![](media/image1.wmf){width="1.1416666666666666in" height="2.0in"}

> **Federal Communications Commission**

**Office of Strategic Planning and Policy Analysis**

**445 12th Street, SW**

**Washington, DC 20554**

#  {#section .unnumbered}

#  {#section-1 .unnumbered}

#  {#section-2 .unnumbered}

#  {#section-3 .unnumbered}

**OSP Working Paper Series**

+--------------+-------------------------------------------------------+
| 41           | Enhancing Spectrum's                                  |
|              |                                                       |
|              | Value Through Market-informed 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

**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](#introduction)

2 Formal Analysis of the Tragedy of the Commons
[2](#formal-analysis-of-the-tragedy-of-the-commons)

2.1 A Simplified Model [3](#a-simplified-model)

2.2 Tragedy of the Commons Problem: Nash Prediction
[6](#tragedy-of-the-commons-problem-nash-prediction)

3 Congestion Etiquettes [8](#congestion-etiquettes)

3.1 Enhancing Efficiency By Changing Strategy Payoff
[8](#enhancing-efficiency-by-changing-strategy-payoff)

3.2 Enhancing Efficiency Via Rationing -- Randomization
[9](#enhancing-efficiency-via-rationing-randomization)

3.3 Enhancing Efficiency Via Rationing -- Willingness to Pay
[12](#enhancing-efficiency-via-rationing-willingness-to-pay)

3.4 Congestion Etiquettes -- Nash Predictions
[14](#__RefHeading___Toc191881609)

4 Experimental Analysis -- Congestion Etiquette Performance
[16](#experimental-analysis-congestion-etiquette-performance)

4.1.1 No Exclusion Etiquette -- Fairness and Pay to Connect
[17](#no-exclusion-etiquette-fairness-and-pay-to-connect)

4.1.2 Exclusion Etiquettes [18](#exclusion-etiquettes)

4.1.2.1 Randomization Etiquette [18](#randomization-etiquette)

4.1.2.2 Lump Sum WTP-based Greedy Algorithms
[20](#lump-sum-wtp-based-greedy-algorithms)

4.1.2.3 Unit-based WTP-based Greedy Algorithms
[21](#unit-based-wtp-based-greedy-algorithms)

4.1.2.4 WTP-based Full Optimization Algorithm
[22](#wtp-based-full-optimization-algorithm)

4.2 Experimental Results [23](#experimental-results)

4.3 Concluding Comments [26](#concluding-comments)

Appendix A: Figures and Charts [28](#appendix-a-figures-and-charts)

Appendix B: Detailed Data from Examples
[29](#appendix-b-detailed-data-from-examples)

# 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 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.

# 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 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.

## 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 some desired value to zero.[^3] Figure 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**

![](media/image2.wmf){width="5.789583333333334in"
height="3.8048611111111112in"}

Spectrum users increasingly face a choice between using either dedicated
spectrum provided through a subscription service or using shared
spectrum allocated to unlicensed 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 ![](media/image3.wmf){width="1.125in" height="0.375in"},
consumer surplus is defined as
![](media/image4.wmf){width="1.9861111111111112in" height="0.375in"},
*q~i~* represents user *i*'s demand, *v~i~* represents value per unit of
demand for user *i*, and *P~A~* and *P~B~* represent the prices for
options A and B respectively.[^5]

Figure 2: Efficient Assignment of Spectrum in Example 1

![](media/image5.wmf){width="5.998611111111111in"
height="2.9680555555555554in"}

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.

## 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 (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%.

# 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]

## 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 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
non-refundable 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%.

## 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 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**

![](media/image6.wmf){width="6.001388888888889in"
height="3.584722222222222in"}

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 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.

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%.

## 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 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.

Figure 4: Willingness to Pay in Example 1

![](media/image7.wmf){width="5.541666666666667in"
height="3.238888888888889in"}

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%.

## 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 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 pro-active 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%
  --------------------------------- ------------------ ------------------

**Table 2:** Summary of Predicted Consumer and Total Surplus Values

  ----------------- ------------ ------------ ------------ ----------------
  Etiquette         Example 1                 Example 2    

                    **Total      **Consumer   **Total      **Consumer
                    Surplus**    Surplus**    Surplus**    Surplus**

  Fairness          386          126          1018         628

  Pay to Connect    743          363          1018         528

  Simple            643.367      383.367      1018         628
  Randomization                                            

  Informed          560.25       430.25       609.593      479.593
  Randomization                                            

  WTP               512          137          857          309
  ----------------- ------------ ------------ ------------ ----------------

# Experimental Analysis -- Congestion Etiquette Performance

#  {#section-4 .unnumbered}

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.

### 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.

Figure 5: Screen 1 -- No Exclusion

![](media/image8.jpeg){width="5.3375in" height="3.6791666666666667in"}

### 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.

#### 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 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)

![](media/image8.jpeg){width="5.3375in" height="3.6791666666666667in"}

#### 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.

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

![](media/image8.jpeg){width="5.3375in" height="3.6791666666666667in"}

#### 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 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)

![](media/image8.jpeg){width="5.3375in" height="3.4604166666666667in"}

#### 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.

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

![](media/image8.jpeg){width="5.3375in" height="3.6791666666666667in"}

## 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 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 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

+----+-------+-----+---+---------+----------+---+---------+----------+
| E  |       |     | E |         | Nash     | E |         | Nash     |
| ti |       |     | x |         | Pre      | x |         | Pre      |
| qu |       |     | a |         | dictions | a |         | dictions |
| et |       |     | m |         |          | m |         |          |
| te |       |     | p |         |          | p |         |          |
|    |       |     | l |         |          | l |         |          |
|    |       |     | e |         |          | e |         |          |
|    |       |     | 1 |         |          | 2 |         |          |
+----+-------+-----+---+---------+----------+---+---------+----------+
|    |       |     | * | **Effic | **Effi   | * | **Effic | **Effi   |
|    |       |     | * | iency** | ciency** | * | iency** | ciency** |
|    |       |     | N |         |          | N |         |          |
|    |       |     | * |         |          | * |         |          |
|    |       |     | * |         |          | * |         |          |
+----+-------+-----+---+---------+----------+---+---------+----------+
| Fa |       |     | 1 | 42%     | 50.1%    | 2 | 57%     | 91.4%    |
| ir |       |     | 8 |         |          | 2 |         |          |
| ne |       |     |   |         |          |   |         |          |
| ss |       |     |   |         |          |   |         |          |
+----+-------+-----+---+---------+----------+---+---------+----------+
| P  |       |     | 2 | 52%     | 96.5%    | 3 | 74%     | 91.4%    |
| ay |       |     | 7 |         |          | 3 |         |          |
| to |       |     |   |         |          |   |         |          |
| C  |       |     |   |         |          |   |         |          |
| on |       |     |   |         |          |   |         |          |
| ne |       |     |   |         |          |   |         |          |
| ct |       |     |   |         |          |   |         |          |
+----+-------+-----+---+---------+----------+---+---------+----------+
| Gr | Inf   |     | 2 | 70%     | 72.8%    | 3 | 63%     | 54.7%    |
| ee | ormed |     | 7 |         |          | 3 |         |          |
| dy | Ran   |     |   |         |          |   |         |          |
| A  | domiz |     |   |         |          |   |         |          |
| lg | ation |     |   |         |          |   |         |          |
| or |       |     |   |         |          |   |         |          |
| it |       |     |   |         |          |   |         |          |
| hm |       |     |   |         |          |   |         |          |
+----+-------+-----+---+---------+----------+---+---------+----------+
|    | > W   | L   | 2 | 72%     | 66.5%    | 3 | 68%     | 76.9%    |
|    | illin | ump | 7 |         |          | 3 |         |          |
|    | gness | Sum |   |         |          |   |         |          |
|    | > to  |     |   |         |          |   |         |          |
|    | > Pay |     |   |         |          |   |         |          |
+----+-------+-----+---+---------+----------+---+---------+----------+
|    |       | U   | 2 | 66%     | \-       | 3 | 74%     | \-       |
|    |       | nit | 7 |         |          | 3 |         |          |
|    |       | Bid |   |         |          |   |         |          |
+----+-------+-----+---+---------+----------+---+---------+----------+
| Fu |       |     | 2 | 75%     | \-       | 3 | 73%     | \-       |
| ll |       |     | 7 |         |          | 3 |         |          |
| Op |       |     |   |         |          |   |         |          |
| ti |       |     |   |         |          |   |         |          |
| mi |       |     |   |         |          |   |         |          |
| za |       |     |   |         |          |   |         |          |
| ti |       |     |   |         |          |   |         |          |
| on |       |     |   |         |          |   |         |          |
+----+-------+-----+---+---------+----------+---+---------+----------+
| T  |       |     | 1 | 64%     | \-       | 1 | 69%     | \-       |
| ot |       |     | 5 |         |          | 9 |         |          |
| al |       |     | 0 |         |          | 0 |         |          |
+----+-------+-----+---+---------+----------+---+---------+----------+

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

+----+------+-----+---+---------+----------+----+---------+----------+
| E  |      |     | E |         | Nash     | E  |         | Nash     |
| ti |      |     | x |         | Pre      | xa |         | Pre      |
| qu |      |     | a |         | dictions | mp |         | dictions |
| et |      |     | m |         |          | le |         |          |
| te |      |     | p |         |          | 2  |         |          |
|    |      |     | l |         |          |    |         |          |
|    |      |     | e |         |          |    |         |          |
|    |      |     | 1 |         |          |    |         |          |
+----+------+-----+---+---------+----------+----+---------+----------+
|    |      |     | * | **C     | **       | *  | **C     | **       |
|    |      |     | * | onsumer | Consumer | *N | onsumer | Consumer |
|    |      |     | N | Su      | S        | ** | Su      | S        |
|    |      |     | * | rplus** | urplus** |    | rplus** | urplus** |
|    |      |     | * |         |          |    |         |          |
+----+------+-----+---+---------+----------+----+---------+----------+
| Fa |      |     | 1 | 120     | 126      | 22 | 260     | 628      |
| ir |      |     | 8 |         |          |    |         |          |
| ne |      |     |   |         |          |    |         |          |
| ss |      |     |   |         |          |    |         |          |
+----+------+-----+---+---------+----------+----+---------+----------+
| P  |      |     | 2 | 62      | 363      | 33 | 260     | 528      |
| ay |      |     | 7 |         |          |    |         |          |
| to |      |     |   |         |          |    |         |          |
| C  |      |     |   |         |          |    |         |          |
| on |      |     |   |         |          |    |         |          |
| ne |      |     |   |         |          |    |         |          |
| ct |      |     |   |         |          |    |         |          |
+----+------+-----+---+---------+----------+----+---------+----------+
| Gr | Info |     | 2 | 390     | 430.25   | 33 | 470     | 479.59   |
| ee | rmed |     | 7 |         |          |    |         |          |
| dy | R    |     |   |         |          |    |         |          |
| A  | ando |     |   |         |          |    |         |          |
| lg | miza |     |   |         |          |    |         |          |
| or | tion |     |   |         |          |    |         |          |
| it |      |     |   |         |          |    |         |          |
| hm |      |     |   |         |          |    |         |          |
+----+------+-----+---+---------+----------+----+---------+----------+
|    | Wil  | L   | 2 | 250     | 137      | 33 | 280     | 309      |
|    | ling | ump | 7 |         |          |    |         |          |
|    | ness | Sum |   |         |          |    |         |          |
|    | to   |     |   |         |          |    |         |          |
|    |      |     |   |         |          |    |         |          |
|    | >    |     |   |         |          |    |         |          |
|    |  Pay |     |   |         |          |    |         |          |
+----+------+-----+---+---------+----------+----+---------+----------+
|    |      | U   | 2 | 270     | \-       | 33 | 340     | \-       |
|    |      | nit | 7 |         |          |    |         |          |
|    |      | Bid |   |         |          |    |         |          |
+----+------+-----+---+---------+----------+----+---------+----------+
| Fu |      |     | 2 | 210     | \-       | 33 | 300     | \-       |
| ll |      |     | 7 |         |          |    |         |          |
| Op |      |     |   |         |          |    |         |          |
| ti |      |     |   |         |          |    |         |          |
| mi |      |     |   |         |          |    |         |          |
| za |      |     |   |         |          |    |         |          |
| ti |      |     |   |         |          |    |         |          |
| on |      |     |   |         |          |    |         |          |
+----+------+-----+---+---------+----------+----+---------+----------+
| T  |      |     | 1 | \-      | \-       | 1  | \-      | \-       |
| ot |      |     | 5 |         |          | 90 |         |          |
| al |      |     | 0 |         |          |    |         |          |
+----+------+-----+---+---------+----------+----+---------+----------+

## 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 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.

# Appendix A: Figures and Charts {#appendix-a-figures-and-charts .unnumbered}

> ![](media/image9.wmf){width="5.001388888888889in"
> height="4.106944444444444in"}Figure A1. User Spectrum Demand &
> Applications

Figure A2. Ethernet Packet Loss Function

> ![](media/image10.wmf){width="6.001388888888889in"
> height="3.4993055555555554in"}

#  {#section-5 .unnumbered}

# Appendix B: Detailed Data from Examples {#appendix-b-detailed-data-from-examples .unnumbered}

**Table 9: Parameters for Example 1**

+------+------------------+----------------+----------+--------------+
| P    |                  |                |          |              |
| rice |                  |                |          |              |
| of   |                  |                |          |              |
| Op   |                  |                |          |              |
| tion |                  |                |          |              |
| A:   |                  |                |          |              |
| 130  |                  |                |          |              |
| Capa |                  |                |          |              |
| city |                  |                |          |              |
| of   |                  |                |          |              |
| Op   |                  |                |          |              |
| tion |                  |                |          |              |
| B:   |                  |                |          |              |
| 100  |                  |                |          |              |
|      |                  |                |          |              |
| T    |                  |                |          |              |
| otal |                  |                |          |              |
| Sur  |                  |                |          |              |
| plus |                  |                |          |              |
| Max: |                  |                |          |              |
| 770  |                  |                |          |              |
| Cons |                  |                |          |              |
| umer |                  |                |          |              |
| Sur  |                  |                |          |              |
| plus |                  |                |          |              |
| Max: |                  |                |          |              |
| 528  |                  |                |          |              |
+------+------------------+----------------+----------+--------------+
| User | Value per Unit   | Unit Demand    | Surplus  | Congestion   |
|      |                  |                |          |              |
| \    | (v~i~)           | (q~i~)         | (v~i~    | Limit        |
| (i\) |                  |                | q~i~)    |              |
+------+------------------+----------------+----------+--------------+
| 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-Existence**[^22]

  ---------- ------------- --------------- ------------- ------------------
  **Option   **Option B**  **Neither       **Total       **Consumer
  A**                      Option**        surplus**     surplus**

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

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,                   643.367       383.367
             7, 8                                        
  ---------- ------------- --------------- ------------- ------------------

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,                560.25        430.25
            7, 8                                        
  --------- -------------- -------------- ------------- -----------------

Table 14. Undominated Nash Equilibrium Assignments for Example 1

Assuming Lump-Sum Willingness to Pay Etiquette

  ---------- ----------------- -------------- ------------ ----------------
  **Option   **Option B**      **Neither      **Total      **Consumer
  A**                          Option**       surplus**    surplus**

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

**Table 8: Parameters for Example 2**

+------+------------------+----------------+----------+--------------+
| P    |                  |                |          |              |
| rice |                  |                |          |              |
| of   |                  |                |          |              |
| Op   |                  |                |          |              |
| tion |                  |                |          |              |
| A:   |                  |                |          |              |
| 130  |                  |                |          |              |
| Capa |                  |                |          |              |
| city |                  |                |          |              |
| of   |                  |                |          |              |
| Op   |                  |                |          |              |
| tion |                  |                |          |              |
| B:   |                  |                |          |              |
| 100  |                  |                |          |              |
|      |                  |                |          |              |
| T    |                  |                |          |              |
| otal |                  |                |          |              |
| Sur  |                  |                |          |              |
| plus |                  |                |          |              |
| Max: |                  |                |          |              |
| 1114 |                  |                |          |              |
| Cons |                  |                |          |              |
| umer |                  |                |          |              |
| Sur  |                  |                |          |              |
| plus |                  |                |          |              |
| Max: |                  |                |          |              |
| 628  |                  |                |          |              |
+------+------------------+----------------+----------+--------------+
| User | Value per Unit   | Unit Demand    | Surplus  | Congestion   |
|      |                  |                |          |              |
| \    | (v~i~)           | (q~i~)         | (v~i~    | Limit        |
| (i\) |                  |                | q~i~)    |              |
+------+------------------+----------------+----------+--------------+
| 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-Existence**[^23]

  ---------- ----------- --------------- -------------- ------------------
  **Option   **Option    **Neither       **Total        **Consumer
  A**        B**         Option**        surplus**      surplus**

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

**Table 16: Nash Equilibrium Assignment for Example 2**

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

  ---------- ---------- ---------------- -------------- -------------------
  **Option   **Option   **Neither        **Total        **Consumer
  A**        B**        Option**         surplus**      surplus**

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

**Table 17: Nash Equilibrium Assignment for Example 2**

**Assuming Simple Randomization Etiquette**

  ---------- ----------- --------------- -------------- ------------------
  **Option   **Option    **Neither       **Total        **Consumer
  A**        B**         Option**        surplus**      surplus**

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

**Table 18: Nash Equilibrium Assignment for Example 2**

**Assuming Informed Randomization Etiquette**

  ---------- --------------- -------------- ------------- -----------------
  **Option   **Option B**    **Neither      **Total       **Consumer
  A**                        Option**       surplus**     surplus**

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

**Table 19: Undominated Nash Equilibrium Assignments for Example 2**

**Assuming Lump-Sum Willingness to Pay Etiquette**[^24]

  ---------- ------------- --------------- ------------- ------------------
  **Option   **Option B**  **Neither       **Total       **Consumer
  A**                      Option**        surplus**     surplus**

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

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

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

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

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

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

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

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

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

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

[^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>.

[^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.

[^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.

[^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, *P~B~* , may
    be assigned to users of Option B. In the above notation, producer
    surplus is defined as *P~A~ n~A~ + P~B~ n~B~,* where *n~A~* and
    *n~B~* represent the number of subscribers choosing options *A* and
    *B* respectively*.*

[^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]: 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.

[^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.

[^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.

[^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.

[^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.

[^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.

[^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.

[^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.

[^21]: In general, Pay to Connect does not result in a unique
    equilibrium, or guarantee that the highest equilibrium surplus is
    attained.

[^22]: There are 18 Nash equilibria altogether. Total surplus ranges
    from 386 to 743. Consumer surplus ranges from 126 to 483.

[^23]: There are two Nash equilibria in total. Both equilibria achieve
    the same total and consumer surplus values as reported in this
    table.

[^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.