.4 describes the derivation of equilibrium outcomes.

6.1 Mathematical Representations for Interference and SIR

Chapter 5 discusses how interference affects demand for a wireless service in general
terms. However, explicit functional forms are required for the simulation exercises
described later. This section describes and explains these functional representations of

interference and SIR.

Some of the variables introduced in this section are related to the production of a wireless
service and to competition among firms as well as interference and SIR. It is important
to clarify in advance how these variables enter into the specification of the demand
function. Figure 6.1 depicts the chain of relationships described earlier in Sections 4.1
and 4.2. Regardless of network configuration and the technology employed, a wireless
service user’s utility ultimately depends on the Signal strength of the service and Strength
of effective interference, while the strength of effective interference depends on an array

of factors.

On the other hand, in modeling effective interference and SIR, we also need to recognize
the differences between network configurations and technologies described in Sections
4.3 and 4.4. Table 6.1 summarizes those differences discussed in Chapter 4 and lists the

characteristics of the two types of networks modeled in this chapter.

41

Figure 6.] Factors Determining Interference Level and Utility

Number of interfering sources

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Signal Strength Of Power of the interfering sources
h effective _
Strengt interference Spectral separation
Spatial separation
Receiver robustness
SIR
Throughput
Utility

 

 

 

Next we describe the expression for signal strength and break down effective interference
into its components. The engineering concepts summarized in Figure 6.1 and Table 6.1

will be incorporated in the specifications.

42

Table 6.1 Comparisons of a Direct Two-way P2P Network and a Cellular-Type Network

 

Direct Two-way P2P Network

 

 

 

 

 

 

 

 

 

Characteristics Modeling Implications
Network 1. Individual user’s utility increases with signal. reach
configuration. 2. On average, spatial distance between a receiver and a
No backbone rela . . .
y desrred source rs the same as that between the receiver and
an unwanted source
3. No significant fixed cost investment and fixed cost is
independent of firm choice variables
Duplex: TDD 1. Each firm operates at only one frequency band
2. The device used by the person a user is communicating
with does not contribute to the interference she experiences
Symmetric uplink and Devices communicate with each other directly and all transmit
downlink transmission with the same power; therefore throughput Specifications for
power . . . .
sending and recervrng links are the same
Cellular-type Network
Characteristics Implications
Network 1. Utility independent of signal reach
configuration. 2. Spatial distance between a receiver and a desired source
Users assi ed to cells . . . .
gn (wrthrn cell radius) IS the smaller on average than that
connected through
backbone relay between the receiver and an unwanted source (anywhere rn

 

the service area)

 

43

 

 

3. Significant fixed cost, which depends on cell size and

transmission power

 

Duplex: FDD 1. Each firm operates at two frequency bands; one for uplink

and one for downlink

2. The device used by the person a user is communicating
with and the base station transmitters contribute to the

interference She experiences

 

 

Asymmetric uplink Devices communicate with each other via base stations. Base

and downlink stations transmit at higher power than mobile device; therefore

transmission power . _ . . . . .
throughput specifications for sending and recervrng links differ

 

 

6.1.1 Signal strength

Applying the definition of SIR in Section 4.2, signal strength is measured at the location
of the receiver in question. Because signals attenuate as they travel, Signal strength at the

receiver depends on the Spatial distance between the signal source and the receiver.

In this study, we assume that devices are mobile, but at any given time all firrns’ devices
are distributed uniformly on a sphere with fixed surface area. This is a common
assumption employed in engineering Studies as it bypasses the complications that arise

due to edge of territory asymmetries.

We will discuss signal strength in a direct two-way P2P network and a cellular-type

network separately because expected Signal strength depends on network configuration.

 

6.1.1.1 Direct Two-way P2P Networks

Unlike a cellular-type network, where desired signals only need to reach pre-assigned
base stations, in a direct two-way P2P network, devices communicate with each other
directly and the Signals they send out usually travel far enough to reach receivers
anywhere in the service area. With a uniform distribution of devices on a sphere, the
expected signal strength from a transmitter measured at the location of any given receiver
can be obtained by averaging the signal level measured at locations across the entire
surface of the sphere. Given a uniform distribution of devices, the expected signal
Strength will be independent of the locations of the transmitter and receiver. Let TP be
the transmission power of a Signal source. The uniform distribution assumption allows us
to define a spatial averaging factor, s: so that the expected Signal strength for a receiver
at any given location is s ’-TP. For a given base station transmission power and a
minimum acceptable signal power level, Equation (4.2) can be used to determine cell size

of a cellular—type network.

6.1.1.2 Cellular-Type Networks

Expected signal strength in a cellular network depends partially on cell size. Let the
expected Strength of a Si gnal of transmission power TP from distance R be s(R)xTP,

where s(R) is referred to as the averaging factor. Applying the free space path loss

model described by Equation (4.2),

45

R 2
[(12] x27rrdr
£ng 9

R - 87:2(R2 -I)’
IZflrdr

l

 

which is decreasing in R.
Rearranging Equation (4.3), which describes the relationship between TP and R for a

,1

2
guaranteed minimum power level of 1 within a cell of Size R, we have R2 = 4—] .
7:

Plug this into the above expression for s(R) and we can obtain s as a function of TP:

LogTP —2Log(4zz/,t)
TP — (MI/{)2

 

s(TP) = , (6.1)

As Figure 6.2 shows, s(TP) is decreasing in TP. This implies that s(TP) Should always be
greater than s’= s(TPmax) , where TP,,m is the transmission power required to serve the

entire service area with a single cell.

Figure 6.3 Shows the expected Signal strength, s(TP) x TP, as a function of TP. The
pattern suggests that, in spite of the fact that the averaging factor diminishes with TP and
cell size (which increases with TP), increasing transmission power in a cellular-type

network tends to increase expected Signal strength.

 

9 To avoid the technical problem that this integral will be indeterminate if the lower bound is zero, the
assumption is made that the device is not used for communication needs with a range of less than 1 meter.
Reducing this range will make the averaging factor, s. decrease at a greater rate with R. but the overall
shape does not change.

46

Figure 6.2 s(TP) vs. TP
s(TP)
0.005 7;
0.004 }
0.003 f -. . 2120.33m (f=9OOMHz)
0.002 [

)t=O.l7m (f=18OO MHz)
0.001i - . .

1.1 . .. .,. r....,..r . ...r_... . 'IP
20 4O 6O 80 100

Figure 6.3 Expected Signal Strength as a Function of Transmission Power

S (I? ) xTP
0.2
0.15 A=0.33m (f=900 MHz)
0.1
f 1:0.17 m (f:1800 Mn; )

0.05 :

20 4O 6O 80 100

Note that with the assumption of a uniform distribution of devices on a sphere,

geographic locations of individual devices do not directly enter the demand functions for

both types of networks.

47

6.1.2 Strength of Effective Interference

The basic principles discussed in Sections 4.1 and 4.2 determine the Strength of effective
interference in both direct two-way P2P networks and cellular-type networks; however,
the detailed functional forms vary with network configuration and the technologies
employed (Sections 4.3 and 4.4). In this subsection we first look at the specification of
effective interference for a direct two-way P2P network, the specification will then be

modified to describe effective interference for a cellular-type network.

6.1.2.1 Direct Two-way P2P Network

Section 4.1 defines effective interference as the residual APFUS (aggregate power from
unwanted signals) not intercepted by the receiver’s interference-suppressing mechanisms.

For a given APFUS, effective interference is determined by robustness (Section 4.2.2).

Section 4.2.2 states that an unwanted Signal’s contribution to APFU S at a receiver
increases with the transmission power of the unwanted signal but decreases with the
spectral separation between the source and the receiver. Since firms may operate at

different frequencies, their contributions to APFUS at a given receiver may differ.

Assume there are n firms and each firm chooses a unique operating frequency within the
band allocated to the service. Let i be a representative firm and index its rivals by j, j=l,

2, ..., n, j¢i. For an i customer, we assume the contribution to APFUS at her location by

 

firm j is proportional to , where dij is the spectral separation between systems i

+ rydl-j

and j, and the scaling factor ncan be adjusted to allow for variation in the magnitude of

the effect of spectral separation depending on the spectral characteristics of the

48

technology employed. Given this specification, for a direct two-way P2P network, we
can write the APFUS firm i’s other devices and firm j’s devices cause for an i customer

.Bj((1j.TPj)

1+7]de

 

as ,6,- (qi,TP,-) and , respectively, where ij is firm j’S transmission power.

To avoid the modeling complications that arise from locational asymmetry at the edges of
the band, we assume the band is circular. This is an assumption commonly used to avoid
the edge-of-the-territory problem in the economics literature; it can considerably Simplify

the analysis when firms are symmetrically spread around the circle (Salop, 1979).

The analysis of the previous subsection applies to interfering Signals as well. Since
power cannot be confined within any specific region, unwanted signals can interfere with
any device within the service area (although the practical effect may be small). The
expected strength from an interfering device (with transmission power TP) measured at
any given receiver should therefore be s’x T P, which is obtained by averaging the power
levels of the received interfering signals across the entire service area and s' is the

corresponding averaging factor.

As shown in Table 6.1, in a direct two-way P2P network, devices communicate with each
other directly and all transmit with the same power. We also assume that TDD (Time
Division Duplex) is employed, so that each firm operates at one central frequency and
incoming and outgoing signals do not interfere with each other. That is, for an i
customer, the contribution to APFUS by other firm i devices is

,6(qi ,TPi) = s' - TPi -(qi — 2), the product of expected Si gnal strength and the number of

interfering devices. Note that the number of interfering devices is qi -— 2 because the

49

user’s own device and the device the individual user is communicating with do not create

interference for the user.

3’ . TP . . q .
Similarly, the contribution to APFUS for an i device by firm j’s devices is l Jd 1
+7] ij
’7 SI‘TPJ' qj
and APFUS can be written as s'-TPi °(ql- — 2) + Z—
._ 1+r]d~
1—1 U
j¢i

In specifying effective interference, we use cm, the cost of the receiver unit, as a proxy for

robustness of a device and assume effective interference varies inversely with cgi , where

5 is a positive parameter that determines the rate at which increases in expenditures on

robustness are manifest in reductions in effective interference. For 6: l, robustness is

inversely proportional to cgi. For §< l, robustness increases less than in proportion to

6

CRi and for 6>l, robustness increases more than in proportion to Cgi' Now the SIR for
an i device in a direct two-way P2P network can be expressed as

s'- TP-

SIRl- ‘

 

n s’.TP..q.

, J J 5
i=1. " u‘
j¢l

5
= RI 1 _ (62)

 

TPi'(qi—2)+ Z 71—}.
i=1 ”"0

j¢i

 

50

 

In this study we focus only on symmetric equilibria. Since firms have an incentive to
Stay as far apart from each others’ operating frequencies as possible to minimize inter-

system interference, in equilibrium the n identical firms will spread out across the band

evenly. Let the overall bandwidth allocated to this service be L, dl-j is then 5| j — il.
n

In the discussion up to this point we have not explicitly distinguished the SIR for the
Signals a user receives and the SIR for the Signals others receive from her, both of which
Should affect her utility. The reason is that in a direct two-way P2P network these two
SlR’s should be the same, and we further assume equal contributions to the user’s overall
utility from the quality of reception of signals she receives from others and the quality of
reception of signals others receive from her. The SIR for the signals a user receives and
the SIR for the Si gnals others receive from her are the same in a direct two-way P2P
network because all devices in a firrn’s network have the same transmission power and
robustness and devices are distributed uniformly in both geographic and spectral Space,
which leads to same expected Signal Strength and expected Strength of effective

interference at all devices.

6.1.2.2 Cellular-Type Services

With FDD and asymmetry in uplinks and downlinks in a cellular network, expected
signal strengths, expected effective interference and the SIR for uplinks and downlinks
may no longer be the same. Since both uplinks and downlinks contribute to a user’s
utility, we need to specify uplink and downlink SIR’S separately. Next we modify the
Specifications for effective interference and SIR to account for the complications arising

from FDD and asymmetry in uplinks and downlinks in a cellular network.

51

First, I assume the duplex mechanism in the cellular-type service to be FDD as in most
cellular networks. With FDD each firm operates at two frequencies, one for uplink and
the other downlink. Assume the bandwidth of the band allocated to this service is L.

Without loss of generality, we Simplify the analysis by assuming that each firm’s uplink
and downlink frequencies are % apart and all firms’ uplinks operate in the upper half of

the circular band while the lower half of the band is for downlinks (Figure 6.4).

The locations of the uplink and downlink frequencies for firms i and j are indicated by i u,

in and jU, jD, respectively in Figure 6.4. The spectral separation between firm i’s

downlink frequency, i0, and that of firm j, jD, is dij. Since jD is % away from firm j’s

uplink frequency ju, the spectral distance between in and ju is %— dij'
Figure 6.4 Frequency Allocation in an FDD System

’u

Uplink

 

Downlink
U2-d--

’l

 

52

Next, let the uplink (from terminal device to base station) and downlink (from base
station to terminal) transmission power be TP and TTP, respectively. The ratio T, which
can be greater than or equal to 1, reflects the power asymmetry resulting from using
receiving antenna arrays at the base station (Section 4.4). If transmission power and
robustness of the mobile device are fixed, rcan be increased if more sophisticated

receiver units are used at the base station.

Figure 6.5 illustrates mutual interference between devices in a cellular-type network.
User 1 communicates with User 2 via the base station. Although not shown in the figure,
there are other devices operating in the same environment. While in a TDD direct two-
way P2P network user I and user 2 do not interfere with each other (Section 4.4), in a

FDD cellular-type network each of the communication links A, B, C, D is interfered with

by the other three. Given that firm i sells qi devices, there will be q,- uplinks (at TP) and

q,- downlinks (at t'TP) in the network. For User l’s uplink, B, the contribution to APFUS

from other i devices are from all the other qi-l uplinks and (1) downlinks.

Figure 6.5 Mutual interference between devices in a cellular-type network

 

53

For a representative firm i customer’s uplink, the contribution from all other i devices to

s'tTP.- .

q
the APFUS for this uplink is s'TPi -(ql. — l) +—-'——'— , the sum of the products of
77

1+ L/ 2
expected strength of unwanted signals and the number of sources of such signals. Note
that here the term L/2 replaces dij in the previous specification of effect of spectral

separation because in and in are U2 apart. Similarly, the contribution from firm j’s

s'TP.-q. s'tTP.-q.
devices to the APFUS for this uplink is J J + J J . Let CRU; be the
1+77dij 1+7](L/2-dij)

 

robustness of receiver at the base Station and assume effective interference varies in

inverse ro ortion with c5 -. Then the effective interference for this 11 link is
P P RU: P

.— —

s’fl'P.. . n s'TP- -q- s't‘TP- .q-
s’TPi-(qi—I)+——li+z J 1+ J J xcgw,
1+17L/2 11:1. 1+77dij 1+r7(L/2—d--
J95!

 

U

 

 

and the uplink SIR for an i device is

s TP- -TP-
SIRUi= _ ( ‘) l , (6.3)

1773.. . n TP--q- zTP--q-
s TPi-(qi-l)+—'——q—'+Z J ’+ J J “iii/i
1+7]le 1:1. I+ndij 1+”(L/2‘dij
_ J?” .

 

L

 

 

 

It is worth noting that the expected signal strength s(TPi) . TPI. must be greater than the

expected strength from an unwanted Signal s'TPl. in a cellular network (unless the entire

service area is served by a single cell). The reason is that while desired signals only
travel within cells, interfering signals on average travels longer since they can come from

anywhere in the territory, and thus attenuate more.

Similarly, the SIR for the downlink of an i device is

54

s(TPi) - m),-

 

 

 

SIRDi= _ , _ (6.4)
11).. . n zTP--q- TP--q-
s’a‘Pi-(qi—r)+——‘—q’— 2 J 1+ J J mg”
1+77L/2 j=1 1+7]de 1+”(L/2—dij
_ 1*" l

 

where cm; is the cost of the receiver unit in the access device (which reflects robustness).

6

There is little information about the relationship between c R Ui

(uplink or base station

6

robustness) and cRDi (downlink or the robustness at the mobile terminal), although it

should be a function of t: For analytical tractability, we specify the relationship as

ng = T ' 6301' = 7 ' CR1" (65)

so that tis the ratio of base station robustness to the robustness of mobile terminals as

well as the ratio of downlink to uplink power.

6.2 Specification of the Demand Functions

This section builds the demand functions for a direct two-way P2P network and a
cellular-type network based on the framework laid out in Chapter 5, as well as the

throughput model of Equation (4.1) and the SIR specifications presented in Section 6.1.

6.2.1 Direct Two-way P2P Network

It is Stated in Section 4.3 that an individual user’s utility is likely to increase with signal
reach and transmission power in a direct two-way P2P network. In this case, firms can
increase the transmission power of their devices and charge higher prices for their

services (if other firms’ transmission powers do not change). As discussed in Chapter 5,

55

the effect of such a unilateral increase in power is an upward shift in a firrn’s perceived

demand curve.

Assume each user’s utility increases linearly with TPx , where TP is transmission power,
and x is a positive constant, the value of which reflects the benefits associated with
increased signal reach to a user. User valuation may increase due to increased signal
reach or a larger area covered, or both. For example, if signal reach is the major concern
and utility varies linearly with Signal reach, x Should be about 0.5 Since signal reach
increases proportionally with the square-root of the transmission power. And if utility is
linearly dependent on signal coverage area, x should be about 1 because the area covered
by a signal increases proportionally with transmission power. When utility increases less
than in proportion to signal reach or coverage, which is likely to be the case, x Should be

less than 0.5.

Given that utility increases with TP"C , we let the utility of the customer with the highest

valuation for the service be a - TPx in the absence of interference, which is the new

intercept (or the choke price) for the SI demand curve.

In specifying the demand function for a wireless service, we assume that utility realized
from using the service is increasing in throughput. Section 4.1 points out that the rate at
which utility increases with throughput is likely to be diminishing in throughput, which

increases linearly with (l -e allow utility to increase at a diminishing rate

—k-SIR)g

with throughput, we assume utility to be proportional to (l — e , where

0 < g < I. As mentioned in Section 6.1, in a direct two-way P2P network, the

56

specification of SIR for the signals a user receives is the same as that for the signals
others receive from her, so the expected incoming and outgoing throughput should be the
same. With the assumption that a user values quality of reception of Si gnals from others
and the quality of others’ reception of signals from her equally, the average throughput
and utility should be the same for the incoming and outgoing links and it is not necessary

to distinguish between the incoming and outgoing signal paths.

In addition, we assume the effects of signal reach and throughput on utility are
multiplicative and the same for all users. The intercept for firm i’s perceived demand

-k-SIR

curve thus becomes aTPl-x (l — e i )g , and the perceived demand for firm i’s

service is

—k-SIR,-

Pi =a-TPl-x(l—e )8 —b(qi +Q_l-), (6.6)

where SIR,- has the functional form given in Equation (6.2).

Comparing Equations (6.6) and (5.1), we have

1:,- +y(q,-)=a-TP,."[I—(I—e‘k‘S’Ri)8].

6.2.2 Cellular-Type Network

This subsection modifies the demand function derived in the previous subsection to

model demand for a cellular—type service.

AS mentioned in Section 4.3, in a cellular-type network where full coverage is guaranteed
by the service provider, signal reach has no direct impact on utility as in a direct two-way

P2P network and the only channel through which transmission power affects utility is

57

SIR. In other words, x=0. Another difference here is that since uplink and downlink
powers are asymmetric in a cellular-type network, we need to determine uplink and
downlink throughput levels separately and use a weighted sum of them as a measure for
overall utility. AS before, we assume users value the quality of reception for both signals
they send and receive equally. The overall utility is then an average of the utility levels

associated with the uplink and downlink throughput, and the demand function is

 

l —koSIR . g -koSIR . g "
Pi=§[a[l—e U1] +a[1—e D') J-b(qi+ZqJ-), (6.7)
'=1
14,-
where
Sam-TP,.

 

fl’P..q. n TP..q. flp..q. 5
s’- TP-- -—1+—‘—'+ ’ J + J 1 (no )
l (ql ) 1+7IL/2 Z[ RU!

1:1. 1+rydij 1+”(L/2‘dij
11-1
(6.8)
and
sTP- -2‘TP-
SIRDi= ( I) l

 

 

 

Tp.. . n tTP--q- TP..q.
S" flpi.(qi_])+—l_q_l_+z J 1+ J .1 lchi
1+77L/2 j=l 1+rydij 1+r](L/2—dij)

j¢i
(6.9)
Equation (6.8) is obtained by combining Equations (6.3) and (6.5), and Equation (6.9) by

combining Equations (6.4) and (6.5). s(TP,-) is as specified in Equation (6.1).
In a cellular-type network each firm operates at two frequencies; therefore in a symmetric

equilibrium the spectral Spacing between operating frequencies will be 2: , and dij in
n

Equations (6.7) and (6.8) will be zili — jl.
n

58

6.3 Transmitter Cost, Fixed Cost and the Profit Function

The analysis up to this point has focused on transmission power, TP, as a potential policy
variable or firm choice variable. In this section we introduce CT, the cost of the
transmitter unit in the access device, as a proxy for TP. By doing so we can also examine

the profit implications of a firm’s choice of transmission power. The relationship
between TP and cr is represented as TP = w - cz , where w is a constant scaling factor and

0<z<l because over the long run power is likely to increase less than in proportion with .

the cost of the transmitter unit.

Fixed costs limit the number of firms that can profitably operate in a market. Therefore,
even in a direct two-way P2P service where there is no fixed cost for building a network
infrastructure, we still need to take the cost of setting up and managing a firm as a
limiting factor. For a service where users directly communicate with each other without
going through base stations and/or other infrastructure, it is reasonable to assume that this

cost, denoted as F, is a constant independent of firms’ choice variables, q, c1 and cR.

In sum, with a direct two-way P2P network, firm i’s profit is

”i =(Pi ‘CRi ‘CTiMi ‘F
, (6.10)

—k-SIR- "
= A-(wcfi-txa —e ogq, —(cT,- +cR,->q,- —b(q,- + quq; — F

I=l.
Ii]

where SIR; is represented as Equation (6.2).

On the other hand, in a cellular-type network, cell size has a significant impact on fixed

cost. As discussed in Section 4.3, depending on traffic volume per unit area, total fixed

59

cost could be either increasing or decreasing in cell size, which is determined by

downlink power 2' - T P(ch.) . We assume the relationship between fixed cost and

transmission power is proportional to sl(z'-TP(cT,-))‘2 + s2(r-TP(cT,-))‘3 , where s], 32 and

53 are constants. For very small values of Cu, the s1(r - TP(cT,-))_2 term will become very

large, which means that firms cannot increase profit by reducing cell size and increasing
cell density without limit. Depending on the values of 32 and s3, fixed cost could be
increasing or decreasing in cell size. This functional form can be used to describe cost

functions with a wide range of Shapes by varying sl, s2 and s3.

Moreover, given the same cell size, increasing 2', while allowing terminals to transmit at
lower power, requires more expensive receiving equipment at the base station, adding to
the fixed cost. It is reasonable to assume that this additional cost will be increasing with
cell size since more users will be served in a larger cell and more processing power will
be required. Therefore, we represent total fixed cost as a function of transmission power

and r, as
Fen-,1) = r’ [31(2' . Tr>(c7-,-))‘2 + s2(t' . TP(cT,-))‘3], with t >0.

Equation (6.11) gives the profit function for firm i, which provides a cellular-type

service, as:
_ . . 8 _ . . 8 '1
thigh-6’ k SIR“) +(1-e k SIRD') J‘Ii-(CTI'+CRi)qi‘b(qi+ZqI)
i=1

i: j
- r’ [sl(t' . TP(cT,-))'2 + 32(1- TP(cT,-))93]
(6.1 l)
where SIRU; and SIRD; are specified by Equations (6.8) and (6.9).

60

6.4 Derivation of Equilibria and Welfare Outcomes

With the two profit functions specified by Equations (6.10) and (6.11), we can calculate
market equilibria for all eight policy regimes described in Chapter 3. Absent any
government regulations, firms can adjust their output levels, transmission power and
robustness levels for profit maximization, but firrns’ freedom in setting power and
robustness is limited in some regimes. Also, while the number of firms will be set by the
government in a property rights regime, it is determined by market forces in an open
commons. In economic terms, the first order profit-maximizing conditions with respect
to variables that firms can control should hold in all regimes and the zero-profit condition

Should be satisfied in an open commons regime.

Table 6.2 lists the eight regimes along with the policy instruments set by government, as

well as the market equilibrium conditions for each regime.

The equilibrium values of firms’ choices of q, or and Q; can be obtained by solving these
conditions. Prices and profits can then be determined by plugging the equilibrium values

of firms’ choices of q, c1 and cR into the demand and profit functions.

Calculation of equilibrium welfare is a little more complicated. The assumptions of a
symmetric equilibrium and linear SI demand curve make it relatively simple to
incorporate the utility reducing effects of interference in welfare calculations. The
interference experienced by a user reduces the amount she is willing to pay for a
provider’s wireless service by the dollar equivalent of the reduction in utility delivered by
the service. Recall that we have assumed that for a given amount of interference all users
experience the same reduction in utility regardless of how much they would value the

service in the absence of interference. Because all users experience the same level of

61

interference in a symmetric equilibrium, the effect of equilibrium interference on demand
can be represented by a downward and parallel Shift in the market SI inverse demand
function, with the amount of the shift equal to I“: the reduction in each subscriber’s

willingness to pay at the equilibrium level of interference.

Table 6.2 Regimes and Equilibrium Conditions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regime Variables set by Equilibrium conditions
government

I n, ('7', CR 37:,-
aq,

2 n, CT 875i afli
— : , — : 0

3 n, c atr- 37!-

R ——'=0, —' —0

aql OCT!

4 n Brri an, arr,
__ = , = o , = o
aq, 8cm- 8ch-

5 c , c 37!-

T R —l- = 0 , fl"- —‘) O

6 c7 arr- arr,-
— = O , = O , fl": —) 0
aql OCR,

7 CR afl’i afli
— = O , = 0 , ”I. —) 0

8 - an, an, an.

 

 

—- =0 ' =0 7t-—>0
9 9 9 l
qu aCRi OCT,-

 

 

 

Let cn*,cR.-*, n*, q*, Q*=q*n* and F (or F *( cn*) in a cellular-type network) represent
the equilibrium values for the per unit cost of a transmitter and a receiver unit in a device,

the number of wireless service providers, the number of customers for a representative

62

 

firm, and the number of customers served by the industry and fixed cost. Then the

industry’s net contribution to social welfare is given by:

Q4:
W= {(aTPx —1"*—bq)dq-(cT +cR)Q*—n*F
o (6.12),

=(aTPx —bQ*-T*)Q*+%(Q *)2 -(cT +cR)Q*—n * F

where a .. bQ * ..1“ * is the equilibrium market price.

jSa - r*—bq)dq is the gross value of the service to consumers and is represented by the

0
shaded region in Figure 6.6. Consumer surplus is the triangular portion of the shaded
region above the dashed line. Aggregate revenue collected by the wireless service
providers is the rectangular region below this line. For the two open commons regimes,
free entry drives profits to zero, so this rectangle is also equal to total industry costs
(07Q*+cRQ *+n *F). AS profits may be positive when government sets the number of
firms at its optimal level through the assignment of property rights, some portion of the

rectangle below the dashed line may be industry profits for the two property rights

regimes.

With the chosen parameter values, the equilibrium conditions in Table 6.2 determine the
equilibrium values of output (q), robustness (proxied by ck, the cost of the receiver unit in
the access device), transmission power (proxied by cT, cost of receiver unit in the access
device), price, profit, and welfare. Solving for equilibria, however, is not so straight-
forward due to the complex form of the first-order conditions. The profit function and
the first order conditions are highly non-linear and cannot be solved analytically;
therefore we solve the equation or equation systems computationally for specified

parameter values using Mathematica. Procedures for solving the equilibrium conditions

63

vary somewhat from regime to regime. The procedures for implementing the calculations
required for each regime are presented in the Appendix to this dissertation.

Figure 6.6 Equilibrium Consumer Surplus

Price
A

 

I‘fl

H—W

I Market St demand curve

./

 

      
 

b0

 

 

Market demand curve given
Interference level at I"

 

 

 

 

 

12" Output 7

Chapter 7 Welfare Analysis

This chapter presents the results of a welfare analysis based on the models presented in
Chapter 6. For clarity, the research findings are presented in the same order as the
corresponding research questions posed in Section 1.2. Section 7.] discusses the
parameter values used to derive the results for both models. The findings reported in
Section 7.2 describe the effects of policy instruments. Based on these findings, Section
7.3 compares welfare outcomes under property rights regimes and the open commons
regimes for a baseline set of parameter values. Section 7.4 examines the sensitivity of the

results with respect to the parameter values.

7 .1 Parameter Values Used in the Baseline Analyses

Due to the complexity of the profit functions, investigating the welfare properties of
different governance regimes by algebraically solving the models for different parameter
values is impractical. Instead, we compare computed numerical solutions for a wide
range of values for critical parameters. Tables 7.1 and 7.2 list the parameter values used
in the baseline analyses for both the models described by Equations (6.10) and (6.1 1),

respectively.

A key difficulty of this study is that for many parameters there is little information as to
what a reasonable base case value might be. When there is no literature or studies
suggesting a value for a parameter, the base case parameter value is chosen by first
limiting the possible range of values by excluding obviously unreasonable values and

then selecting the mid point value for the resulting range of values, when this approach

65

cannot be used, we start with a best guess and vary the parameter values across a wide

range to see whether the initial value chosen tilted the results.

Table 7.] Parameter Values for Baseline Case in a Two-way Point-to-Point Network

 

 

 

 

 

 

 

 

 

 

 

 

 

Category Symbol and Interpretation Parameter
Value

7p scaling factor reflecting the effect of inter-system l
interference on SIR

Technology
k: scaling factor for the effect of SIR on throughput, the 0.6
value of which depending on modulation technique used
a: intercept of the SI demand curve 100
b: slope of the SI demand curve I
x: exponent determining the relative effect of signal reach 0.5

Demand on utility
( x>l: increasing; x<l: decreasing; x=l: constant)
g: exponent determining the relative effect of throughput 0.5
on utility
F: fixed cost l0
& exponent determining the relative effect of cost of 0.9
receiver unit in the access device on robustness

Cost 2: exponent determining the relative effect of cost of 0.3
transmitter unit in the access device on transmission power
w: scaling factor for the effect of transmitter unit cost on 1
output power

Bandwidth L: total bandwidth allocated to the service 10

 

 

 

The base case value of r] is l and is varied from 0.1 to 10 in the sensitivity analysis to see

how variation in 17 changes the welfare comparison. The value of k depends greatly on

66

 

the technology, application and environment, and the initial value is chosen to be 0.6,

based on the modeling work of Mehta and Goldsmith (2001).

The effects of signal reach and throughput on utility, while both positive, are likely to be
diminishing; therefore we chose values smaller than one. Similarly, returns to investment
in robustness and transmission are likely to be positive but diminishing as well, so 5 and z
are both chosen to be smaller than one. Parameters a and b together determine market
size. We choose an initial value for b that produces a market demand curve with non—

extreme slope.

Table 7.2 lists the choice of base case parameter values for the model of a cellular-type
service. For a cellular-type network, ris at least one, and the baseline study sets it at 2.
Unlike the two-way P2P network model, I. explicitly enters into the cellular-type network
model because 2 determines the rate of attenuation for power, which depends on cell size
in this case. We choose I=ll6m for the base case value, which is the wavelength at 1.8
GHz. AS discussed in Sections 4.3, depending on per area traffic volume, total cost can
be increasing or decreasing in cell size so s3 does not necessarily have to be smaller than
zero. We start the baseline case with s3<0, and in the sensitivity analysis we will also
look at the result when s3>0. Section 6.3 states that t, the effect on total fixed cost of
increasing z'while fixing cell size, will be positive, but since the receiver antennas only
account for a fraction of total infrastructure cost, the value of this parameter Should not be

large.

67

Table 7.2 Parameter Values for Baseline Case in a Cellular Type Network

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Category Symbol and Interpretation Parameter
Value
7p scaling factor of the effect of inter-system interference on SIR l
k: scaling factor for the effect of SIR, depending on modulation 0.6
scheme

Technology 1'. ratio of downlink power to uplink power (or base station 2
robustness to that of mobile terminal)

7.: wave length of the technology employed 1/6
a: intercept of the SI demand curve 100
b: slope of the SI demand curve 1

Demand g: exponent determining the relative effect of throughput on 0.5
utility
(g>l: increasing; g<l: decreasing; g=l: constant)
s1: scaling factor determining the effect of reduce cell size on 300
fixed cost at high cell density
s2: scaling factor for the effect of s3 on fixed cost 1
s3: exponent determining the relative effect of transmission -0.3
power on fixed cost at given 2'

Cost t: exponent determining the relative effect of ton fixed cost 0.2
& exponent determining the relative effect of cost of thd 0.9
receiver unit in the access device on robustness
z: exponent determining the relative effect of cost of the 0.3
transmitter unit in the access device on transmission power
w: scaling factor for the effect of transmitter unit cost on output 1
power

Bandwidth L: total bandwidth allocated to the service 10

 

 

 

68

 

7.2 Effects of the Policy Instruments

The choice of spectrum governance regimes is as much about how to set the policy
instruments as what policy instruments should be regulated. Ideally, by controlling
policy instruments a social planner can mitigate negative extemalities and maximize
overall welfare. In reality, even with powerful policy instruments in hand, the social
planner may not have all the information necessary for welfare maximization, and this
might lead to bad policies that actually reduce welfare relative to what an unregulated
market might produce. This section provides a more complete picture of the effects of
policy instruments by showing what may happen when the policy instruments are set

optimally and when they are not.

7.2.1 Welfare Comparison of Governance Regimes

To facilitate comparisons of regimes, the typology of governance regimes in Figure 3. l is
presented again as Figure 7.1. Figure 7.2 compares the best possible welfare outcomes
(solid markers) for all eight regimes for base case parameter values and a two-way
P2Pservice. The welfare optima are achieved when the policy instruments controlled by
government are set at their optimum. The hollow markers also indicate outcomes under
property rights regimes, although in those cases the number of firms is not set at it
optimum.

Figure 7.2 illustrates several important findings of this research:
(I) The effect of robustness regulation is negligible

It might seem that only four regimes are presented here. Actually, outcomes under all

eight regimes are graphed, but the paired outcomes (Regimes I vs. 2, Regimes 3 vs. 4,

69

etc.) are so close that the difference cannot be discerned at this scale. This pattern has

been observed for all other sets of parameter values examined as well.

Figure 7.] Classification of Spectrum Governance Regimes

 

G: government G Regime 1
M: market ‘

    

 

 

 

Regime 2

Regime 3

Regime 4

Regime 5

Regime 6

Regime 7

Regime 8

Who sets Who sets Who sets
number of transmission robustness?
firms? power?

70

Figure 7.2 Welfare Optima under Eight Regimes (Two-way point-to—point network)

W Regimes 112

J

 

 

2000 - * 0 6
g g I . 6 0 o 6
a . o .
. o . . e . 6 o Regimes 576 _
’-.,°°°o¢.°\. Effectof
l '°-.,°° 6power
in. .. ..., ..., .. .. .. .. .. .. .. .. .. .. .. .. .. .- .. .. .- ._ . _. -
m, . / restrictions
. Regimes 3” Regimes 78
10110 ~ C
5.00 ..
t
r A r L - A . A . A L - n
S 10 15 20 25

71

Although the firms’ first order conditions for profit maximization are not exactly the
same with or without a robustness requirement, simulation results Show that profit-
maximizing and welfare-maximizing levels of robustness are always very close. This is
likely due to the fact that there is no Spill-over effect in robustness. As implicit in the
demand function, a firm’s choice of robustness level, unlike transmission power, does not
impact others’ profit calculations and their choices of output, transmission power or
robustness. This is because one firm’s choice of robustness does not affect the utility
experienced by other firms’ customers and because each firm’s Nash beliefs lead it to
raise its price by an amount equal to the value of improved robustness to its customers.
As a result, other firms’ sales are not affected and its value of increase robustness at the

margin is largely internalized by the firm.

Given the finding that welfare optima are very close under the paired regimes (Regimes l
and 2, Regimes 3 and 4, etc.,) in the following we will just report the welfare optimum

for the regime with robustness regulation (the odd numbered regimes).
(2) The effects of transmission power and entry regulations are interdependent

Comparing the welfare optima under different regimes can reveal the effects of individual
policy instruments. Since transmission power is set at its optimum level in both Regimes
l and 5, the difference in welfare between the welfare outcomes for these regimes is the
effect of limiting entry. Similarly, the difference between Regimes l and 3 (as well as

between Regimes 5 and 7) is the effect of transmission power regulations.

Obviously, the effect of transmission power regulations on welfare depends on the

number of firms in the market. When the number of firms is set at 6, which is the

72

optimum number for Regimes I-4, the welfare difference iS relatively small (1,927 for
Regime 3 vs. 1,970.4 for Regime 1, or about 2.2%), and the difference increases with the
number of firms. In an open commons regime, where the number of firms is larger, the
potential welfare improvement from regulating transmission power is larger (1,547.4 for
Regime 3 vs. 1,652.8 for Regime l, or 6.4%. Depending on parameter values, this
difference can be as much as 58%.) This makes intuitive sense. The negative extemality
associated with power increases with the number of firms; therefore the benefit of
limiting that negative extemality should be greater when there are more firms competing

with each other.

(3) The potential loss associated with a “tragedy of the Spectrum commons” is not great

for most sets of parameter values

The notion of a “tragedy of the Spectrum commons” hinges on the prediction that there
will be excessive entry and an escalating power war resulting in excessive interference.
1f the predicted tragedy is about a power fight that negatively affects social welfare, the
results seem to suggest that its potential magnitude is not as dramatic as the term

“tragedy” implies.

When the government controls power in a spectrum commons (Regime 5), the difference
between the welfare outcome and the global maximum (Regime l), i.e. the effect of n,
mostly has to do with redundant investment in fixed costs, an effect not unique to
spectrum and the wireless industry. This examination of theoretical optima suggests that
the potential loss associated with a “tragedy of the commons” is not great when

government sets power.

73

Figure 7.3 shows how the welfare-maximizing values of receiver cost (CR), which is a
proxy for robustness, and transmitter cost (c7), which proxies transmission power, vary
with the number of firms when the government sets both cR and c7 (Regime l), and
Figure 7.4 shows the relationship between the welfare-maximizing cR and n when or is

set by firms (Regime 3). The two patterns for cR are very similar.

Figure 7.3 Welfare-Maximizing cR and cr as a function of n

CT/CR

40
35 CR

.........,.eeoeooeeeoeeeooo

30

25

20 CT
.0000.00000000000000.000...

15

10

S
- - - . . n

S 10 15 20 25

 

Figure 7.4 Welfare-Maximizing CR and Profit-Maximizing c1 as a function of n

 

 

40 CR

351 ..,ooo'v'°00°ovoo..-v-.

30E .........ooooeooooo
O

25 .. CT

20 ’

e

15*

10,

S
5 10 15 20 25 n

74

Figure 7.3 suggests that the optimal or should not vary much with the number of firms.
However, when cr is set by firms, Figure 7.4 shows there indeed will be a power war that
escalates as the number of firms increases, which is what leads to the welfare difference
between the two trend lines in Figure 7.2. When the number of firms is small, price is
higher and the overall number of devices and the aggregate interference in the market is
small. At this stage, interference is less of a problem, and by reducing cn and price, the
increase in the number of users and its positive welfare effect outweighs the cost of the
increase in interference due to more devices. As the number of firms increases,
countering interference becomes more important than increasing the number of users and
the welfare-maximizing ck increases as well. This is why in both Figures 7.3 and 7.4 the
welfare-maximizing cR first declines and then goes up again as the number of firms

increases.

Similar patterns are observed with a cellular-type network (Figures 7.5, 7.6 and 7.7).
Again, the welfare outcomes with and without robustness requirements are too close to
distinguish, and the potential benefit of regulating transmission power is dependent on

the number of firms in the market.

Whereas in the two-way point-to—point network model it is the benefits of increased
communication range and throughput that motivate firms to increase power, in the
cellular-type network the incentive to increase power comes from lower infrastructure
costs and higher throughput. Although a smaller cell size can reduce interference, it
requires higher base station density across the service area and leads to higher total fixed
cost. Similar to Figures 7.3 and 7.4, Figures 7.6 and 7.7 Show the welfare-maximizing c1

and cR as functions of n for Regimes l and 3, respectively. The gradual increase in the

75

optimal cr in Regime 1 indicates that the welfare gain associated with smaller cell size
and less interference is outweighed by the increase in fixed cost resulting from smaller
cells. Under Regime 3, where firms set their own power, the incentive to use higher
power to reduce fixed cost is even stronger when the number of competitors is larger,

since competition reduces individual firms’ revenues.

Figure 7.5 Welfare Optima for Eight Regimes (Cellular-Type Network)

 

 

Regimes 1/2
" l
1400 3 s f g 0
I \ 0 <3 0 Regimes 516
1200 F o o O O l
L - ._ - - - - - Regimes—3141 ........ ° _ _ ,¢_— Effectofpewer
1000 f restrictions
800 Regimes 718
600
400 g
r- i
4'00 f
l
’ T ‘ n
2 4 6 8 10

76

Figure 7.6 Welfare-Maximizing cR and c1 as a function of n (Cellular-Type Network)

CT/CR

 

 

25
9R
20 , . .
15
10
ct .
s
o 0 . . . .
0 ° o
A A A = A n
2 4 6 8 10

Figure 7.7 Welfare-Maximizing cR and Profit-Maximizing c1 as a function of n (Cellular-
Type Network)

cT/cR

 

 

25 r
. CR
20 : . o P ' ' . .
r O
i .
i
i
15 t
i
10 i Cf
b . O O
I , ° °
5: . °
r e
t .
2 4 6 8 10 n

Underlying the comparisons just presented is the assumption that no errors are made in
setting govemment-controlled policy variables. The next subsection discusses the

potential loss associated with errors in setting the policy instruments.

77

7.2.2 Effects of Poor Policy Choices

When set at levels that depart significantly from their optimum values, government
control of all three policy instruments can have significant negative impacts on social

welfare.

Figure 7.8 shows for the direct two-way P2P model under Regime 1 (all three variables
set by government) how welfare varies with CR and c1 when n=6. At low cR levels (left
edge of the contour map), loss associated with interference more than offsets the benefit
of lower cost and more affordable devices. In this region increasing cR improves both
profits and social welfare. The dashed line in Figure 7.8 labeled cR(c7~) gives the profit-
maximizing value of cR for each value of 67‘. Similarly, the dashed line in Figure 7.8
labeled c1(cR) gives the profit-maximizing value of CT for each value of cR. Because
robustness requirements only set a lower bound on robustness, in the region to the left of
cR(cT), firms can do better by setting robustness above the floor. Any cR requirement in
this region has no effect. The arrows pointing to cR(c1) indicate this tendency. Only
when the govemment-set cg exceeds the profit-maximizing level of cR are an
requirements binding and firms are forced to invest more in robustness than they would
in the absence of robustness requirements. However, welfare does not increase with
robustness indefinitely. Beyond a certain level, the welfare increase associated with the
reduced interference is outweighed by the loss associated with the users who are driven

out of the market by a higher price, and welfare drops as a result.

Similarly, when CT is set too low (lower edge of the contour map), society suffers from
under-investment in transmission power because the reduction in utility associated with

lower power and shorter transmission range is greater than the gain from reduced

78

interference and lower cost for the transmitter unit. In the region below C7(cR), the CT
limits are binding and firms can only produce devices with very low transmission power,
which have little value to customers and firms’ profits suffer too. In the lower part of this
region, government can improve both welfare and firm profits by relaxing the power
limit. However, when the power limit is relaxed beyond the welfare-maximizing level,
firms will take advantage of it and produce devices that transmit at overly high power
levels and reduce welfare. This is shown by the fact that c1(cR) is located above the
welfare optimum. When the cr limit is set above c1(cR), the or limit is also non-binding
and firms will choose the profit-maximizing levels of 03, a tendency indicated by the

downward-pointing arrows.

Figure 7.8 Welfare as a Function of CR and CT for n :6 under Regime l

 

70 7I l V'I'Vfi' V’V’1'V‘r'l V‘ I

 

 

 

 

Together, c7(cR) and cR(cT) divide the graph into four regions. In the lower right region
both power and robustness restrictions are binding. On the other hand, since neither a
power cap higher than the profit-maximizing c1 nor a robustness requirement lower than
the profit-maximizing cR is binding, any government requirements in the two upper
regions will lead to equilibrium outcomes on c1(cR) and any government requirements in
the two left regions in the figure will lead to equilibrium outcomes on cR(cT). Any
combination of government requirements in the upper-left corner will lead to market

equilibrium at the intersection of c1(cR) and cR(cT).

The difference between the maximum welfare and welfare at the profit-maximum is the
potential gain from regulating ck and c1, and the difference between welfare at the profit-
maximum and any point in the lower right region outside of the inner most contour is the
potential harm from errors in setting the policy instruments. Similar patterns can be
observed for all values of n. Obviously, the potential gain from regulating cR and cr is
smaller than the potential harm of setting them incorrectly although the potential gain of
regulating c1 becomes greater as n increases. This is essentially the same finding as seen

in Subsection 7.2.1.

Figure 7.9 presents the relationship between welfare and govemment-set n and c1- when
firms set cR (Regime 2). The dashed line labeled as c1(n) is the profit-maximizing level
of transmission power at any given n. Similar to the analysis of Regime I, when
govemment-set cT falls to the right of c7(n), the power restrictions have no effect and
firms will set transmission power on c1(n). Figure 7.9 suggests that the potential benefit

of power restrictions is not large, but under-investment in transmission power due to

80

incorrectly set or can significantly reduce welfare. When the predetermined number of

firms is far from the optimum, welfare is also considerably lower.

The relationship between welfare and govemment-set n and CR under Regime 3 when
firms set cr is shown in Figure 7.10. The dashed line labeled as cR(n) is the profit-
maximizing level of robustness at any given n. When govemment-set cR falls to the left
of cR(n), the robustness requirements have no effect and firms will set robustness on
cR(n). The danger of setting robustness overly high or setting n at extremely low values

can also be significant.

Figure 7.9 Welfare as a Function of n and or under Regime 2

 

 

 

 

 

81

Figure 7.10 Welfare as a Function of n and cR under Regime 3

 

 

 

 

 

7.3 Ownership vs. Commons

Figure 7.1 1 compares welfare outcomes for Regime 2 (ownership regime with no
robustness requirements) and Regime 6 (open commons with no robustness
requirements). The contour map shows welfare levels for government set n and c1 levels.
Since the difference between them is that n is set by the government in the ownership
regime while in the commons regime it is left for the market to decide, the open
commons boundary is characterized by the set of zero-profit equilibria under the

ownership regime.

In the absence of power restrictions and robustness requirements, for each n there is a

profit-maximizing value of CT, indicated by the dashed line labeled as c;(n), which tends

82

to exceed the welfare-maximizing level of or. For example, if government sets n=15 and
c7: cT’, firms will find it more profitable to produce devices with lower transmission
power because cr’ is to the right of c7(n). Since a power limit does not prevent firms

from lowering power, the Regime 2 property rights equilibrium will be at point B.

Same as under an ownership regime, when c1 under the open commons regime is set at
cT’, which is to the right of c7(n), the power restriction is not binding as the profit-
maximizing CT is lower than cT’. Firms will depart from cr’ and set power levels on c7(n),
moving from point D on the open commons boundary to point C. This move will yield
higher profits but give room to new entrants as point C is below the open commons
boundary, indicating more firms can enter the market profitably. Consequently, the
number of firms will keep increasing until it hits the open commons boundary again
(moving from point C to point A). Similarly, for any CT to the right of c7(n), the open
commons equilibrium will be at point A. The welfare level at point A iS marked as the

thick welfare contour for comparison with the ownership regime.

Obviously, the welfare level at point B is greater than that at point A, indicating better
performance under the ownership regime. It can be seen from the graph that except when
n is very small, the equilibrium always falls within the thick welfare contour. In other
words, given the same cr restrictions, unless n under the ownership regime is set
significantly below the optimal n, an ownership regime always performs better than an
open commons regime. Moreover, given the same CT on the left-hand side of the locus of
profit-maximizing cT’x, Figure 7.11 also suggests that the ownership regime tends to

outperform the commons regime as long as n is not set too low.

83

Figure 7.11 Spectrum Ownership vs. Open Commons

 

Open
commons
/ boundary

 

 

 

 

cT'

7 .4 Parameter Values and Sensitivity

This subsection examines the sensitivity of the welfare comparisons to variation in
parameter values. The parameters will be examined one at a time, and except for the

variable under discussion all the others will be held at the baseline case values.

Table 7.3 reports the results of the sensitivity analysis and provides definitions for the
parameters varied for the direct two-way P2P network model. MW Stands for maximum
welfare with a subscript indicating the regime to which it applies. For example,

MWchimm/z refers to the maximum welfare for Regimes l and 2. n indicates the number

84

of firms at these welfare maxima. The results for the baseline case are italicized. The
entries in the data (number of firms and welfare) cells corresponds to the parameter
values listed under the parameter definition (in the same order). Since the outcomes with
and without robustness regulations are very close, results for Regimes 1 and 2 (Regimes
3 and 4, etc.) are combined in the table. To facilitate comparison, the MW outcomes

under various regimes are also reported as percentages of the global optimum welfare

(MWRegimel /2) in the parentheses following the absolute welfare values.

The results for varying b Show that when market demand becomes very flat the welfare
under an unconstrained open commons regime (Regime 8) can deviate significantly from
that under an ownership regime with all policy variables set at their optimum (Regime 1).

For example, at b=0.01 the unconstrained commons welfare is only about 42.2% of the
global optimum. By comparing MwRegime5/6 to the global optimum, we can see that the
effect of entry restrictions is greater when the demand is flatter. Similarly, comparison of
MWRegime5/6 and MWRegime7/8 shows the effect of power regulations, which is also

stronger with a flatter demand.

Because it affects the number of firms an open entry market can support, F does seem to
have some effect on the relative merits of the regimes in non-extreme ranges. When F
becomes larger, welfare under Regime 6 as a percentage of the global optimum drops
from 92.8% to 79.6%, indicating that open commons (even with power control) is less

attractive relative to ownership when fixed costs are high.

A larger 77 means lower level of spillover signal power from neighboring systems in the

spectral space. Obviously, a larger 7] will be associated with higher welfare outcomes

85

and the band can support more firms. It is also not surprising to see that the difference

between MwRegime5/6 and the global optimum increases as 77 goes down, since a smaller

77 means more interference and the beneficial effect of limiting entry will be more

pronounced. Similarly, comparing MwRegime5/6 to MWRegime7/8 while varying n
shows the effect of power restriction is also bigger at smaller values of 77.

Because k is a constant multiplier of the SIR term in the demand function, a larger k
reduces the effect of interference on throughout and user utility and hence leads to greater

welfare. Similar to the pattern described for 77, a greater value for k is also associated
with a smaller difference between MwRegime5/6 and the global optimum. This means

that the potential benefit of restricting entry diminishes with k. On the other hand, the

differences between MWRegime5/6 and MwRegime7/8 are small so the effect of k on the
effectiveness of power restrictions is not significant.

x reflects the relative effect of signal reach (which is assumed to be a function of power,
or CT) on utility. A larger value for x means that utility increases more rapidly with
power. x’s effect on the relative advantages of regimes and the benefits of regulations of

entry and power is also unclear, as when we vary the value of x, the difference between

MWRegime5/6 and MVVRegime7/8 is very small.

On the other hand, the results suggest that increasing g, which means that utility increases
more rapidly with throughput, leads to greater loss associated with open entry. However,

the effect of g on the effectiveness of power restrictions is also not clear as the difference

86

6 determines the relative effect of investment in receiver quality on robustness. When
firms can more effectively improve robustness by investing in receiver units, welfare
tends to increase and the effects of power and entry regulations on welfare are smaller.

These results are fairly intuitive.

Lastly, 2 Shows how effectively investment in cost for the transmitter unit can increase

power. Comparing MwRegime5/6 (or MWRegime7/8) to the global optimum shows that

when it is less costly to boost power (2 is smaller), the relative welfare difference between

and MwRegime5/6 gets bigger, so does the difference between MwRegime5/6 and

MWRegime7/8. These patterns suggest that entry and power restrictions are more
desirable when firms can increase power at lower cost.

In summary, the major findings of the study are as follows: First, left to themselves, firms
do have an incentive to produce devices transmitting at power levels significantly in
excess of the welfare-maximizing level. This can be countered by setting power limits;
however, in an unconstrained open access regime, the greatest potential improvement
achievable by setting power limits alone is smaller than that from setting entry
restrictions alone. The potential benefit of setting power limits is further reduced as the
govemment-set number of firms approaches the optimum. Second, robustness
regulations can do little to improve welfare but might have very negative impacts when

set inappropriately.

These observations hold across the parameter ranges examined in the sensitivity analysis.
Three factors have a particularly strong effect on the relative advantages of commons and

open access regimes: the flatness of the demand curve, the level of inter-system

87

interference (interference from neighboring systems in the spectral space) and the cost—
effectiveness of investment in transmitters to increase power. Ceteris paribus, the
difference between the welfare performance of an ownership regime with its govemment-
set policy instruments set optimally and the corresponding open access regime increases
the smaller is b. In addition, the welfare difference between an ownership regime with all
policy instruments set at their optimal values by the government and the unconstrained
open access regimes increases considerably (up to about 40%) as the level of inter-system

interference goes up or as increasing transmission power becomes less costly.

Table 7.4 shows the result of sensitivity analysis for the cellular-type network model.
The effects of b, r], k, 6, z and g on the welfare comparison of regimes are quite

consistent with what was found for the two-way point-to-point network model.

Because higher frequency signals attenuate faster, at a wavelength (xi) of 1/800 m (2.4
GHz) path loss is much greater than that for the base case, where )1 is 1/3 m (900 MHz).
Therefore, welfare levels are significantly lower for xi = 1/800 m for all regimes, but the

little variation in relative welfare levels under different regimes suggests this factor do

not have much impact on the choice of regimes.

The finding that welfare increases with tsuggests the use of more sensitive antenna
arrays at base stations has positive welfare impacts, although at some point this gain
presumably will be outweighed by the higher cost of more sensitive antennas. Also
relevant is the effect of t, which reflects the rate at which fixed cost increases with the use

of more sensitive antenna arrays at base Stations. Higher t means fixed cost increases at a

88

faster rate, and not surprisingly, we find that welfare is declining in t. However, neither 2'

nor t seem to have significant impact on the relative merits of the regimes.

s3, which is negative is fixed cost is decreasing in cell Size (this would be the case if
traffic volume is low) and positive when fixed cost increases with cell size (this would be
the case if traffic volume is high), does not seem to have much impact on either welfare

magnitudes or the relative merits of the regimes, although the difference between

MWRegimeI/z and MWRegime5/6 increases moderately with 33, suggesting that it may be

desirable to restrict entry when fixed cost increases with cell size. s2 is a scaling factor
for the term describing the effect of cell size on fixed cost and its impact depends on the

value of s3. In general, increasing s2 increases fixed cost and the gap between

MWRegime 1 [2 and MWRegime5/6a but the change is rather small. Comparing

MWRegime5/6 to MwRegime7/8, we find little evidence suggesting a significant impact of

s2 and 53 on the effectiveness of power restrictions.

89

Table 7.3 Result of Sensitivity Analysis (two-way point-to-point type network)

 

 

 

 

 

 

 

 

 

 

b: the slope of the F : fixed cost 1; scaling factor k: a constant
demand curve of the multiplier of
_ interference aggregate
(b = 0 01 0 1 I (Ir—1' 10' ‘00) effect of interference,
10) ’ ' ‘ ' neighboring affecting the
systems in the effect of SIR on
spectral space throughput
on SIR
(k=0.3, 0.6. 0.9)
(11:01. 1, 10)
4 8 2 6
n .
Regrmel/2 4 6 6 6
6 4 32 6
4
2763.7 2027.7 1186.6 1219.1
MW -
Reg'mem 2714.7 1970.4 1970.4 1970.4
1970.4 1551.5 4570.2 2541.1
639.1
4 6 2 5
nRegime3/4 4 6 6 6
6 4 30 6
4
MW , 2659.5 (96.2%) 1980.9 (97.7%) 1170.5 (98.6%) 1187.9 (97.4%)
Reg‘me3/4 2685.5 (98.9%) 1926.9 (97.8%) 1926.9 (97.8%) l926.9 (97.8%)
1926.9 (97.8%) 1527.9 (98.5%) 4497.5 (98.4%) 2493.8 (98.1%)
636.4 (99.6%)
. 40 26 18 19
“Reg"“e5/6 41 26 26 26
26 8 43 31
4
MW . 1323.6 (47.9%) 1886.7 (93.0%) 773.0 (65.1%) 985.4 (80.8%)
Regime5/6 1708.3 (3.6%) 1652.8 (85.8%) 1652.8 (85.8%) 1652.8 (85.8%)
1652.8 (85.8%) 1235.7 (79.6%) 4533.9 (99.2%) 2179.1 (85.8%)
639.1 (100%)
_ 40 26 18 19
nRegrme7/8 41 26 26 26
26 8 43 31
4
MW _ 1165.1 (42.2%) 1781.4 (87.9%) 697.7 (58.8%) 912.1 (74.8%)
Regime“ 1511.8 (55.7%) 1547.4 (78.5%) 1547.4 (78.5%) 1547.4 (78.5%)
1547.4 (78.5%) 1177.4 (75.9%) 4443.6 (97.2%) 2060.9 (81.1%)
636.4 (99.6%)

 

 

 

 

 

90

 

Table 7-3 Result of Sensitivity Analysis (two-way point-to-point type network)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(Continued)

x: exponent g: exponent 6: exponent z: exponent
determining the determining the determining the determining the
relative effect relative effect of relative effect relative effect of
of signal reach throughput on of receiver cost transmitter cost
on utility utility for access for access device

device on on transmission

(x=0.25, 0.5, (g=0.5. 1) “’busmess WW"

0.75) (6 =0.3, 0.6, 0.9)
(z=0.3, 0.6, 0.9)

, 6 6 4 6
n Regrmel/Z 6 6 6 6
6 6 6
1326.5 1970.4 550.2 1970.4

MW '
Reg‘mcm 1970.4 1458.4 975.3 7868.3
3533.8 1970.4 101171
. 6 6 4 6
nRegrme3/4 6 S 5 6
6 6 4
MW _ 1279.1 (96.4%) 1926.9 (97.8%) 543.4 (98.8%) 1926.9 (97.8%)
Regm‘fi/4 1926.9 (97.8%) 1410.4 (96.7%) 953.9 (97.8%) 7467.1 (94.9%)
3478.1 (98.4%) 1926.9 (97.8%) 93227.7
(92.1%)
_ 21 26 12 26
"Reg‘mesm 26 20 17 50
36 26 159
MWR _ 5/6 1122.4 (84.6%) 1652.8 (85.8%) 444.0 (80.7%) 1652.8 (85.8%)
614"“ “552-8 (353%) 1324.6 (90.8%) 732-5 (802%) 6495.3 (82.6%)
2925.5 (82.8%) 1652.8 (85.8%) 77887.1(77.0%)
_ 21 26 12 26
“Reg‘mem 26 20 17 50
36 26 159
MW _ 1024.9 (77.3%) 1547.4 (78.5%) 412.3 (74.9%) 1547.4 (78.5%)
Reglme7’8 1547.4 (78.5%) 1034.7 (70.9%) 720.6 (73.9%) 5395.9 (68.6%)
2764.3 (78.2%) 1547.4 (78.5%) 52756.8 (52.1%)

 

91

 

Table 7.4 Result of Sensitivity Analysis (Cellular-Type network)

 

 

 

 

 

 

 

 

 

 

s2: scaling s3: exponent 2: ratio of r: exponent L-
factor for the determining downlink to detemiining wavelength
effect of 33 the relative uplink the relative
on fixed effect of power effect of 1'
cosst transmission on fixed (’1': I/ 6'
power 0“ ( 1:1 2 3) cost “800)
(s2=l, 10, 5.2:?“ at ' '
100) 3‘ (1:02, 0.5)
(33: 0.3.
0.1, 0.5)
3 3 2 3 3
2 3 3
MW , 1456.4 1456.4 1029.8 1456.4 1456.4
Reg'mel/z 1432.3 1454.8 1456.4 1416.0 881.3
1250.6 1453.2 1625.5
. 3 3 2 3 3
nRegime3/4 2 3 3 3 2
2 3 -
MW _ 1405.8 1405.8 1014.6 1405.8 1405.8
Reg'me3/4 (96.5%) (96.5%) (98.5%) (96.5%) (96.5%)
1383.5 1404.6 1405.8 1371.6 868.5
(96.6%) (96.5%) (96.5%) (96.9%) (98.5%)
1223.4 1402.9 - ()
(97.8%) (96.5%)
_ 10 10 5 10 10
nReg1meS/6 9 10 [0 9 8
5 10 I 3
MW . 1066.9 1066.9 786.4 1066.9 1066.9
RegImCS/G (73.3%) (73.3%) (76.4%) (73.3%) (73.3%)
1056-6 1054.6 1066.9 1059.4 616.9
(733%) (72.5%) (73.3%) (74.8%) (70.7%)
945.0 1025.3 1189.3
(75.6%) (70.5%) (73.2%)
_ 10 10 5 10 10
nReg1me7/8 9 10 lo 9 8
5 10 13
MW . 1036.0 1036.0 766.7 1036.0 1036.0
Reeling/3 (71.1%) (71.1%) (74.5%) (71.1%) (71.1%)
1020.2 1031.0 1036.0 1020.2 599.2
(71.2%) (70.9%) (71.1%) (72.0%) (68.0%)
894.8 1023.1 1158-4
(71.5%) (70.4%) (71-3%)

 

 

 

 

 

 

92

 

Table 7-4 Result of Sensitivity Analysis (Cellular-Type network) (Continued)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

g: exponent 6: exponent z: exponent 17: scaling k: a constant
determining detemtining determining factor of the multiplier of
the relative the relative the relative interference aggregate
effect of effect of effect of effect of interference.
throughput receiver cost transmitter neighboring affecting the
on utility for access cost for systems in the effect of SIR

device on access device spectral space on
_ robustness on on SIR throughput
(3—0'5’ ]) (6 :03. 0.6, transmission
09) Power (17:01. 1, 10) (k=0.3, 0.6,
0.9)
(z=0.3. 0.6,
0.9)
_ 3 2 3 2 2
n Reg1mel/2 3 2 3 3 3
3 3 8 3
MW . 1456.4 465.2 I 456.4 949.7 923.9
Reg'me ”2 1456.0 795.4 1491.1 1456.4 1456.4
1456.4 1506.2 2363.7 1811.5
. 3 2 3 2 2
nReg1me3/4 3 2 2 3 3
3 2 8 2
MW _ [405.8 456.4 1405.8 909.9 (95.8%) 902.3
R881m63/4 (96.5%) (98.1%) (96.5%) 1405.8 (97.7%)
1405.8 795.0 1373.2 (96.5%) 1405.8
(96.5%) (100%) (92.1%) 2341.6 (96.5%)
1405.8 1319.4 (99.1%) 1758.9
(96.5%) (87.6%) (97.1%)
n , 10 6 10 7 8
Regime5/6 10 7 15 10 10
10 16 15 1 1
MW , 1066.9 287.0 1066.9 600.7 (63.3%) 650.4
Regime5/6 (73.3%) (61.7%) (73.3%) 978.0 10669 (70.4%)
1060-0 557.0 (656%) (73.3%) 1066.9 (73.3%)
(723%) (70.0%) 1 '32-9 2190.0 1360.3
10669 (752%) (92.6%) (75.1%)
(73.3%)
n . 10 6 l0 7 8
Reg'me7/8 10 7 15 10 10
I 0 16 15 1 1
MW . 1036.0 280.9 (60.4%) [036.0 569.6 (60.0%) 620.8
Reg‘mem (71-1%) 561.1 (70.5%) (71-1%) 1036.0 (672%)
1036.0 ,0 361, 907.7 (60.9%) (71.1%) 1036.0
(71.2%) (“1%) 731.2 (48.5%) 2167.3 (71.1%)
(917%) 1343.9
(74.2%)

 

93

 

Chapter 8 Conclusions

8.1 Summary of the Dissertation

Up to this point, most studies in this area have taken a top-down approach and sought to
predict the relative merits of the regimes based on broad, general assumptions. This

study takes a different approach and aims at identifying key policy instruments of 1‘
spectrum governance regimes and examining how these policy instruments affect welfare

outcomes under different regimes.

 

The present study starts out by summarizing the major proposals for alternative spectrum
governance regimes; this leads to identification of three key policy instruments: entry
restrictions, transmission power controls, and robustness requirements. A typical
property rights regime is characterized by government control over both entry conditions
and transmission power, while the entry condition in a commons regime is determined by
the market instead. The variants of regimes with robustness requirements are also

included for studying of the effect of robustness requirements.

The study also looks at the engineering aspect of spectrum management, exploring the
relationships between the engineering properties of wireless communication and the
policy instruments. Based on an examination of these relationships, an economic model
of a market for a wireless service is constructed, which serves as a framework for tying
together policy instruments and their impact on firms’ profit-maximizing actions as well
as welfare outcomes.

Analysis of the welfare outcomes gives the following findings. First, government

regulation on robustness is undesirable. Second, the potential benefit of power

94

restrictions increases with the number of firms in the market. Next, when set incorrectly,
all three policy instruments can cause significant welfare 1088. Moreover, comparison of
a prototype property rights regime and a prototype commons regime suggests, given the
same power restrictions, that the property rights regime tends to outperform the commons
regime as long as the number of firms is not set significantly below the optimum number,
which is often a small fraction of the number that can be supported with an open
commons. These observations on the effect of fundamental policy instruments and the

theoretical framework are the major conclusions of this study.

8.2 Future Research

This study is the first of its type. As an explorative study, it employs some simplifying
assumptions to help keep the analysis tractable. Some of these assumptions, however,
put limits on the generality of the findings. Specifically, the services modeled in the
study are homogeneous, and the equilibria examined are outcomes of one-shot games
among firms with identical cost structures. These assumptions rule out the possibility of
investigating a market in which spectrum blocks can be dynamically reallocated to other
services and firms can trade their blocks as they see fit. Such a possibility, however, is
the major selling point of the spectrum property rights proposal; therefore it is desirable

to relax these limiting assumptions.

There are two approaches to tackling the problem of non-identical firms and
heterogeneous services. First, as commonly seen in economic and engineering studies,
we can start with a two-firm, two-service model, which is a common compromise
between tractability and generality. For such simplified setting, it is also possible to

extend the model to a two-period game, which can be used to examine dynamic aspects

95

of market development. Alternatively, with more advanced analytical tools, e. g.
multiobjectivity optimization techniques, the optimization procedures can be less time-
consuming and the computed results can be more accurate. The major difficulty of this

approach is that it is very mathematically involved.

Another direction for extending the study is to examine how network effects and scale
economies affect the findings. Network effects tends to increase utility, and scale

economies tend to reduce costs as the number of users increases. Both of these factors
contribute to firms’ incentive to expand output; therefore studying their impacts on firms’
output decisions in a dynamic setting can further our understanding of optimal policy

choices for spectrum governance.

96

Appendix I Implementing Calculations for Equilibria

Direct Two-way P2P Network

Regime l

1.

Plug the chosen parameter values into the profit function

. Den've the first order condition with respect to q,-

Choose a region of feasible combinations of CT and CR where the equilibrium q*,
01 and we make economic sense (q* >2 so that communication is possible between

users; 07 >1 and cR>l)

Choose a scanning resolution, which determines the number of equilibrium points

calculated within the feasible (c1, CR) region.

Apply symmetry conditions so that all firms’ output, transmission power and

robustness levels are the same
For 11 starting from one, perform the following steps:

i. With the scanning resolution chosen in Step 4, for each (c7, 611) point
in the region of (61, CR) chosen in Step 3, solve the first order condition

derived in Step 2 for equilibrium q*

ii. Derive equilibrium price and profit at each (CT, 0);) point by plugging

q*, c1 and CR back to the demand and profit functions

iii. Calculate equilibrium total output Q* at each (cT, cR) point

97

iv. Derive equilibrium welfare at each (CT, CR) point using Equation (6.8)

and Q*, q*, c1 and CR

v. If the maximum equilibrium profit is positive,lo increase 11 by one and

repeat these five steps

For all the procedures described in this section, some pilot simulations are needed to

ensure all feasible combinations of (CT, CR) are covered.
Regime 2
1. Plug the chosen parameter values into the profit function

2. Derive the first order conditions with respect to ql- and cm

3. Choose a region of feasible range of or where the equilibrium q* >2 and cR* >1

4. Choose a scanning resolution, which determines the number of equilibrium points

calculated within the feasible cr range.

5. Apply symmetry conditions so that all firms’ output, transmission power and

robustness levels are the same
6. For 12 starting from one, perform the following steps:

i. Scan the chosen region of CT. At each 67‘ point, solve the first order

conditions derived in Step 2 for equilibrium q* and cR*

ii. Derive equilibrium price and profit at each CT point by plugging q*, or and

cR* back to the demand and profit functions

 

'0 Since there can be numerous feasible combinations of (Cr, CR), there will be multiple equilibria under
Regime l.

98

iii. Calculate equilibrium total output Q* at each cT point

iv. Derive equilibrium welfare at each c1 point using Equation (6.8) and Q*,

q*, c1 and cR*

v. If the maximum equilibrium profit is positive, increase 11 by one and

repeat these five steps

Procedures for calculating equilibrium outcomes under Regime 3 is the same except that

the roles of c1- and CR are exchanged.
Regime 4

1. Plug chosen parameter values into the profit function

2. Derive the first order condition with respect to q), CT.- and CR,-

3. Apply symmetry conditions so that all firms’ output, transmission power and

robustness levels are the same

4. For 11 starting from one, perform the following steps:

1. Solve the first order conditions derived in Step 2 for equilibrium q*,
61* and C R*
ii. Derive equilibrium price and profit by plugging q*, 07* and cR* back

to the demand and profit functions

iii. Calculate equilibrium total output Q*
iv. Derive equilibrium welfare using Equation (6.8) and Q*, q*, c7* and
CR*

99

v. If the equilibrium profit is positive, increase 11 by one and repeat these

five steps

In this regime, three equilibrium conditions are available to solve for equilbrium value of

three variables; therefore for each n there is only one unique equilibrium.
Regimes 5-8

The difference between Regimes l and 5 is that n is determined by market forces in
Regime 5. This means that the equilibria in Regime 5 are the set of zero-profit equilibria
under Regime 1. Therefore the equilibria under Regime 5 can be obtained by collecting

the zero-profit equilibria under Regime 1.

Similarly, equilibria under Regime 6/7/8 can be obtained by collecting zero-profit
equilibria under Regime 2/3/4 because Regime 6/7/8 differs from Regime 2/3/4 only in

that it has to meet the additional condition of zero-profit.

100

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