Federal Communications Commission

Office of Strategic Planning and Policy Analysis

445 12th Street, SW

Washington, DC 20554

OSP Working Paper Series

41 Enhancing Spectrum’s

Value Through Marketinformed Congestion 

Etiquettes 

February 2008

Mark M. Bykowsky

Kenneth R. Carter

Mark A. Olson

William W. Sharkey
Enhancing Spectrum’s Value Through

Market-informed Congestion Etiquettes

Mark M. Bykowsky

1

Office of Strategic Planning and Policy Analysis

Federal Communications Commission

Washington, D.C.

Kenneth R. Carter

WIK

Mark A. Olson

George Mason University

Arlington, Virginia

and

William W. Sharkey

Wireline Competition Bureau

Federal Communications Commission

Washington, D.C.

February 2008

OPP Working Paper No. 41

1 The authors would like to thank Weiren Wang, William Lehr, and Charles Needy for very helpful 

comments on an earlier draft. Mark Olson participated in this project under a contract with the FCC, while 

Kenneth Carter participated in this project as an employee of the FCC. This document is available on the 

FCC’s World Wide Web site at http://www.fcc.gov/osp/workingp.html. 

The FCC Office of Strategic Planning and Policy Analysis’s Working Paper Series 

presents staff analysis and research in various states. These papers are intended to 

stimulate discussion and critical comment within the FCC, as well as outside the 

agency, on issues in communications policy. Titles may include preliminary work 

and progress reports, as well as completed research. The analyses and conclusions 

in the Working Paper Series are those of the authors and do not necessarily reflect 

the view of other members of the Office of Strategic Planning and Policy Analysis, 

other Commission Staff, or any Commissioner. Given the preliminary character of 

some titles, it is advisable to check with the authors before quoting or referencing 

these working papers in other publications.
Abstract

This paper evaluates the ability of different wireless spectrum congestion etiquettes 

to promote the efficient use of wireless spectrum in the presence of licensed and 

unlicensed operations. Under the examined environment, theory predicts that society 

leaves half of the value it can receive from spectrum “on the table.” One new approach 

utilizes various types of user information to address the inefficient use problem. The 

superiority of this new class of etiquette is established both in theory and by experimental 

results. Assuming a close similarity between the naturally occurring environment and the 

experimental one, analysis reveals that the average efficiency of the existing etiquette 

employed in most unlicensed equipment is 42%. In comparison, experimental analysis 

reveals that the average efficiency of one market-informed etiquette - the Informed 

Greedy Algorithm - is 70%. These results form the factual basis for generating an 

entirely new type of spectrum allocation wherein a given band of spectrum is treated as a 

common pool resource in the absence of excessive spectrum congestion, but is treated as 

an excludable private good in the presence of such congestion.
TABLE OF CONTENTS

1 Introduction ................................................................................................................1

2 Formal Analysis of the Tragedy of the Commons.....................................................2

2.1 A Simplified Model ...................................................................................................... 3

2.2 Tragedy of the Commons Problem: Nash Prediction............................................... 6

3 Congestion Etiquettes.................................................................................................8

3.1 Enhancing Efficiency By Changing Strategy Payoff................................................. 8

3.2 Enhancing Efficiency Via Rationing – Randomization ............................................ 9

3.3 Enhancing Efficiency Via Rationing – Willingness to Pay..................................... 12

3.4 Congestion Etiquettes – Nash Predictions ............................................................... 14

4 Experimental Analysis – Congestion Etiquette Performance.................................16

4.1.1 No Exclusion Etiquette – Fairness and Pay to Connect.........................................................17

4.1.2 Exclusion Etiquettes..............................................................................................................18

4.1.2.1 Randomization Etiquette .......................................................................18

4.1.2.2 Lump Sum WTP-based Greedy Algorithms .........................................20

4.1.2.3 Unit-based WTP-based Greedy Algorithms..........................................21

4.1.2.4 WTP-based Full Optimization Algorithm.............................................22

4.2 Experimental Results................................................................................................. 23

4.3 Concluding Comments............................................................................................... 26

Appendix A: Figures and Charts.....................................................................................28

Appendix B: Detailed Data from Examples ....................................................................29
- 1 -

1 Introduction

The development and growing acceptance of bandwidth-intensive applications (e.g., 

video and user generated content) has made it more difficult for wireless network 

operators to manage their transmission capacity and minimize congestion. While 

innovation and network investment may alleviate some of the problem, these activities 

take time to complete and, thus, do little to address existing congestion problems. 

Moreover, there is the issue of whether increases in supply can ever keep up with 

increases in demand. Congestion concerns appear highest under operations where 

spectrum is treated as a common pool resource. Like other forms of congestion (e.g., 

highway and airport congestion), wireless spectrum congestion imposes an important and 

real cost on society. This cost can be reduced significantly if the market for radio 

spectrum worked in a manner that better assigned existing spectrum capacity to those 

users that value it the most. 

This study employs economic methods to evaluate the efficiency with which 

spectrum is assigned to users when spectrum is allocated to both licensed and unlicensed 

operations. The study places particular emphasis on unlicensed operations. The source 

of the economic problem related to unlicensed operations is straightforward. Markets 

work best when the choices economic actors make reflect the cost their decisions impose 

on society.

2

Economic agents typically incur the cost of their decisions by paying an 

appropriately informed market price. Due to the free entry, open access condition 

inherent in unlicensed use, there is no assurance that consumers will take into account the 

negative effect of their spectrum consumption decisions on the value other consumers 

place on using the same spectrum. Thus, rational users may “over-consume” freely 

available spectrum and “under-consume” non-freely available spectrum compared to the 

levels that would promote both consumer and society’s interests. This welfare reducing 

outcome is referred to as the “Tragedy of the Commons.” 

Based on two simple examples that contain many of the economic features that exist 

in the naturally-occurring world, economic theory indicates that society leaves half of the 

value it can receive from spectrum “on the table.” Fortunately, theory suggests ways in 

2

Simultaneous use of radio waves at the same point in time and space by independent users makes it 

difficult for receivers to differentiate between signals and, thus, differentiate between wanted and unwanted 

information. 
- 2 -

which the efficiency of the spectrum market can be improved. One approach involves 

designing better etiquettes that determine who gets assigned spectrum and how much. 

One examined etiquette employs market clearing prices during periods of excessive 

spectrum congestion to address the congestion problem. The superiority of a new class 

of etiquette - herein referred to as “market-informed” etiquettes - is established both in 

theory and by experimental results. Indeed, both theory and experimental evidence 

indicate that society can experience a substantial increase in its welfare if it employs one 

or more members of this new class of etiquette to address wireless spectrum congestion. 

Importantly, analysis also indicates that, despite paying a fee to access spectrum under 

conditions of excess congestion, consumers are in general much better off under these 

new market-informed etiquettes than under the standard, existing congestion etiquette. 

These results form the factual basis for generating an entirely new type of spectrum 

allocation wherein a given band of spectrum is treated as a common pool resource in the 

absence of excessive spectrum congestion, but is treated as an excludable private good in 

the presence of such congestion. Results of this analysis have implications for a variety 

policy issues. For example, by reducing concerns that the unassigned frequencies 

between broadcast TV channels – so-called “white spaces” – will be over-used, the value 

society receives from the FCC’s proposal to allow unlicensed devices in these channels 

can be greater than anticipated.

2 Formal Analysis of the Tragedy of the Commons

The Tragedy of the Commons refers to a situation in which myopic, self-interested 

behavior leads to the excessive use of a common pool resource. Because of this 

excessive use, the welfare of individual users is not maximized and, further, society fails 

to obtain the most efficient use of its scarce resources. Importantly, users of a common 

pool resource (e.g., spectrum designated to unlicensed use) can avoid the Tragedy of the 

Commons problem by coordinating their use. While such coordination has been 

successful in other instances, the radio spectrum market has several characteristics that 

make user coordination particularly difficult. 

One market characteristic is the wide variation in uses to which entities employ 

spectrum. Some users employ spectrum to download streaming video, while other users 
- 3 -

employ spectrum to text message. The level of satisfaction a user obtains from 

employing spectrum depends importantly on the amount of unused capacity available to 

satisfy his or her desired application. Equally important, the level of available capacity 

needed to provide satisfactory streaming video service is different (i.e., substantially 

greater) than the level needed to provide satisfactory text messaging service. Such 

differences in the amount of spectrum required by different applications complicate the 

ability of users to coordinate their uses. In particular, to avoid the Tragedy of the 

Commons problem, users must not only recognize that their spectrum use negatively 

affects other users, but that the extent to which it affects other users depends on the 

specific demands of other users. The economic cost of adding one additional user who 

wishes to download streaming video to a wireless network may be zero if all current 

users are employing spectrum for text messaging, but may be very high if existing users, 

because of their applications, are relatively spectrum congestion intolerant.

2.1 A Simplified Model

A simple example can be used to describe the unique and complicated nature of the 

Tragedy of the Commons problem involving spectrum usage. Assume that there are 

eight different spectrum users, each defined by a set of characteristics. The users vary in 

the minimum amount of bandwidth that each needs in order to satisfy their service needs, 

as well as in the value they place on having their service needs fully satisfied. Because of 

differences in service needs, users also vary in the extent to which they can tolerate 

spectrum congestion. For example, a user requiring a very high quality of service (e.g. 

video streaming or other applications that require a high and reliable data transmission 

rate) might find quality unacceptable whenever aggregate demand exceeds 60% of 

system capacity. Users that can tolerate a lower quality of service, however, would find 

quality acceptable when aggregate demand exceeds a higher percentage of system 

capacity (e.g. 80%). In what follows we measure a user’s demand for service quality by 

his or her “congestion limit,” expressed as the maximum amount of spectrum congestion 

the user can tolerate before the value he or she places on employing spectrum falls from 
- 4 -

some desired value to zero.3Figure 1 presents data for a hypothetical set of spectrum 

users, including the value that each user places on spectrum (expressed on a per megabit 

basis), the minimum amount of spectrum required by the user, and each user’s quality of 

service requirement as measured by his/her congestion tolerance limit. 

Figure 1: Spectrum User Characteristics in Example 1

Willingness to Pay

per MB

Quantity Demanded (MB)

5

10

#3

10¢

17 MB

60%

#1

9¢

24 MB

60%

#4

7¢

16 MB

60%

#5

7¢

18 MB

80%

7¢

13MB

80%

#8

#6 #7

5¢

17 MB

80%

141

5

11 MB

80%

#2

5¢

25 MB

60%

$2.16 $1.25 $1.70 $1.12 $1.26 $0.55 $0.85 $0.91

60% Congestion Tolerance

80% Congestion Tolerance

Key

¢ Per bit

Megabits

Congestion

$ Total

Willingness to Pay

per MB

Quantity Demanded (MB)

5

10

#3

10¢

17 MB

60%

#1

9¢

24 MB

60%

#4

7¢

16 MB

60%

#4

7

#5

7¢

18 MB

80%

7¢

13MB

80%

#8

#6 #7

5¢

17 MB

80%

141

5

11 MB

80%

#2

5¢

25 MB

60%

216 125 170 112 126 55 85 91

60% Congestion Tolerance

80% Congestion Tolerance

Key

¢ Per bit

Megabits

Congestion

$ Total

Key

¢ Per bit

Megabits

Congestion

Key

Value/MB

Megabits

Congestion

Total Value

Total Valuation = 980

Willingness to Pay

per MB

Quantity Demanded (MB)

5

10

#3

10¢

17 MB

60%

#1

9¢

24 MB

60%

#4

7¢

16 MB

60%

#5

7¢

18 MB

80%

7¢

13MB

80%

#8

#6 #7

5¢

17 MB

80%

141

5

11 MB

80%

#2

5¢

25 MB

60%

$2.16 $1.25 $1.70 $1.12 $1.26 $0.55 $0.85 $0.91

60% Congestion Tolerance

80% Congestion Tolerance

Key

¢ Per bit

Megabits

Congestion

$ Total

Willingness to Pay

per MB

Quantity Demanded (MB)

5

10

#3

10¢

17 MB

60%

#1

9¢

24 MB

60%

#4

7¢

16 MB

60%

#4

7

#5

7¢

18 MB

80%

7¢

13MB

80%

#8

#6 #7

5¢

17 MB

80%

141

5

11 MB

80%

#2

5¢

25 MB

60%

216 125 170 112 126 55 85 91

60% Congestion Tolerance

80% Congestion Tolerance

Key

¢ Per bit

Megabits

Congestion

$ Total

Key

¢ Per bit

Megabits

Congestion

Key

Value/MB

Megabits

Congestion

Total Value

Total Valuation = 980

Spectrum users increasingly face a choice between using either dedicated spectrum 

provided through a subscription service or using shared spectrum allocated to unlicensed 

3 A user’s need for quality is in fact a demand for a number of data transmission characteristics including 

file transfer rate, latency tolerance, and allowable level of jitter. See in Appendix A: Figures and Charts. 

For purposes of the experiments, we have assumed that the relationship between service quality and 

spectrum congestion for congestible service (defined later as Option B) follows an “Ethernet curve.” At 

low levels of congestion users can obtain bit rates close to the maximum the air link can support. As 

system demand approaches 80% of total system capacity, the bit rate drops precipitously. For example, 

when demand is equal to 90% of capacity, bit rates are approximately 50% of the maximum possible. See 

Figure A2. Ethernet Packet Loss Function in Appendix A: Figures and Charts. The Ethernet curve can be 

well approximated by a function f of z = X/K, where K is maximum capacity, f(0) = 1, f(1) = 0 and f¢(z) < 0 

for all z such that 0 < z < 1. In the theoretical analysis of this paper, and in the experiments based on that 

theory, we approximate this function by a simple step function in which user valuations are constant until 

demand reaches a critical percentage of available capacity. This “congestion limit” is allowed to vary by 

user type.
- 5 -

devices.4 Our model, therefore, assumes that each user in our example has the option to 

choose between a reliable and non-congestible transmission system that requires a fixed 

payment of 130 units (Option A), and a transmission system that is “free,” but where the 

value to each user depends on the congestion level of the free service’s transmission 

system (Option B). The capacity of the free service is assumed to be 100 units. The 

identification of the efficient assignment of spectrum involves considering the amount of 

spectrum demanded by the users, the value users place on this spectrum, and the 

minimum quality of service that each user needs to obtain that value.

The unique efficient assignment of spectrum in this example involves assigning 

spectrum to users as shown in Figure 2, where total surplus is defined as 

å å Î Î

+

i B

i i

i A

viqiv q , consumer surplus is defined as å( ) å( )

Î Î

- + -

i B

i i B

i A

viqi PAv q P , qi

represents user i’s demand, vi represents value per unit of demand for user i, and PA and 

PB represent the prices for options A and B respectively.5

Figure 2: Efficient Assignment of Spectrum in Example 1

Q u antity D e m a nded (M B )

# 3

1 0 ¢

17 M B

60%

# 1

9 ¢

24 M B

60%

# 4

7 ¢

16 M B

60%

# 5

7 ¢

18 M B

80%

7 ¢

13M B

80%

# 8

# 6

# 7

5 ¢

17 M B

80%

60% C a pacity

C o ngestio n 

L im it 5

11 M B

80%

O p tio n A O p tio n B

C o nsu m e r S u r p lu s = 384

5

1 0

5

1 0

E x c luded

4 1 5 8

$2.1 6 $1.7 0 $1.1 2 $1.2 6 $0.5 5

$0.8 5

$0.9 1

# 2

5 ¢

25 M B

60%

$1.2 5

W illin gness to Pa y

per M B

Q u antity D e m a nded (M B )

# 3

1 0 ¢

17 M B

60%

# 3

1 0

# 1

9 ¢

24 M B

60%

# 1

9

# 4

7 ¢

16 M B

60%

# 4

7

# 5

7 ¢

18 M B

80%

# 5

7

7 ¢

13M B

80%

# 8

7

# 6

# 7

5 ¢

17 M B

80%

# 7

5

60% C a pacity

C o ngestio n 

L im it

60% C a pacity

C o ngestio n 

L im it 5

11 M B

80%

O p tio n A O p tio n B

5

1 0

5

1 0

E x c luded

4 1 5 8

216 170 112 126 5 5

8 5

9 1

C o n s u m e r Sur p lu s = 126

P r ovider Sur p lu s = 260

T o ta l S u r p lu s = 770

# 2

5 ¢

25 M B

60%

# 2

5

125

Q u antity D e m a nded (M B )

# 3

1 0 ¢

17 M B

60%

# 1

9 ¢

24 M B

60%

# 4

7 ¢

16 M B

60%

# 5

7 ¢

18 M B

80%

7 ¢

13M B

80%

# 8

# 6

# 7

5 ¢

17 M B

80%

60% C a pacity

C o ngestio n 

L im it 5

11 M B

80%

O p tio n A O p tio n B

C o nsu m e r S u r p lu s = 384

5

1 0

5

1 0

E x c luded

4 1 5 8

$2.1 6 $1.7 0 $1.1 2 $1.2 6 $0.5 5

$0.8 5

$0.9 1

# 2

5 ¢

25 M B

60%

$1.2 5

W illin gness to Pa y

per M B

Q u antity D e m a nded (M B )

# 3

1 0 ¢

17 M B

60%

# 3

1 0

# 1

9 ¢

24 M B

60%

# 1

9

# 4

7 ¢

16 M B

60%

# 4

7

# 5

7 ¢

18 M B

80%

# 5

7

7 ¢

13M B

80%

# 8

7

# 6

# 7

5 ¢

17 M B

80%

# 7

5

60% C a pacity

C o ngestio n 

L im it

60% C a pacity

C o ngestio n 

L im it 5

11 M B

80%

O p tio n A O p tio n B

5

1 0

5

1 0

E x c luded

4 1 5 8

216 170 112 126 5 5

8 5

9 1

C o n s u m e r Sur p lu s = 126

P r ovider Sur p lu s = 260

C o n s u m e r Sur p lu s = 126

P r ovider Sur p lu s = 260

T o ta l S u r p lu s = 770

# 2

5 ¢

25 M B

60%

# 2

5

125

4

For a discussion of spectrum sharing in the context of the larger debate on spectrum management reform, 

see Peha, Jon, “Emerging Technology and Spectrum Policy Reform,” International Telecommunications 

Union (ITU) Workshop for Spectrum Management, ITU Headquarters, Geneva, January, 2007. 

5 By default, the price of Option B is equal to zero. Under some etiquettes, to be discussed later, a positive 

price might be assigned. In the following section, a per unit price, PB , may be assigned to users of Option 

B. In the above notation, producer surplus is defined as PA nA + PB nB, where nA and nB represent the 

number of subscribers choosing options A and B respectively.
- 6 -

Notice that in the efficient assignment, users 2 and 7 are excluded from spectrum 

available via Option A or Option B. In particular, under Option A, both users 2 and 7 

would receive negative surplus, because the value they place on service is less than the 

subscription fee of 130. Moreover, including either user 2 or user 7 under the free service 

(Option B) would require displacing at least one of the existing users of that service, and 

one can verify that any such change would result in a reduction in total surplus.

2.2 Tragedy of the Commons Problem: Nash Prediction

Suppose users simultaneously and independently choose whether to select the 

subscription service (Option A), the free service (Option B), or neither service. A Nash 

equilibrium is a particular joint selection such that no individual user could increase his 

or her payoff by selecting an alternative strategy assuming that all other users maintain 

their equilibrium strategy choices. We can now see immediately that the efficient 

assignment in Example 1 is not a Nash equilibrium. For example, suppose that user 7 

contemplates joining the free service. Such a change would increase the total demand for 

this service from 58 to 75 units, but since user 7 expects to receive acceptable quality of 

service as long as total demand is less than 80 units, this alternative selection would 

increase user 7’s surplus from zero to 85 valuation units.6 Under Nash equilibrium 

assumptions, user 7 would therefore choose this alternative. With a total demand of 75 

for Option B, however, user 4 no longer receives a satisfactory quality of service, and 

under our assumptions, her entire surplus of 112 valuation units is assumed to be 

forfeited.

While the efficient assignment cannot be sustained as a Nash equilibrium, there are 

alternative joint user selections that satisfy the Nash equilibrium conditions. The 

magnitude of the Tragedy of the Commons problem in Example 1 is measured by the 

difference between the total surplus under the efficient assignment and total surplus under 

the Nash equilibrium condition. The value of this measure, as predicted by Nash 

Equilibrium Theory, depends on the joint user selection. One common element of each 

Nash assignment is that both users 1 and 3 are assigned to the subscription service 

6 User 7 has a congestion tolerance of 80%. Given that the free service’s capacity is 100 Mb, user 7 would 

obtain value from selecting Option B
- 7 -

(Option A). To see this, suppose that users 1 and 3 select Option A, users 5, 6, 7, and 8 

select Option B, and that users 2 and 4 choose neither option. These selections satisfy the 

Nash equilibrium conditions. If either user 1 or user 3 attempts to switch to the free 

service in order to avoid paying the subscription fee, demand for Option B would rise 

above either of their congestion limits and they would forfeit the value received by 

selecting Option A. Each of the users choosing Option B would clearly see a reduction in 

surplus by switching to Option A since they would be required to pay the subscription fee 

of 130, under which they receive negative surplus. Finally, users 2 and 4 receive zero 

surplus by choosing neither option, but would do no better by choosing either Option A 

or Option B. 

Total surplus in this equilibrium selection is equal to 743 valuation units. In fact, 

this is the highest total surplus obtainable in any of the Nash equilibria, although it is 

lower than the surplus of 770 obtained under the efficient assignment. Thus, if this 

equilibrium was obtained, the social cost of the Tragedy of the Commons problem would 

be very small. However, as noted earlier, there are many joint user selections that satisfy 

the Nash equilibrium conditions, many of which generate much lower levels of total 

surplus.

While there a large number of outcomes predicted under the assumption that users 

follow Nash equilibrium behavior, there are strong theoretical grounds for assuming that 

the outcomes that generate the greatest amount of social loss are the ones that are the 

most likely to occur. To see this, note that users who select Option B are guaranteed to 

receive at least a zero payoff, and there is a possibility that they could receive a positive 

payoff if other users deviate (contrary to Nash assumptions) from the assumed 

equilibrium. Those who select “neither option” receive a zero payoff with certainty. In 

the language of non-cooperative game theory, in this case a strategy in which a user 

chooses “neither option” is “weakly dominated” by the strategy in which that user 

chooses Option B. There is only one equilibrium in which no user selects a weakly 

dominated strategy. In this equilibrium, users 1 and 3 again select Option A, while all 

remaining users (i.e. users 2, 4, 5, 6, 7 and 8) select Option B. This outcome, 

summarized in Table 10 of Appendix B, is the worst of all Nash equilibrium outcomes, 

with total surplus equal to 386 and total efficiency equal to 50.1%.
- 8 -

3 Congestion Etiquettes

There are several approaches to addressing the Tragedy of the Commons problem.7

One approach involves treating spectrum as a “private good” wherein a spectrum owner 

can employ market prices to ration spectrum among competing users. To the extent that 

this approach applies only to licensed spectrum owners, it fails to promote 

experimentation and innovation in spectrum usage. Another approach involves the use of 

administrative rules which restrict the technical characteristics of unlicensed radio 

equipment so that excessive use of unlicensed spectrum, in its common pool resource 

form, is an acceptably low probability.

8

In spite of such restrictions, excessive use of 

spectrum is still a distinct possibility. To address this problem, some unlicensed devices 

(e.g., wireless routers) employ congestion etiquettes, which are a set of rules that 

determine the set of users who can access spectrum, and the amount of spectrum assigned 

to each user.9 Because there are a wide variety of rules, there are a wide variety of 

spectrum etiquettes.10

3.1 Enhancing Efficiency By Changing Strategy Payoff

We first consider an etiquette that addresses the congestion problem by changing the 

payoffs of users and, in so doing, their service choice. This etiquette is based on the 

observation that the Tragedy of the Commons problem is made worse by the fact that the 

7

For a discussion of the Tragedy of the Commons problem related to real time access to spectrum, see 

Peha, Jon, “ Spectrum Sharing Without Licenses: Opportunities and Dangers,” in Interconnection and the 

Internet: Selected Papers From the 1996 Telecommunications Research Conference, G. Rosston and D. 

Waterman (Eds). Mahwah, N.J.: Lawrence Erlbaum Associates, 1997, pgs. 49-75. 

8 Technical restrictions such as power transmission limits on unlicensed devices limit the number of users 

that have access to the service and, thus, the likelihood of excessive spectrum use. To address signal 

interference, unlicensed devices employ filtering and error correction technologies to sort out the desired 

signal from other signals and background noise. The existence of such filters enables, for example, 

multiple Wi-Fi routers to co-exist within a given geographic area. 

9

It has been suggested that advances in technology are beginning to solve the congestion problem. For 

example, so-called “intelligent systems” are being developed that attempt to match available supply with 

demand and, in so doing, eliminate the amount of unused spectrum that exists at any moment. However, 

while this matching process is important, it doesn’t address, in the presence of spectrum scarcity, whether 

the economically efficient set of matches are taking place. 

10 The only instance of an etiquette mandated by the FCC occurs in the Part 15 rules on unlicensed PCS. 

The etiquette, in the form of a “listen-before-talk” rule, is a spectrum-sharing technique that reduces the 

probability of conflicting signals by requiring the device to monitor for other spectrum signals for a fixed 

period of time before emitting its own signal. Unlicensed PCS devices must also limit transmission for a 

fixed duration. Due to the fact that unlicensed PCS was never widely adopted, the FCC changed its rules, 

amending the listen before talk rule and rendered this requirement all but moot. 
- 9 -

strategy of selecting Option B weakly dominates the strategy of selecting neither Option 

A nor B. One method of changing user incentives is to charge users a small nonrefundable fee if they select Option B. Herein called the “Pay to Connect” etiquette, a 

user who selects Option B, but who also expects that his/her decision would raise the 

demand for spectrum available under Option B to a level above his or her own congestion 

limit, would prefer to choose to sit on the sidelines and earn a zero payoff rather than to 

choose Option B and earn a negative payoff equal to the non-refundable fee.

Given a fee for selecting Option B, the strategies that sustain the inefficient Nash 

equilibrium reported above and in Table 10 of Appendix B no longer represent 

equilibrium strategies. Rather than select the free service while expecting to receive a 

negative payoff equal to the non-refundable fee, users 2, 4, 5, 6, 7 and 8 would each 

prefer to select neither option. In Example 1, the only Nash equilibrium strategy 

selection that survives the imposition of a small but positive fee for Option B is the 

highest surplus Nash outcome as described above and as reported in Table 11 of 

Appendix B. In this outcome total efficiency is equal to 96.5%.

3.2 Enhancing Efficiency Via Rationing – Randomization

We next consider two etiquettes that employ a randomization technique to more 

efficiently allocate spectrum to those users that select Option B. As before, users first 

decide whether to select Option A or Option B. For those who select Option B, a random 

number generator is used to assign a priority level to each such user. If n users select 

Option B, then there are n! permutations of users, and each permutation is assumed to be 

chosen with equal probability.

11 Users are then assigned spectrum under Option B until 

the total demand exceeds a pre-determined level, which we assume to be equal to the 

highest congestion limit of all users who are expected to make use of the system.12 Herein 

referred to as “Simple Randomization,” this etiquette addresses the Tragedy of the 

11 When there are 8 users there are 40,320 possible permutations.

12 In an alternative version of this randomization etiquette, users could be served only until total demand 

exceeds the lowest congestion limit of expected users. There are clear trade-offs involved in selecting the 

appropriate system capacity, and neither rule is optimal in all situations. With a high limit, some high 

priority users with low congestion limits would be granted service under the etiquette, but the service 

would be worthless to them if the total demand exceeded their personal congestion limit. On the other 

hand, there can be situations in which some users would be served when system capacity is set at the high 

congestion limit but would be rejected under the lower limit.
- 10 -

Commons problem by guaranteeing that some users (those with high priority and high 

congestion limits) receive some value from their assigned spectrum under Option B. 

The algorithm which underlies the above approach is known as a “greedy algorithm.” 

The algorithm addresses the congestion problem by evaluating, in a sequential fashion, 

each user’s spectrum demand. The term “greedy” refers to the “take what you can get 

now” strategy inherent in its solution rule. The failure to consider the demands of all 

users simultaneously may result in a solution value that falls far short of the global 

optimum.13

A particular implementation of the simple randomization etiquette for Example 1 is 

illustrated in Figure 3 below. In this case, all 8 users are assumed to select Option B, and 

the random priority assignment ranks users in the order {5, 8, 1, 2, 4, 3, 7, and 6}.

Figure 3: Simple Randomization in Example 1

$1.26 $0.91 $2.16 $1.25 $1.12 $1.70 $0.85 $0.55

Quantity Demanded (Mbps)

5

10

#3

10¢

17 Mbps

60%

#3

10¢

17 Mbps

60%

#1

9¢

24 Mbps

60%

#1

9¢

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60%

#4

7¢

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60%

#4

7¢

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60%

#5

7¢

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80%

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7¢

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80%

7¢

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80%

#8

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#8

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5¢

17 Mbps

80%

#7

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80%

141

#2

5¢

25 Mbps

60%

60% Capacity

Congestion

Limit

$1.26 $0.91 $2.16 $1.25 $1.12 $1.70 $0.85 $0.55

80% Capacity

Congestion

Limit

Willingness to Pay 

per Mbps

Quantity Demanded (Mbps)

5

10

#3

10¢

17 Mbps

60%

#1

9¢

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60%

#4

7¢

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#5

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80%

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#8

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141

#2

5¢

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60%

$1.26 $0.91 $2.16 $1.25 $1.12 $1.70 $0.85 $0.55

Willingness to Pay 

per Mbps

Quantity Demanded (Mbps)

5

10

#3

10¢

17 Mbps

60%

#1

9¢

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60%

#4

7¢

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60%

#5

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#8

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141

80%

#2

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60%

$1.26 $0.91 $2.16 $1.25 $1.12 $1.70 $0.85 $0.55

Quantity Demanded (Mbps)

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10

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10¢

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141

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60% Capacity

Congestion

Limit

126 91 216 125 112 170 85 55

80% Capacity

Congestion

Limit 5

$1.26 $0.91 $2.16 $1.25 $1.12 $1.70 $0.85 $0.55

Quantity Demanded (Mbps)

5

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10¢

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141

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Congestion

Limit

60% Capacity

Congestion

Limit

$1.26 $0.91 $2.16 $1.25 $1.12 $1.70 $0.85 $0.55

80% Capacity

Congestion

Limit

Willingness to Pay 

per Mbps

Quantity Demanded (Mbps)

5

10

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10¢

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$1.26 $0.91 $2.16 $1.25 $1.12 $1.70 $0.85 $0.55

Willingness to Pay 

per Mbps

Quantity Demanded (Mbps)

5

10

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10¢

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#1

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$1.26 $0.91 $2.16 $1.25 $1.12 $1.70 $0.85 $0.55

Quantity Demanded (Mbps)

5

10

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10¢

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60% Capacity

Congestion

Limit

126 91 216 125 112 170 85 55

80% Capacity

Congestion

Limit 5

Under this etiquette, users 5, 8, 1, and 2 are provided spectrum, while all lower 

priority users are excluded, because including any additional user would raise total 

13 For example, it is possible that global welfare optimization considerations might require that a high 

priority user, who is initially guaranteed service, should later be excluded in order for one or more higher 

valued, but lower priority users, to be served.
- 11 -

demand above the system capacity of 80, which is equal to the maximum congestion 

limit. In this case, users 1 and 2 would receive no value from their spectrum assignment 

since the total demand would exceed their personal congestion limits, and the resulting 

total efficiency would be equal to 16.3%.14 Alternative user selections between Options 

A and B will result in different outcomes under the Simple Randomization etiquette. In 

fact, there is a unique Nash equilibrium in this case whose outcome is shown in Appendix 

B. In this equilibrium, total efficiency is equal to 83.6%.

In an alternative version of the randomization etiquette, to be called “Informed 

Randomization”, users are first asked to report their personal congestion limits to a 

system manager.15 As in simple randomization, a random number generator is used to 

assign a priority level to each user who selects Option B. Service is now assigned, 

however, by taking account of the congestion limits of each potential user. If the demand 

of the highest priority user is less than that user’s congestion limit, that user is guaranteed 

service. The etiquette then considers each additional user’s demand and personal 

congestion limit in order of decreasing priority. The etiquette ensures that total demand 

always remains less than or equal to the minimum congestion limit of all users who are 

guaranteed service. With each new user, the relevant system congestion limit is set equal 

to the minimum limit of the current user being considered, and the limits of all higher 

ranking users already guaranteed service. If the total demand, including the current user, 

is less than or equal to the congestion limit, that user is granted service. Otherwise, that 

user is not served and the next highest priority user is considered. The etiquette continues 

to examine users until all have been considered, or until demand is exactly equal to the 

system limit as determined by the currently served users.

14 The sensitivity of the randomization (and later) etiquettes to personal congestion limits raises the 

question of whether users will have the incentive to report their limits truthfully. In fact, “truth telling” is 

in this case is a weakly dominant strategy (in game theoretic terminology) since a user who selects Option 

B can never increase his or her payoff by falsely reporting a congestion limit. To see this, note that a high 

priority user with a low (e.g. 60%) congestion limit would never wish to report a higher limit. If the user 

would have been excluded under a truthful (60%) report, while a false (e.g., 80%) report might result in 

receiving service, the service would be of no value to the user. Similarly, a user with a high congestion 

limit would never wish to report a lower limit, since in some cases this would result in that user being 

denied service, while in no cases would a lower total demand increase the quality of service under the 

present assumptions.

15 The system manager would most likely be embodied in a hardware device, and user reports about 

personal congestion limits would correspond to priority bits under existing internet protocols. 
- 12 -

Under the Informed Randomization Etiquette, users 2, 4, 5, 6, 7, and 8 would expect 

to receive positive surplus under Option B, since there is positive probability that they 

will be assigned a high priority rank. They will therefore choose Option B in preference 

to choosing neither Option A nor Option B. In addition, user 3 in this example has an 

incentive to select Option B over Option A, because the expected surplus to him or her 

under the randomization protocol is higher than could be achieved with certainty by

choosing Option A. For user 1, the certain surplus under Option A is higher than that 

under the randomization etiquette, whether or not user 3 chooses Option B. The resulting 

outcome is shown in Appendix B.

While the informed randomization etiquette guarantees that those users who select 

Option B, and who have a sufficiently high priority level, receive positive surplus, this 

protocol does not necessarily create the correct incentives for users to make optimal 

selections between Options A and B. In particular, by raising a high valued user’s 

expected return from selecting Option B, the randomization etiquette may induce such a 

user to select Option B, a choice that while private welfare maximizing for the user, ends 

up reducing total surplus. In this example, the total surplus under the informed 

randomization etiquette is equal to 560.25 and the corresponding efficiency is equal to 

72.8%.

3.3 Enhancing Efficiency Via Rationing – Willingness to Pay

We next consider etiquettes that utilize reported information on a user’s congestion 

tolerance and willingness to pay to more efficiently allocate spectrum to those users that

select Option B.16 In one version of a WTP etiquette (hereafter called the “Lump Sum 

WTP Etiquette”), users who select Option B would be asked to report both their personal 

congestion limit and their willingness to pay to receive or send information. The reported 

16 In his article “Beyond Spectrum Auctions”, Eli Noam, Beyond Spectrum Auctions: Taking the Next Step 

to Open Access” Journal of Law and Economics Vol. 41 pp. 465 (1998). Noam proposes a system of open 

access to replace the current auction-based licensing system. Under the proposed approach spectrum users 

pay an access fee based on the level of congestion in frequency bands at a particular time. Under this 

arrangement, users would employ intelligent agents to pay for their spectrum consumption using electronic 

tokens and a set of clearing houses. A similar approach was proposed by Lehr (2004). See, William Lehr, 

“Economic Case for Dedicated Unlicensed Spectrum Below 3GHz,” page 19, Unpublished Manuscript. 

Our WTP approach differs in several important respects to these approaches. The above approach attempts 

to solve the spectrum allocation problem conditional on the existing level of spectrum congestion. In 

contrast, our approach attempts to solve the spectrum allocation problem on an unconditional basis. 
- 13 -

willingness to pay values would then be used to define a priority ranking of users, and the 

etiquette would proceed in a similar manner as the randomization etiquette (but without 

the random component). In one important difference, however, users under the WTP 

etiquette would be required to actually pay a price to receive service. Under this 

etiquette, the price is determined by the reported willingness to pay of the marginal user 

who is excluded from service by the etiquette. Only users who are guaranteed service 

under the etiquette are required to pay this price.17

For example, suppose that in Example 1, all users bid “truthfully” in the following 

sense: users 1 and 3 bid 130, which is the price they would have paid if they had selected 

Option A, and all remaining users bid their actual value, which in each case is less than 

130.18 Users 1 and 3 would then be tied for the highest priority of service, and they

would be followed in order by users 5, 2, 4, 8, 7 and 6. This WTP etiquette employs a 

greedy algorithm to solve the congestion problem. In particular, users 1, 3 and 5 would 

therefore be assigned spectrum under Option B and would each pay a price equal to 125, 

which is the highest rejected bid. No other users will be assigned spectrum, since the 

addition of any other user would violate the requirement that total demand remain less 

than or equal to the minimum congestion limit of all users who are guaranteed service.

17 This pricing rule is based on standard “second price” auction theory. In the present context, there is 

some ambiguity about the definition of the marginal user. The present version of the etiquette assumes that 

the extra-marginal user is defined as the highest priority user who is excluded from service, and such that 

no lower priority user is assigned service.

18 In general, truthful bidding of this form is not guaranteed. While truthfully revealing a personal 

congestion limit is still a weakly dominant strategy, there can be situations in which users may prefer to 

misrepresent their willingness to pay in an effort to lower the market price.
- 14 -

Figure 4: Willingness to Pay in Example 1

Quantity Demanded (MB)

10¢

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141

60% Capacity 

Congestion 

Limit

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Congestion 

Limit

$1.70 $2.16

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Lump Sum Bids

100

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55

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Limit

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50

The ability of users to express their willingness to pay introduces some surprising and 

important strategic effects. For example, users with high valuations can now predict with 

greater certainty whether or not they will be served if they choose Option B. No user 

who can afford to pay the subscription price for Option A can gain by choosing Option B 

and making a bid higher than the subscription price for Option A (for which satisfactory 

service is guaranteed).19 Assuming that all users place “truthful” bids as described above, 

in the set of undominated Nash equilibria for Example 1, reported in Appendix B, all 

users select Option B. In this equilibrium both total surplus and consumer surplus are 

lower than surplus under both of the randomization etiquettes and under the Pay to 

Connect etiquette. Total efficiency under this WTP etiquette for Example 1 is equal to 

66.5%.

3.4 Congestion Etiquettes – Nash Predictions

The full set of Nash equilibrium predictions for Example 1 and an additional 

example are summarized in Tables 1 and 2 below, and full results are presented in 

Appendix B. Efficiency is defined as the surplus earned by both spectrum users and 

19 A bid for service under Option B that is higher than the price of Option A would differ from a bid equal 

to the price of Option A only if the bid of the marginal user under Option A was higher than the price of 

Option A. In such a case, the bidder would be better off choosing Option A instead of Option B.
- 15 -

service providers under the corresponding etiquette, as a fraction of maximum possible 

surplus, expressed in percentage terms, while consumer surplus measures the amount of 

surplus enjoyed by spectrum users. Each row reports only the equilibrium efficiency

associated with un-dominated strategies under the corresponding etiquette. Examples 1 

and 2 refer to different user valuation environments. They differ primarily in terms of the 

set of users who can afford to purchase the subscription service under Option A. In 

Example 1, two out of eight users can afford Option A as illustrated in Figure 1, while in 

Example 2 user demands and values of service are changed in such a way that five out of 

eight users can afford Option A. 

In Example 1, each of the four pro-active etiquettes achieves higher efficiencies than 

that achieved under the fairness etiquette, with the pay to connect etiquette achieving by 

far the best performance in terms of both efficiency and consumer surplus. In Example 2, 

Nash equilibrium theory predicts a benign outcome for the fairness etiquette suggesting 

the absence of a Tragedy of the Commons problem in this case. Now, two of the proactive etiquettes (pay to connect and simple randomization) achieve outcomes close or 

equal to the default outcome, while the remaining two etiquettes (informed randomization 

and willingness to pay) achieve significantly worse outcomes.

Table 1: Summary of Predicted Efficiencies

Etiquette Example 1 Example 2

Fairness 50.1% 91.4%

Pay to Connect 96.5% 91.4%

Simple Randomization 83.6% 91.4%

Informed Randomization 72.8% 54.7%

WTP 66.5% 76.9%
- 16 -

Table 2: Summary of Predicted Consumer and Total Surplus Values

Example 1 Example 2

Etiquette Total 

Surplus

Consumer 

Surplus

Total 

Surplus

Consumer 

Surplus

Fairness 386 126 1018 628

Pay to Connect 743 363 1018 528

Simple Randomization 643.367 383.367 1018 628

Informed 

Randomization

560.25 430.25 609.593 479.593

WTP 512 137 857 309

4 Experimental Analysis – Congestion Etiquette Performance

Eight subjects are assigned a set of characteristics, including the value they place on 

having the ability to transmit or receive information, the minimum amount of bandwidth 

he/she needs to transmit or receive such information, and a “congestion limit,” expressed 

as the maximum amount of spectrum congestion the user can tolerate before the value 

he/she places on employing spectrum falls from some desired value to zero. To test the 

sensitivity of the results to changes in the assigned characteristics, two different valuation 

environments were created. One environment contained the valuations shown in 

Example 1. 

Each subject had the option to choose between a reliable and non-congestible 

transmission system that requires a fixed payment of 130 units (Option A), and a 

transmission system that is “free,” but where the value to each user depends on the 

congestion level of the free service’s transmission system (Option B). The capacity of 

the free service is assumed to be equal to 100 units. If two or more subjects choose 

Option B, depending on the total amount of bandwidth demanded, a congestion etiquette 

may be employed that determines how much spectrum each subject is assigned and the 

value each subject obtains from their bandwidth assignment. The etiquettes fall into two 

broad categories – etiquettes that do not exclude users and etiquettes that employ 

algorithms to exclude users. 
- 17 -

4.1.1 No Exclusion Etiquette – Fairness and Pay to Connect

Under a no exclusion etiquette, spectrum is allocated to all users independent of the 

total amount of bandwidth demanded. However, depending on the total amount of 

bandwidth demanded, the assigned spectrum may translate to a transmission speed that is 

unacceptable to some users given their desired service application (e.g., streaming video). 

If total demand results in a congestion level in excess of 80%, then no user obtains any 

value from their allocated spectrum. If the total amount of bandwidth demanded results 

in a congestion level greater than 60%, but less than 80%, only those users who are 

tolerant of high congestion receive value from their allocation. Finally, if total amount of 

bandwidth demanded results in a congestion level less than or equal to 60%, all users 

receive value from their spectrum allocation. Two types of no exclusion etiquettes were 

tested. Under the fairness etiquette, there is nothing in the economic environment, other 

than the desire of subjects to coordinate their service option choices, which addresses the 

spectrum congestion problem. Under the Pay to Connect etiquette, a small fee placed on 

the “free” service is designed to discourage some subjects from selecting that option. 

Figure 5 presents the electronic interface subjects used to make their option choice. 

The interface provides each subject personalized information on the value he/she places 

on accessing spectrum, the amount of spectrum the he/she needs, and the subject’s 

spectrum congestion limit. Each participant is asked to choose between a subscription 

service (Option A) and a free service (Option B). In instances where the subject chooses 

Option B, the interface also provides amount of spectrum actually assigned to the subject 

given the choices made by other subjects. 
- 18 -

Figure 5: Screen 1 – No Exclusion

4.1.2 Exclusion Etiquettes

We examine the performance properties of four different market-informed etiquettes 

that exclude users. Three of the etiquettes employ a greedy algorithm to exclude users, 

while one etiquette excludes users by solving for the efficient allocation of bandwidth 

across prospective users based on their reported willingness to pay and congestion limits. 

4.1.2.1 Randomization Etiquette

In the randomization etiquette, the subjects first choose between Options A and B. 

Those who choose Option B report their bandwidth congestion limits and are randomly 

assigned a priority number.20 The etiquette ranks all subjects based on this random

priority assignment. Given the size of existing capacity, relative to the total demand of 

all subjects choosing Option B, the highest ranked subject is assigned bandwidth 

provided that his or her demand is less than their congestion limit. The subject with the 

20 In a technical appendix, it is demonstrated that truthful reporting is a dominant strategy for each 

experimental subject. In any case, the algorithm behind allocates spectrum to users as if all subjects have 

reported truthfully.
- 19 -

next highest priority ranking is allocated spectrum if the total demand of the two subjects 

is less than the minimum congestion limit associated with both subjects. The etiquette 

proceeds by evaluating, in a sequential fashion whether subjects with successively lower 

rank should be assigned bandwidth. At every stage, if total bandwidth demand is less 

than the relevant congestion limit (i.e., minimum congestion of all subjects who are 

assigned spectrum), then that user is assigned bandwidth. If a user's demand exceeds the 

relevant congestion limit, then the protocol rejects that user and it goes on to evaluate the 

bandwidth needs of the next lowest ranked user. This process continues until all users 

have been examined. 

Figure 6 presents the electronic interface subjects used to express their option 

choice. The interface provides each subject personalized information on the value he/she 

places on accessing spectrum, the amount of spectrum the he/she needs, and the subject’s 

spectrum congestion limit. Each participant is asked to choose between a subscription 

service (Option A) and a free service (Option B). In instances where the subject chooses 

Option B, the interface also provides amount of spectrum actually assigned to the subject 

given the choices made by other subjects. 

Figure 6: Screen 1 – Greedy Algorithm (Random)
- 20 -

4.1.2.2 Lump Sum WTP-based Greedy Algorithms

In this etiquette, the subjects first choose between Options A and B. Those who 

choose Option B report their congestion limits and submit a lump sum bid that represents 

the amount of money they are willing to pay in order to be assigned a priority level for 

service. The etiquette ranks all subjects from the highest to the lowest rank, based on the 

size of the reported lump sum bids. The algorithm then proceeds exactly as the 

randomization etiquette. The highest ranked subject is assigned bandwidth if his or her 

demand is less than or equal to his or her congestion limit. The second ranked subject is 

allocated bandwidth if the total demand of the two subjects is less than the minimum 

congestion limit associated with those subjects. The etiquette proceeds by evaluating, in 

a sequential fashion, whether subjects with successively lower rank should be assigned 

bandwidth, and continues until all users have been examined. 

Figure 7 presents the electronic interface subjects used to make their option choice. 

The interface provides each subject its assigned information on the value he/she places on 

accessing spectrum, the amount of spectrum he/she needs, and the subject’s spectrum 

congestion limit. Each participant is asked to choose between a subscription service 

(Option A) and a free service (Option B). If Option B is selected, the subject is asked to 

submit the maximum amount of money, on a lump sum basis, he/she is willing to pay in 

order to access its desired amount of spectrum. In instances where the subject chooses 

Option B, the interface also provides the amount of spectrum, if any, that is actually 

assigned to the subject given the choices made by other subjects. Finally, the interface 

identifies the market price the subject pays by accessing spectrum through Option B. 
- 21 -

Figure 7: Screen 1 – Greedy Algorithm (Lump Sum)

4.1.2.3 Unit-based WTP-based Greedy Algorithms

In this etiquette, the subjects first choose between Options A and B. Those who 

choose Option B report their congestion limits and a bid that represents the amount of 

money they are willing to pay, on a per megabit basis, in order to be assigned a priority 

level for service. The etiquette ranks all subjects from the highest to the lowest rank, 

based on the size of the per unit bids. The algorithm then proceeds exactly as the 

randomization etiquette. The highest ranked subject is assigned bandwidth if his or her 

demand is less than or equal to his or her congestion limit. The second ranked subject is 

allocated bandwidth if the total demand of the two subjects is less than the minimum 

congestion limit associated with those subjects. The etiquette proceeds by evaluating, in 

a sequential fashion, whether subjects with successively lower rank should be assigned 

bandwidth, and continues until all users have been examined. 

Figure 8 presents the electronic interface subjects used to make their option choice. 

The interface provides each subject its assigned information on the value he/she places on 

accessing spectrum, the amount of spectrum he/she needs, and the subject’s spectrum 

congestion limit. A subject makes a choice by selecting whether to access spectrum 
- 22 -

either through a pay service (Option A) or a free service (Option B). If Option B is 

selected, the subject is asked to submit the maximum amount of money, on a per unit 

basis, he/she is willing to pay in order to access its desired amount of spectrum. In

instances where the subject chooses Option B, the interface also provides the amount of 

spectrum, if any, that is actually assigned to the subject given the choices made by other 

subjects. Finally, the interface identifies the market price the subject pays by accessing 

spectrum through Option B. 

Figure 8: Screen 1 – Greedy Algorithm (Per Unit)

4.1.2.4 WTP-based Full Optimization Algorithm

In this etiquette, the subjects first choose between Options A and B. Those who 

choose Option B report their congestion limits and submit a lump sum bid that represents 

the amount of money they are willing to pay in order to be assigned a priority level for 

service. A mathematical algorithm then evaluates all the different ways in which the 

users can be assigned bandwidth and identifies that assignment which maximizes the total 

social value of spectrum, given the system capacity of Option B and the demand and 

reported congestion limits of each user. 
- 23 -

Figure 9 presents the electronic interface subjects used to make their option choice. 

The interface provides each subject its assigned information on the value he/she places on 

accessing spectrum, the amount of spectrum he/she needs, and the subject’s spectrum 

congestion limit. A subject makes a choice by selecting whether to access spectrum 

either through a pay service (Option A) or a free service (Option B). If Option B is 

selected, the subject is ask to submit the maximum amount of money, on a per unit basis, 

he/she is willing to pay in order to access its desired amount of spectrum. In instances 

where the subject chooses Option B, the interface also provides the amount of spectrum, 

if any, that is actually assigned to the subject given the choices made by other subjects. 

Finally, the interface identifies the market price the subject pays by accessing spectrum 

through Option B. 

Figure 9: Screen 1 – Full Optimization

4.2 Experimental Results

The results of the experimental investigation are shown in Tables 3 – 4. As shown 

in Table 3, depending on the valuation environment, society captures only between 42% 

and 57% of the gains that are available from its spectrum resource when the Fairness 

Etiquette is used to address spectrum congestion involving unlicensed use. Results also 
- 24 -

show that, in both valuation environments, the average efficiency under the Fairness 

Etiquette is consistently less than the average efficiency achieved by the other examined 

etiquettes. For example, the Full Optimization Etiquette achieves average efficiency 

levels across the two environments that are consistently and substantially higher than the 

efficiency levels achieved by the Fairness Etiquette. The results therefore indicate that 

society can experience a substantial increase in its welfare from using the Full 

Optimization Etiquette to handle spectrum congestion involving unlicensed use. 

Interestingly, as shown in Table 3, each member of the class of new, market-informed 

etiquettes performed better than the Fairness Etiquette. One interesting result is the

performance achieved by the Pay to Connect Etiquette. If the Greedy Algorithm-based 

etiquettes represent high-tech solutions to the wireless congestion problem, the Pay to 

Connect Etiquette is the decidedly low-tech solution. Despite its low-tech nature, the Pay 

to Connect Etiquette’s performance compares favorably to the performances achieved by

the Greedy Algorithm-based etiquettes.

The experimental results provide inconsistent support for the belief that spectrum 

users behave in a manner that is consistent with Nash Equilibrium Theory as measured by 

market efficiency. As shown in Table 3, while Nash Predictions regarding efficiency are 

close to the efficiency levels observed in the experiments for the Informed 

Randomization and Lump Sum –WTP Etiquettes, the theory does not accurately predict 

the efficiency performance of the Fairness and the Pay to Connect Etiquettes. The mixed 

performance of Nash Equilibrium Theory in predicting outcomes is also observed with 

regards to consumer surplus outcomes. As shown in Table 4, while Nash Predictions 

regarding consumer surplus are close to the consumer surplus levels observed in the 

experiments for the Informed Randomization Etiquette, the theory does not accurately 

predict the consumer surplus outcomes generated under the Pay to Connect Etiquette.

Because the market-informed etiquettes use market prices to address the spectrum 

congestion problem, it is useful to assess how spectrum users fair under these etiquettes 

versus the Fairness Etiquette. Experimental results shown in Table 4 shed light on this 

issue. According to the results, with the exception of the Pay to Connect Etiquette 

involving the second valuation environment, consumers are much better off under the 

proposed market-informed congestion etiquettes than under the Fairness Etiquette. In 
- 25 -

particular, despite paying a fee at times of excessive congestion, spectrum users are better 

off under these market-informed etiquettes than under the Fairness Etiquette. The reason 

for this is straightforward. The spectrum congestion problem is really two problems in 

one. Because of the heterogeneous needs of spectrum users, society obtains the highest 

value from its spectrum resource only if: (1) spectrum is being employed by the highest 

valued users and, (2) the “right” quality of service is being provided. Solving this 

problem involves obtaining information on the valuation each users places on sending 

and receiving information and their congestion limit. Each member of the class of new 

etiquettes incorporates this information, in varying degrees, in addressing the spectrum 

congestion problem and, in so doing, identifies a more efficient assignment of users to 

spectrum. This greater efficiency makes it possible for individual users to be better off 

under these new etiquettes than under the Co-Existence Etiquette, despite paying a fee in 

the presence of excessive congestion. 

Table 3: Experimental Results and Nash Predictions: Mean Efficiency

Example 1

Nash 

Predictions

Example 2

Nash 

Etiquette Predictions

N Efficiency Efficiency N Efficiency Efficiency

Fairness 18 42% 50.1% 22 57% 91.4%

Pay to Connect 27 52% 96.5% 33 74% 91.4%

Informed 

Randomization

27 70% 72.8% 33 63% 54.7%

Lump 

Sum

27 72% 66.5% 33 68% 76.9%

Greedy Algorithm

Willingness to 

Pay

Unit

Bid

27 66% - 33 74% -

Full Optimization 27 75% - 33 73% -

Total 150 64% - 190 69% -
- 26 -

Table 4: Experimental Results and Nash Predictions: Mean Consumer Surplus

Example 1

Nash 

Predictions

Example 2

Nash 

Predictions

Etiquette

N

Consumer 

Surplus

Consumer 

Surplus

N

Consumer 

Surplus

Consumer 

Surplus

Fairness 18 120 126 22 260 628

Pay to Connect 27 62 363 33 260 528

Informed 

Randomization

27 390 430.25 33 470 479.59

Lump 

Sum

27 250 137 33 280 309

Greedy Algorithm

Willingness to

Pay

Unit 

Bid

27 270 - 33 340 -

Full Optimization 27 210 - 33 300 -

Total 150 - - 190 - -

4.3 Concluding Comments

This study has employed both theoretical and experimental methods to evaluate a 

number of congestion etiquettes which can potentially address the Tragedy of the 

Commons problem with respect to spectrum congestion. The examined etiquettes fall 

into two categories. One class of etiquette attempts to solve the congestion problem by 

changing the payoffs that some users receive by selecting Option B. In particular, under 

the Pay to Connect Etiquette, users pay a small fee for selecting Option B, and have an 

incentive to refrain from selecting this option (and therefore avoid creating a negative 

externality on other users) when it is expected that their decision would lead to an 

outcome that is both individually non-rational and globally inefficient. Thus, the Pay to 

Connect option can, in theory, lead to superior choices between Options A and B, but at 
- 27 -

the same time, it does not lead to efficient spectrum allocation among the users who 

finally choose Option B.21

Another class of etiquettes attempts to more efficiently allocate spectrum among 

those users that choose Option B. Both the Simple and Informed Randomization 

Etiquettes work by explicitly denying service to low priority users when total demand 

threatens to exceed a pre-defined system congestion limit. However, randomization has a 

potentially perverse effect on user choices between Options A and B. On the one hand, it 

gives every user who cannot afford to choose the subscription service (i.e., Option A) a 

positive incentive to choose Option B, rather than choose neither option. It can also give 

some users an incentive to switch from Option A to Option B, in cases where their 

expected payoff in Option B is higher than the certain payoff in Option A. The latter 

effect is more pronounced under the informed version of the etiquette than under the 

simple version. As with the Pay to Connect Etiquette, an etiquette based on the 

randomized ranking of users does not ensure that the spectrum available under Option B 

is assigned to those users that value such spectrum the most. 

The Willingness to Pay etiquette has both potential advantages and potential 

disadvantages compared to the randomization etiquettes. User willingness to pay can 

potentially allocate service to the highest value users who choose Option B. However, 

high value users (users who would be willing to pay the subscription price for Option A) 

can reduce the uncertainty regarding whether they will obtain service via Option B by 

submitting a bid that is equal to the cost of accessing spectrum via Option A. As a result 

of this reduction in uncertainty, more high value users now have an incentive to select 

Option B, and these decisions can potentially reduce total surplus by leading to more 

potential congestion under Option B. 

21 In general, Pay to Connect does not result in a unique equilibrium, or guarantee that the highest 

equilibrium surplus is attained.
28

Appendix A: Figures and Charts

Bandwidth 

(data transfer rate)

Congestion Tolerance

(as a function of used capacity)

Low High

Low High

Email FTP

Video 

Streaming

Audio

Streaming

IRC

VoIP

Gaming

Video 

Telephony

Bandwidth 

(data transfer rate)

Congestion Tolerance

(as a function of used capacity)

Low High

Low High

Email FTP

Video 

Streaming

Audio

Streaming

IRC

VoIP

Gaming

Video 

Telephony

Figure A1. 

User Spectrum Demand & Applications

Figure A2. Ethernet Packet Loss Function

Loading

Throughput

100% 

Loading

~80% 

Loading

Loading

Throughput

100% 

Loading

~80% 

Loading
29

Appendix B: Detailed Data from Examples

Table 9: Parameters for Example 1

Price of Option A: 130 Capacity of Option B: 100

Total Surplus Max: 770 Consumer Surplus Max: 528

User

(i)

Value per Unit

(vi)

Unit Demand

(qi)

Surplus

(vi qi)

Congestion

Limit

1 9 24 216 60

2 5 25 125 60

3 10 17 170 60

4 7 16 112 60

5 7 18 126 80

6 5 11 55 80

7 5 17 85 80

8 7 13 91 80

Table 10: Undominated Nash Equilibrium Assignments for Example 1

Assuming Co-Existence22

Option A Option B Neither Option Total surplus Consumer surplus

1, 3 2, 4, 5, 6, 7, 8 386 126

Table 11: Nash Equilibrium Assignment for Example 1

Assuming Pay to Connect Etiquette (Price of B = 1)

Option A Option B Neither Option Total Surplus Consumer Surplus

1, 3 5, 6, 7, 8 2, 4 743 479

Table 12: Nash Equilibrium Assignment for Example 1

Assuming the Simple Randomization Etiquette

Option A Option B Neither Option Total surplus Consumer surplus

1, 3 2, 4, 5, 6, 7, 8 643.367 383.367

Table 13: Nash Equilibrium Assignment for Example 1

Assuming Congestion Informed Randomization Etiquette

Option A Option B Neither Option Total Surplus Consumer Surplus

1 2, 3, 4, 5, 6, 7, 8 560.25 430.25

22 There are 18 Nash equilibria altogether. Total surplus ranges from 386 to 743. Consumer surplus ranges from 

126 to 483.
30

Table 14. Undominated Nash Equilibrium Assignments for Example 1

Assuming Lump-Sum Willingness to Pay Etiquette

Option A Option B Neither Option Total surplus Consumer surplus

1, 2, 3, 4, 5, 6, 7, 8 512 137

Table 8: Parameters for Example 2

Price of Option A: 130 Capacity of Option B: 100

Total Surplus Max: 1114 Consumer Surplus Max: 628

User

(i)

Value per Unit

(vi)

Unit Demand

(qi)

Surplus

(vi qi)

Congestion

Limit

1 8 19 152 60

2 10 17 170 60

3 6 16 96 60

4 10 22 220 60

5 7 13 91 80

6 8 18 144 80

7 9 19 171 80

8 5 14 70 80

Table 15: Undominated Nash Equilibrium Assignments for Example 2

Assuming Co-Existence23

Option A Option B Neither Option Total surplus Consumer surplus

1, 2, 4 3, 5, 6, 7, 8 1018 628

Table 16: Nash Equilibrium Assignment for Example 2

Assuming Pay to Connect Etiquette (Price of B = 1)

Option A Option B Neither Option Total surplus Consumer surplus

1, 2, 4 5, 6, 7, 8 3 1018 624

Table 17: Nash Equilibrium Assignment for Example 2

Assuming Simple Randomization Etiquette

Option A Option B Neither Option Total surplus Consumer surplus

1, 2, 4 3, 5, 6, 7, 8 1018 628

Table 18: Nash Equilibrium Assignment for Example 2

Assuming Informed Randomization Etiquette

Option A Option B Neither Option Total surplus Consumer surplus

4 1, 2, 3, 5, 6, 7, 8 609.593 479.593

23 There are two Nash equilibria in total. Both equilibria achieve the same total and consumer surplus values as 

reported in this table.
31

Table 19: Undominated Nash Equilibrium Assignments for Example 2

Assuming Lump-Sum Willingness to Pay Etiquette24

Option A Option B Neither Option Total surplus Consumer surplus

1, 2 3, 4, 5, 6, 7, 8 857 309

1, 4 2, 3, 5, 6, 7, 8 857 309

1, 6 2, 3, 4, 5, 7, 8 857 309

1, 7 2, 3, 4, 5, 6, 8 857 309

2, 4 1, 3, 5, 6, 7, 8 857 309

2, 6 1, 3, 4, 5, 7, 8 857 309

2, 7 1, 3, 4, 5, 6, 8 857 309

4, 6 1, 2, 3, 5, 7, 8 857 309

4, 7 1, 2, 3, 5, 6, 8 857 309

6, 7 1, 2, 3, 4, 5, 8 857 309

24 There are 32 equilibria in all. Table 13 shows the 10 equilibria involving weakly un-dominated strategies. In the 

full set of Nash equilibria, total surplus is equal to 857 in each equilibrium, and consumer surplus ranges between 

207 and 387.