Federal Communications Commission

Office of Strategic Planning and Policy Analysis

445 12th Street, SW

Washington, DC 20554

OSP Working Paper Series

43 A Market-based Approach to 

Establishing Licensing Rules: 

Licensed Versus Unlicensed 

Use of Spectrum 

February 2008

Mark M. Bykowsky

Mark A. Olson

William W. Sharkey
A Market-Based Approach to Establishing Licensing Rules:

Licensed Versus Unlicensed Use of Spectrum

Mark M. Bykowsky

*†

Office of Strategic Planning and Policy Analysis

Federal Communications Commission

Washington, D.C.

William W. Sharkey

Wireline Competition Bureau

Federal Communications Commission

Washington, D.C.

and

Mark A. Olson

George Mason University

Arlington, Virginia

February 2008

OSP Working Paper No. 43

* Mark Olson participated in this project under a contract with the FCC. This document is available on the 

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

† The authors would like to thank Ronald Chase, Gregory Crawford, Ira Keltz, Julius Knapp, Evan Kwerel, 

Ahmed Lahjouji, William Lehr, Jonathan Levy, Martha Stancill, and Weiren Wang for very helpful 

comments on an earlier draft. We would also like to thank Kenneth Carter for early helpful comments on 

the project. 

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

The FCC uses an administrative process for identifying the most desirable set of licensing 

rules for spectrum. Spectrum designated to unlicensed use is made freely available for 

uses which comply with appropriate technical standards. Spectrum allocated to licensed 

use is generally awarded to private parties through an auction mechanism. The allocation 

between licensed and unlicensed use, however, is based on the FCC’s judgment, which in 

turn relies on information provided by interested parties who seek to use the spectrum. 

One method of reducing the incentive that parties have to exaggerate the value they place 

on a given regime involves creating a market for such rules. We examine the feasibility 

of using a “clock auction” to determine, based on the bids submitted by market 

participants for the corresponding licensing rules, the efficient allocation of a given 

amount of spectrum between licensed and unlicensed spectrum use. Analysis indicates 

that market forces, in the form of a clock auction, can be used to determine the efficient 

assignment of license rules to spectrum. 
TABLE OF CONTENTS

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

2 Modeling Licensing Rules – Licensed and Unlicensed Operations.....................................2

3 Modeling Auction Participant Type.......................................................................................4

4 Modeling Bidder Preferences and Valuations ......................................................................5

5 Market Mechanism – A Clock Auction ...............................................................................10

5.1 Allocation Rule – Aggregate Bid Rule ...................................................................................11

5.2 Pricing Rule..............................................................................................................................13

6 The Mechanism Design Problem.........................................................................................15

6.1 Provision Points and “Free Riding”.......................................................................................15

6.2 Nash Equilibria........................................................................................................................17

7 Economic Experiments.........................................................................................................23

8 Concluding Comments.........................................................................................................25
1

1 Introduction

Like many other telecommunications regulatory bodies, the Federal Communications 

Commission (FCC) uses an administrative process for identifying the most desirable set of 

licensing rules for a given band of spectrum. An important recent example involved the use of 

that process in establishing licensing rules for 22 MHz in the 700 MHz band.3 Here, the FCC 

faced the highly contentious issue of whether to impose an “open” versus a “closed” platform 

requirement on the license owner of such a block. Under an “open” platform requirement, the 

license owner would be prohibited from restricting the set of wireless devices that a customer 

can employ on the licensee’s network and the applications the customer can access via that 

network.4In contrast, under a “closed” platform regime, the license owner would not be so 

prohibited. Traditional service providers (e.g., Verizon, AT&T) argued strongly that the 

platform should be closed, while several interested parties (e.g., Google, Skype, Frontline 

Wireless) maintained that the platform should be open.5

Some regulatory bodies have expressed substantial dissatisfaction with the use of an 

administrative process to make such decisions.6The dissatisfaction stems, in part, from the 

manner in which the process obtains information on the value users place on alternative spectrum 

license rules. In contrast to a market mechanism, where users pay a price for having their needs 

met, an administrative process relies simply on the reported needs of interested parties. Because 

of the cost of misrepresenting one’s needs is small relative to the potential private value of 

spectrum acquired, each user has an incentive to exaggerate the value he/she places on a given 

set of licensing rules, as well as how much spectrum to which those rules should apply. 

3

See Federal Communications Commission, Second Report and Order, WT Docket No. 07-132, July 31, 207. 

Another example involves the identification of the most efficient set of license rules for Advanced Wireless Services 

in the 2155-2175 MHz Band. See Federal Communications Commission, Notice of Proposed Rulemaking, WT 

Docket No. 07-195, September 19, 2007. 

4 Currently, carriers typically restrict the models of cell phones that can be employed on their networks as well as the 

software that can be downloaded onto the cell phones that can be employed on their networks.

5 On September 13, 2007, Verizon filed a suit before the U.S. District Court of Appeals for the District of Columbia 

arguing that the FCC’s open access requirements were unlawful. On October 23, 2007, Verizon decided to drop its 

lawsuit after losing its appeal for a speedy resolution on October 3, 2007. On that same day, the Cellular Telephone 

Industry Association (CTIA) stepped in to challenge the same regulation in a lawsuit before the Court. See “CTIA 

Takes UP 700 MHz Challenge,” RCR Wireless News, October 26, 2007. 

6 The European Commission has recently stated that an administrative process for determining licensing rules is 

neither transparent nor objective. See Study of Legal, Economic & Technical Aspects of “Collective Use of 

Spectrum” in the European Community – Final Report, by Mott MacDonald Ltd., Aegis Systems Led., IDATE, 

Indepen Ltd, and Wik Consult (November 2006), pg 13. Recently, Professor Martin Cave called the administrative 

approach to determining license rules “arbitrary and unsatisfactory.” See “New spectrum-using technologies and the 

future of spectrum management: a European policy perspective,” by Martin Cave, in Communications: The Next 

Decade, edited by Ed Richards, Robin Foster and Tom Kiedrowski, Ofcom (November 2006), pg. 224.
2

Therefore, identifying the most desirable set of licensing rules involves both measuring an 

interested party’s “need,” and determining the magnitude by which interested parties have 

exaggerated their license rule needs. The FCC’s license rule assignment problem is similar to 

other assignment problems where an administrative process is used to identify the best use of a 

given resource. For example, city planners are often confronted with the problem of determining 

whether a given parcel of land should be designated to public or private use. 

The FCC’s license rule assignment problem is an example of a broader class of “incentive 

problems” that have been considered in the economics literature. In this instance, a potential 

solution involves creating a mechanism that induces interested parties to reveal their private 

information regarding the value they place on spectrum and the licensing rules that apply to that 

spectrum. One approach, which is explored in this paper, involves the creation of a market for 

licensing rules in which participants bid to have their licensing rule needs met. By reducing the 

incentive that interested parties have to misrepresent their economic interests, this approach may 

substantially improve the efficiency of the licensing process and, thus, the economic benefit 

society receives from one of its most valuable resources. 

Licensing rules come in a wide variety of flavors. We examine, using experimental 

methods, the issue of whether a particular market form can determine an efficient designation of 

a given amount of spectrum between licensed and unlicensed use. Specifically, we 

experimentally examine the ability and willingness of market participants to compete, via a clock 

auction, to have a number of homogeneous units of spectrum designated to licensed versus 

unlicensed use. The clock auction is an ascending price auction wherein bidders reveal to an 

administrator the number of blocks of spectrum they wish to “acquire” at different clock prices 

established by an administrator. The auction concludes when the demand for spectrum is 

consistent with the available supply at that clock price. Because each bid is associated with a 

given license regime, the identification of the efficient assignment of spectrum simultaneously 

determines the efficient set of licensing rules for the blocks of spectrum up for auction, given the 

bids submitted in the auction. Once the efficient allocation of spectrum is identified, a simple 

rule determines the price(s) paid by winning bidders. 

2 Modeling Licensing Rules – Licensed and Unlicensed Operations 

As part of its spectrum management responsibilities the FCC determines the set of rights 

that are assigned to a given block of spectrum used by commercial and non-commercial entities. 
3

At one end of the spectrum rights regime are unlicensed operations. Under unlicensed 

operations, spectrum is treated as an open access resource that is available to all without charge.7

Each user is free to demand as much spectrum as he/she wishes employing the appropriate FCCcertified equipment, which operates at the authorized power levels. However, the service 

quality, in terms of transmission speed, jitter and packet loss, experienced by a given user 

depends on the total spectrum demand of all users. In particular, if the sum of the demands that 

users place on the available spectrum is less than some percentage of the available supply, the 

quality of service is satisfactory for all users. On the other hand, if total demand for spectrum 

exceeds the available supply, spectrum is assigned to the competing users in a manner that 

reduces the quality of service for all.8The most successful example of unlicensed operations is 

Wi-Fi service, a service that operates in the 900 MHz, 2.4 GHz, and 5.8 GHz bands and which is 

employed by millions of users each day to access the Internet.9

At the other end of the spectrum licensing regime are licensed operations. Under licensed 

operations the license owner is granted the right to determine the service to be offered, the 

technology to be employed to provide that service, and the right to exclude non-payers from 

accessing his/her service. In addition, the license owner is assigned a right that protects his/her 

service from harmful interference from other service providers, as well as the right to sell his/her 

license to another party. A prominent example of licensed operations is the highly successful 

Personal Communications Service which operates in the 1.9 GHz band. 

In modeling the licensing rule problem, we assume that, as a result of its engineering and 

policy analysis, the FCC has established a set of technical performance parameters, including 

maximum power and out-of-band emission limits, for a set of four bands of spectrum located in a 

7 While spectrum is available to makers of FCC authorized devices without charge, whether spectrum is fee to users 

depends upon the service and the business enterprise. For example, Panera Bread offers free Wi-Fi service to its 

customers, while Starbucks does not. 

8 Because of differences among spectrum users on the effect spectrum congestion has on the value they place on 

spectrum, the economic relationship between quality of service, spectrum congestion, and valuation is more 

complicated in actuality than specified here. For a discussion of this economic relationship, see Bykowsky, M., 

Olson, M., and Sharkey W. (2008) “Modeling the Efficiency of Spectrum Designated to Licensed Service and 

Unlicensed Operations,” OSP Working Paper #42. Some writers use the word “interference” to describe the 

problem of spectrum congestion. See Stuart Benjamin (2003), “Spectrum Abundance and the Choice Between 

Private and Public Control,” New York Law Review, vol. 78, Number 6, pgs 2007-2102.

9 More precisely, the FCC has authorized devices to operate on an unlicensed basis in these bands. Moreover, 

technological improvements continue to enhance the transmission capabilities of spectrum designated to unlicensed 

operations. Such improvement may in the future prove effective in enhancing competition in the broadband access 

marketplace.
4

single geographic area (see Figure 1).10 We further assume that, as part of its traditional 

spectrum management responsibilities, the FCC is confronted with the problem of identifying 

whether each block should be designated to either licensed or unlicensed operations, and, for 

licensed operation it must further identify the user(s) that most highly value the block(s). The 

current analysis assumes that equal power is designated for all block of licensed or unlicensed 

spectrum. 

Figure 1: Hypothetical Band Plan

3 Modeling Auction Participant Type

In an auction to allocate spectrum between licensed and unlicensed use, participating firms 

fall into two distinct categories as a result of differences in their business models. The business 

model of “L-Type” firms (e.g., Verizon, AT&T, T-Mobile) involves constructing the necessary 

telecommunications infrastructure and earning a return on that investment based on revenue 

obtained from subscribers. Consequently, all L-Type firms strongly prefer to acquire spectrum 

10 Spectrum congestion is a problem for all service providers, regardless of whether they utilize spectrum designated 

to licensed use or spectrum designated to unlicensed operations. However, due to the free entry conditions of 

unlicensed operations, congestion is considered a greater problem under unlicensed operations than licensed use. To 

reduce the likelihood of congestion, the FCC typically authorizes a lower power limit for unlicensed operations than 

licensed use. Nevertheless, we assume in this analysis that there is no difference in authorized power levels between 

the two service types. The assumption is appropriate if certain enforceable congestion protocols are established 

within the unlicensed spectrum bands. For a discussion of several possible protocols, see Bykowsky, M., Carter, K, 

Olson, M., and Sharkey W. (2008) “Enhancing Spectrum’s Value Through Market-informed Congestion 

Etiquettes,” OSP Working Paper #41. For a discussion of the incentive equipment manufacturers have to design 

unlicensed devices that are “greedy,” thereby increasing the likelihood of spectrum congestion, 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. 

Market Area

Transmission 

Power

Block #2 Block #2 Block #3 Block #4

Frequency
5

with licensing rules that enable them to exclude non-payers and to receive protection from 

harmful interference from other service providers. 

Another type of bidder – a “U-Type” firm – has a preference for licensing rules that promote 

free, open access to spectrum. A variety of firms fall within the U-Type category. Rather than 

derive revenue from subscribers, one class of U-Type firms earns revenue from advertisers 

and/or retail customers that sell good/services to customers via the Internet. The most prominent 

examples are firms (Ask.com, Google, Microsoft, Yahoo) that obtain revenue from selling to 

advertisers access to viewers/listeners that are attracted to Internet-based content and services. 

Another class of U-Type firm (Cisco, Fujitsu, Juniper Networks, Motorola) obtains revenue from 

selling hardware (e.g., wireless routers) to firms that provide Wi-Fi service (Marriott Hotels, 

Panera Bread, Starbucks) or obtains revenue directly from consumers that purchase products 

(e.g., cellular handsets or automatic garage door openers) that utilize spectrum designated to 

unlicensed operations.

The greater the number of viewers or users to which a U-Type firm can obtain access, all 

things being equal, the greater the value it places on licensing rules that provide for nonexclusive, open access use. It also follows that the greater the demand for a product that is 

necessary to either provide Wi-Fi service or to enable consumers to utilize spectrum designated 

to unlicensed operations, the greater the value the U-Type firm places on licensing rules that 

provide for non-exclusive, open access use. Because market participants vary in the demand for 

their products, as well as in their profit margins, U-Type firms will vary in the value they place 

on having spectrum allocated to unlicensed operations, but they nevertheless have a common 

interest in obtaining spectrum authorized for unlicensed use.

4 Modeling Bidder Preferences and Valuations

Under the current FCC administrative process to determine the amount of spectrum assigned 

to market participants, it is possible that the spectrum assigned to any given user is less than what 

that user desires. This mis-estimation makes it likely that market participants will desire 

multiple blocks of spectrum. However, legitimate concerns about system congestion also create 

a demand for multiple blocks for any given user.11 Because of diminishing marginal revenue 

product considerations, the value each firm places on the first block of spectrum may exceed the 

11 See Bykowksy, et al. (2008), op cit.
6

value a firm places on additional blocks of spectrum.12 In addition, given the stronger ownership 

and use rights associated with spectrum designated to licensed versus unlicensed operations, our 

model assumes that L-Type firms uniformly place a higher value on a block of spectrum than UType firms.13

In this analysis, the actual values assigned to market participants are driven less by actual 

market valuation considerations derived from empirical data than by a desire to stress test our 

market approach to achieving the efficient allocation of spectrum. In particular, we wish to 

establish a valuation environment that tests whether the proposed mechanism efficiently 

designates spectrum to unlicensed operations when it should clearly do so. Moreover, we wish 

to establish a valuation environment that tests whether the mechanism finds the efficient set of 

license rules when to do so is highly problematic. To that end, we have established two 

valuation environments. Under one set of valuations (Session 1), there are two L-Type bidders 

(A and B), and six U-Type bidders (C through H). Figure 2 shows the distribution of valuations 

across these bidders in this environment.

Figure 2: Session 1 Valuations

12 A market participant’s demand for spectrum is derived from the demand consumers express for the participant’s 

wireless service. In a competitive market, consistent with a firm’s attempt to maximize its profits, a firm will 

acquire spectrum to the point where its marginal revenue product of spectrum is equal to its cost. 

13 The fact that a U-Type firm has never participated in a spectrum auction, let alone place a winning bid in an 

auction, provides weak proof that up to now U-Type firms place a lower value on a given block of spectrum than LType firms.

E F G H

A

B

Suppl

y

Valuation

s

200

400

100

300

500

A

G H

B

C D

E F

C D

400 300 250 200 120 120 80 80 60 60 40 40 40 40 20 20

Unit

s

U-Type 

Bidder

L-Type 

Bidder

A

B

Suppl

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Supply

Valuation

s

200

400

100

300

500

A

B

400 300 250 200 120 120 80 80 60 60 40 40 40 40 20 20

Unit

s

U-Type 

Bidder

L-Type 

U Bidder-Type 

Bidder

L-Type 

Bidder
7

Under another set of valuations (Session 2), there are two L-Type bidders, and five U-Type 

bidders. Figure 3 shows the distribution of valuations across these bidders in this environment. 

Figure 3: Session 2 Valuations

Because each bid is associated with a given license regime, the identification of the efficient 

assignment of spectrum simultaneously determines the efficient set of licensing rules for the 

blocks of spectrum up for auction and the set of winning bidders, given the bids submitted in the 

auction. Identifying the economically efficient set of licensing rules involves measuring the 

value society would receive from each set of license rules. The value society obtains from 

having one or more blocks of spectrum allocated to licensed operations is equal to the value LType firms place on licensed operations. In contrast, the value that society obtains from having 

one or more blocks of spectrum designated to unlicensed operations, given their unfettered open 

access nature, is equal to the summation of the valuations that U-Type subjects place on having 

such a designation. Figure 4 shows the efficient assignment of spectrum, including the efficient 

set of licensing rules, involving Session 1’s valuation set. As shown, efficiency considerations 

dictate that one block of spectrum be assigned to subjects A and B (for licensed operations) and 

two blocks of spectrum to subjects C – H (for unlicensed operations). 

U-Type 

Bidder

L-Type 

Bidder

A

B

B

D

Valuation

s

200

400

100

300

500

A

C

Suppl

y

G

400 300 250 220 200 120 80 80 60 60 4

Unit

s

U-Type 

Bidder

L-Type 

U Bidder -Type 

Bidder

L-Type 

Valuation

s

200

400

100

300

500

Suppl

y

Supply

400 300 250 220 200 120 80 80 60 60 40 40 20 20

Unit

s

C D

E F

E F G
8

Figure 4: Session 1 Efficient Assignment

The objective of our analysis is to examine – in proof of concept terms – whether a market 

can be used to allocate spectrum between licensed and unlicensed operations.14 At the minimum, 

the chosen market mechanism should designate spectrum to unlicensed operations where it is 

obvious, from an efficiency perspective, that it should do so. Here, we define the level of 

“obviousness” by the size of the discrepancy between the value U-Type bidders place on having 

spectrum designated to unlicensed operations and the value society would receive from having 

the extra-marginal unit included in the allocation. For example, as shown in Figure 4, the sum of 

the values U-Type subjects place on having spectrum designated to unlicensed operations (i.e., 

440) is substantially greater than the value Subject A places on a second block of spectrum (i.e., 

250). Therefore, in this environment a successful mechanism is one that nearly always

designates at least one block of spectrum to unlicensed operations. 

Ideally, the chosen market mechanism should also designate spectrum to unlicensed 

operations in instances where just a small amount of under-revelation by U-Type participants 

would cause the market to designate spectrum to licensed operations when efficiency 

considerations dictate it should be designated to unlicensed operations. One measure of the 

degree of difficulty U-Type firms will have in overcoming the under-revelation problem is 

represented by the amount of value they collectively must give up in order to obtain a given 

14 A Proof of Concept is a realization of a given process or technique that is designed to demonstrate the feasibility 

and workability of a set of core ideas. 

A

B

= 440

Valuation

s

200

400

100

300

500

400 300

A

B

2

H

G

F

E

D

C

Supply

250 200

Unit

s

U - Type Bidder

L - Type Bidder

H

G

F

E

D

C

A

B

∑ = 440

Valuation

s

200

400

100

300

500

400 300

A

2

H

G

F

E

D

C

∑ = 280

Suppl

y

Supply

250 200

Unit

s

U - Type Bidder

L - Type Bidder

U - Type Bidder

L - Type Bidder

H

G

F

E

D

C
9

amount of value. How much value U-Type firms need to give up depends on the mechanism’s 

pricing rule. As will be discussed later, under the proposed mechanism all blocks of spectrum 

are sold at a uniform price which is equal to the highest rejected bid. For example, as shown for

Session 1 in Figure 4, in order for U-Type firms to collectively obtain 30 units of value from 

having a second block of spectrum allocated to unlicensed use (i.e., 280 -250), they must give up 

250 units of value (88% of the combined total value). 

Figure 5 shows the efficient assignment of spectrum, including the efficient set of licensing 

rules for Session 2’s valuation set. As before, efficiency considerations again dictate that one 

block of spectrum should be assigned to bidders A and B under licensed operations, and two 

blocks of spectrum to bidders C – H under unlicensed operations. As measured by the difference 

in value between the fifth highest valuation (i.e., 250) and the value U-Type bidders collectively 

place on having a first block of spectrum allocated to unlicensed operations (i.e., 500), a 

successful mechanism is one that consistently designates at least one block of spectrum to 

unlicensed operations. While the Session 2 two valuation environment poses less of an 

allocation challenge for the market mechanism regarding the first block of spectrum, it is 

substantially more difficult than Session 1 regarding the second block of spectrum. As shown in 

Figure 5, in order for U-Type bidders to obtain 10 units of value (i.e., 260 – 250) from having a 

second block of spectrum allocated to unlicensed use, collectively they must give up 250 units of 

value (96% of the combined total value). 

Figure 5: Session 2 Efficient Assignment

U - Type Bidder

L - Type Bidder

A

B

Valuation

s

200

400

100

300

500 G

F

E

D

C

400 300

Suppl

y

A

B

250 200

G

F

E

D

C

Unit

s

U - Type Bidder

L - Type Bidder

U - Type Bidder

L - Type Bidder

A

B

Valuation = 500

s

200

400

100

300

500 G

F

E

D

C

400 300

Suppl

y

Supply

A

B

250 200

= 260

G

F

E

D

C

Unit

s

∑

∑
10

5 Market Mechanism – A Clock Auction

Experiments conducted for other spectrum auctions have revealed that bidders may engage 

in “jump bidding” in an ascending English auction in an effort to forestall or signal competition 

and, as a result, may lead to an inefficient assignment of items.15 More recently, analysis 

indicates that the threat of financial exposure increases the likelihood of this behavior during a 

simultaneous multiple round auction involving multiple heterogeneous items.16 Moreover, jump 

bidding appears to be a significant feature of FCC spectrum auctions.17 One solution to this 

problem is a “clock auction.” A clock auction is an iterative auction procedure where bidders 

express there willingness to pay for one or more units of an item based on prices established by

the auctioneer and where a set of rules determines the efficient allocation and a set of market 

clearing prices. 

In this study we propose a new auction mechanism that is based on, but not identical to, 

previous clock auctions.18 The proposed auction begins with the Auctioneer (e.g., the FCC) 

announcing a single opening price – the clock price – for each spectrum block up for auction.19

Subjects respond by identifying the number of blocks they wish to acquire at that clock price. 

All responses, including the identities and license regime preferences of bidders, are kept private. 

A simple set of rules enables the auctioneer to assess the value bidders place on having one or 

more blocks of spectrum designated to licensed versus unlicensed operations.

1. If a bidder requests zero blocks at the initial clock price, then the value the bidder 

places on the first and second blocks of spectrum is equal to zero. 

2. If a bidder requests one block of spectrum at the initial clock price, then the value 

the bidder places on a second block of spectrum is equal to zero.

15 Jump bidding occurs in an ascending bid auction when one or more bidders place bids in excess of the minimum 

bid increment established by the auctioneer. See McCabe, K., Rassenti, S. and Smith, V. (1988) “Testing Vickrey’s 

and other Simultaneous Multiple Unit Versions of the English Auction,” revised by Isaac, R.M., ed. (1991) 

Research in Experimental Economics (JAI, Greenwich, CT), vol. 4. See also Avery, C., (1998) “Strategic Jump 

Bidding in English Auctions,” Review of Economic Studies, Vol. 65 (2), pgs 185-210.

16 Porter, D, Rassenti, S, Roopnarine, A, and Smith, V., (2003) “Combinatorial Auction Design,” Proceedings of 

the National Academy of Sciences, vol. 100. 

17 Cramton, Peter, (1997), “The FCC Spectrum Auctions: An Early Assessment,” Journal of Economics and 

Management Strategy Vol. 6(3), pgs. 497-527.

18 The primary focus of our research, however, is directed to the feasibility of using a market mechanism to 

designate spectrum to either licensed or unlicensed use. We leave it to further analysis to determine the most 

appropriate auction design for this purpose.

19 The number of clock prices is equal to the number of heterogeneous items. For simplicity, we have assumed that 

blocks up for auction were homogeneous. 
11

3. To preserve the increasing price nature of the auction, bidders are prevented from 

increasing the number of spectrum blocks they desire as the clock price increases. 

4. If a bidder reduces his/her spectrum block demand from two to one as the clock 

price increases from one level to the next, the lower clock price represents the value 

the bidder places on a second block of spectrum.

5. If a bidder reduces his/her spectrum block demand from one to zero blocks as the 

clock price increases from one level to the next, the lower clock price represents the 

value the bidder places for a single block of spectrum.

6. For subsequent rounds, if a bidder reduces his/her spectrum block demand from 

two to zero blocks in response to the latest clock price increase, the lower clock 

price represents the value the bidder places for both the first and second blocks of 

spectrum. 

If the number of blocks desired by one or more bidders exceeds zero at a given clock price, 

the “clock ticks up” – meaning that the price for a block of spectrum goes up by a predetermined amount.20 Subjects are then given the opportunity to reveal to the auctioneer (and 

not to the market) the number of blocks they desire at that clock price. The auction closes when 

there is zero demand for a spectrum block at the going clock price. 

5.1 Allocation Rule – Aggregate Bid Rule

When the auction concludes, the allocation of spectrum and the prices paid by winning 

bidders can be easily determined. The efficient allocation of spectrum across license regime type 

and users requires comparing, based on the represented willingness to pay of bidders for 

spectrum designated to different use types, the value society will obtain from designating 

spectrum to licensed versus unlicensed use. In contrast to licensed use where license owners 

have exclusive use rights to the allocated spectrum, unlicensed users have unfettered access to 

spectrum designated to unlicensed operations. The open access provision of unlicensed 

operations requires that we apply the same “non-exclusive” treatment to the bids submitted by 

bidders that wish to see spectrum designated to unlicensed operations. Such treatment requires 

that we aggregate the bids U-Type bidders place in the auction. In our model, where bidders 

20 In most clock auctions, the clock price only ticks up if the demand for the auctioned item exceeds its supply. See 

Porter, et. al. (2003) op cit.
12

desire to have multiple blocks of spectrum designated to a given license regime and where they 

have different willingness to pay across these blocks, such aggregation must be performed with 

care. For example, because U-Type bidders may express a higher valuation for a single block of 

spectrum than for a second block of spectrum, such bidders are submitting to the auction two 

distinct bids – one type applies to a single block of spectrum, while another type applies to a 

second block of spectrum.21 Forming the correct aggregate bids requires keeping this distinction 

in mind. To this end, a simple algorithm adds together the highest bids from each U-Type bidder 

to form one aggregate bid – (U1). In addition, a simple algorithm adds together the lowest bids 

from each U-Type bidder to form a second aggregate bid (U2).

Once the two aggregate bids are constructed, identifying the efficient allocation of spectrum 

to license rule regime and, in the case of licensed operations, to the most efficient user(s) is 

straightforward. Under the allocation rule, bids U1 and U2 are ranked, along with the bids 

submitted by L-Type bidders, from highest to the lowest. Given that there are four blocks of 

spectrum up for auction, the four highest bids are each assigned a single block of spectrum. 

Because each bid is associated with a given license regime, this assignment also determines 

whether a block is allocated to either licensed or unlicensed operations. For example, if the U1 

and U2 bids are among the four highest bids, two blocks are designated to unlicensed operations. 

If the four highest bids include two bids from L-Type bidders, then two spectrum blocks are 

allocated to licensed operations and to the bidders whose bids were among the four highest bids. 

A simple example can be used to illustrate the allocation and aggregate bid formation rule. 

Consistent with the information shown in Figure 4 (which is reproduced as Figure 6 below), 

suppose the auction has closed and that bidders have truthfully revealed the value they placed on 

having two blocks of spectrum allocated to either licensed and unlicensed operations.22 Under 

these assumptions, the clock auction would generate an outcome in which two blocks of 

spectrum are assigned to bidders A and B on a licensed basis, and two blocks of spectrum are 

designated to unlicensed operations.

21 Licensed bidders also submit distinct bids for the first and second units of desired spectrum.

22 Truthful bidding is assumed here only to illustrate the allocation and pricing rules in the auction mechanism. 

Later, it will be demonstrated that unlicensed bidders rarely have an incentive to bid completely truthfully.
13

Figure 6: Session 1 Efficient Assignment

5.2 Pricing Rule

The “public good” aspect of the demand by unlicensed bidders also gives rise to a 

“threshold” problem, in which U-type bidders must coordinate their bidding strategies in order to 

reach a favorable outcome. The presence of a threshold problem highlights the importance of 

establishing a pricing rule that encourages subjects to reveal the value they place on having 

spectrum allocated to one use type or the other. To that end, because of its favorable incentive 

properties, all trades in the experimental study occur at a uniform price, where this price is equal 

to the highest rejected bid. In the above example, because there are four blocks of spectrum up 

for auction, the highest rejected bid is equal to the fifth highest bid, including U1 and U2. While 

L-Type bidders pay the highest rejected bid, U-Type subjects that bid in the auction pay a price 

that is “based on” the highest rejected bid. In particular, U-Type subjects that bid in the auction 

are assigned a cost that is proportional to the share their bids represented in the aggregate bid.

A simple example can be used to illustrate the above pricing rules. Continuing with the 

example shown in Figure 6, suppose the auction has closed and that bidders have truthfully 

revealed the value they placed on having spectrum allocated to licensed and unlicensed 

operations. As shown in Figure 7, under these conditions Bidders A and B would receive one 

block of spectrum each, while two blocks of spectrum would be designated to unlicensed 

operations. Under the auction’s pricing rules, all four blocks are sold for a uniform price of 250, 

which represents the highest rejected bid. In addition, winning U-Type bidders are assigned a 

A

B

= 440

Valuation

s

200

400

100

300

500

400 300

A

B

2

H

G

F

E

D

C

Supply

250 200

Unit

s

U - Type Bidder

L - Type Bidder

H

G

F

E

D

C

A

B

∑

Valuation

s

200

400

100

300

500

400 300

A

2

H

G

F

E

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C

= 280

Suppl

y

250 200

Unit

s

U - Type Bidder

L - Type Bidder

U - Type Bidder

L - Type Bidder

H

G

F

E

D

C

∑
14

cost that is proportional to the share their bids represented in the aggregate bid. For example, 

consider Bidder C, a U-Type bidder, and its contribution of 120 to the aggregate bid for 

allocating a single block of spectrum to unlicensed operations. Because Bidder C’s bid of 120 

represents 27% of the value of the accepted aggregate bid of 440, under the adopted pricing rules 

Bidder C is required to pay 27% of the final transaction price (i.e., 250), or 68.2. Similarly, 

because Bidder C’s bid of 80 to have a second block of spectrum designated to unlicensed 

operations represents 29% of the value of the accepted aggregate bid of 280, Bidder C is required 

to pay 29% of the final transaction price, or 71.4.

Figure 7: Session 1 Pricing Rule

To assist readers in visualizing the proposed clock auction, the authors have created a flash 

clip that demonstrates the major features of the described auction. The flash clip can be accessed 

at http://www.fcc.gov/osp/projects/unlicensed.html.

A B

C

Valuation

s

200

400

100

300

500

D

E

F

400 300

C

E

H

Supply

250 200

Unit

s

250

G

H A

B

D

F

G

A B

C

Valuation

s

200

400

100

300

500

D

E

F

400 300

C

E

H

Supply

250 200

Unit

s

250

G

H A

B

D

F

G
15

6 The Mechanism Design Problem

6.1 Provision Points and “Free Riding”

There are several reasons why a market may fail to allocate different license regimes to 

blocks of spectrum in an efficient manner. One general source of market failure is the 

unwillingness of bidders to reveal the true value they place on a particular license regime.23 A 

major cause of under revelation in the current example is free riding behavior involving 

unlicensed operations. The economics are straightforward. Spectrum designated to unlicensed 

operations provides an alternative means by which users can access the Internet. Unlicensed use 

makes it possible for Internet users and entities (e.g., Google, Microsoft, Yahoo) that wish to sell 

access to such users to advertisers to do so without the possibility of paying a fee to an 

intermediary (e.g., Verizon, Comcast). Because of the common pool resource nature of spectrum 

designated to unlicensed use, the benefit that a given firm receives from expending the effort to 

avoid such a fee extends to every U-Type firm. The ability of a given firm to benefit from the 

actions of another firm introduces a public good aspect to the economic problem. In the current 

context, although it is in every U-Type firm’s interest to have spectrum designated to unlicensed 

use, any individual U-Type firm has an incentive to “free ride” off the bids of others bidders in 

an attempt to maximize its own profits. If a significant number of U-Type firms elect to free 

ride, then the efficient designation of spectrum to licensed and unlicensed operations may not 

occur.

24

23 Although not unique to this problem, there are other reasons why a market may “fail.” One reason is the existence 

of non-competitive prices in the retail service market. The price signals generated by a market reflect the 

willingness of buyers and sellers to complete a trade. If the expressed willingness to trade is the result of 

competitive forces, the price signals generated in the market will themselves be competitive and will, thus, 

efficiently allocate resources. One instance where the willingness to trade is too high is when a buyer wishes to 

acquire an asset, in part, because it wishes to avoid having the asset employed by a competitor. In this instance, the 

willingness of the buyer to trade, as measured by the value the buyer places on the asset, is inefficiently high. This 

reasoning points to a possible inefficiency in the use of market forces to guide the licensing rule determination 

process. In particular, if the value that L-Type bidders place on spectrum is driven largely by the profits they would 

earn from not having the spectrum in the hands of a competitor, an auction outcome that relies on market prices to 

guide the licensing rule determination process may not lead to the efficient outcome.

There are several possible solutions to the problem. One solution involves preventing L-Type bidders from 

participating in the market process. This can be achieved by establishing a spectrum cap that limits the amount of 

spectrum each licensee may own in a given geographic area. Another approach involves allowing the firm to 

participate in the market, but discounting the firm’s bid by an amount equal to the value the firm places on owning 

the asset for purely anticompetitive reasons. 

24 Notwithstanding the public good aspect to spectrum acquisition costs for unlicensed bidders, these bidders may 

also compete with each other for retail customers.
16

In many public good problems, free riding behavior is a dominant strategy.

25 In particular, 

it is welfare maximizing for the firm or agent to refrain from engaging in behavior that promotes 

the welfare of the group independent of the behavior of the other firms. This is so because the 

cost of contributing to the welfare of the group always exceeds the private benefit from doing 

so.26 In the current public good problem, however, it is not a dominant strategy for any one UType firm to always “free-ride” off a U-Type bidder’s efforts to have a given band of spectrum 

allocated to unlicensed use.27

One distinguishing feature of the current problem is the existence of a “provision point.”28

A provision point is the minimum aggregate contribution users must collectively make in order 

for any given user to obtain value from his/her contribution.29 In the current context, in order for 

a single block of spectrum to be designated to unlicensed operations, the sum of the bids 

submitted by U-Type bidders must exceed the lowest bid submitted by the L-Type bidders. This 

bid represents for U-Type bidders the provision point for that first block of spectrum. 

Importantly, the provision point represents a Nash equilibrium since any unilateral deviation 

below the provision point value is unprofitable for the contributors. 

The likelihood that an equilibrium without significant free riding will be achieved is 

increased as a result of the so-called “give back” option at work in the current economic 

environment. In a typical public good problem, a player’s payoff is often reduced by the amount 

of his/her contribution, independently of whether other parties have made a contribution. In the 

current example, a contribution by the U-Type bidder only reduces his/her payoff if the sum of 

the U-Type bids exceeds the provision point. A similar effect is achieved when organizations 

25 The classic example of an inefficient dominant strategy equilibrium is the “prisoners’ dilemma,” in which each 

prisoner has an incentive to confess even though their combined welfare is maximized if neither confesses.

26 A variety of experimental studies have shown that even in instances where, according to game theory, free riding 

behavior is a dominant strategy, individuals fail to behave in such a manner. See Marwell, G., and R. Ames (1979), 

“Experiments on the Provision of Public Goods: Resources Interest, Group Size, and the Free-Rider Problem,” 

American Journal of Sociology 84(6):1335-60, Isaac, M, J. Walker, J., and S. Thomas, “Divergent Evidence on Free 

Riding: An Experimental Examination of Possible Explanations,” Public Choice 43(1):113-49.

27 In this case, the public good problem is more closely related to two other well known game situations. In the 

game of “chicken” both players want to follow aggressive strategies as long as their opponent is expected to be 

passive. Nevertheless, the equilibrium outcomes call for only one, but not both of the players to be aggressive. In a 

somewhat different game known as the “battle of the sexes”, one player wishes to attend an event (e.g. a boxing 

match) and the other player wisher to attend a different event (e.g. a ballet). In spite of these preferences, both 

players would rather go to the same event rather than different ones. In both “chicken” and “battle of the sexes” 

there are multiple Nash equilibria, which are welfare superior to the “free riding” equilibrium which also exits in 

these cases.

28 The role of a provision point in public good problems is discussed in detail by John Ledyard, “Public Goods: A 

Survey of Experimental Research,” in Handbook of Experimental Economics, edited by J. Kagel and A. Roth, 

Princeton University Press 1995.

29 Marwell and Ames (1979) were the first to introduce the notion of a provision point in a public good experiment. 
17

conduct fund drives under the rule that the public good will not be provided unless a certain 

minimum level of funding is achieved. By reducing a U-Type bidder’s risk of making a 

contribution, the give back option can be expected to increase the contributions made by such 

bidders.30 However, the give back option and provision point features may not always lead to 

the efficient outcome. Both features give rise to multiple Nash equilibria when participants need 

contribute only a portion of the value they place on having a public good provided. The 

existence of multiple equilibria may create an important coordination problem because 

participants will typically have differing equilibrium preferences.31 The non-dominance of a 

pure free–riding behavior and the existence of multiple equilibria can be demonstrated using the 

parameters included in the Session 1 experimental set-up (reproduced in Table 1 below). 

6.2 Nash Equilibria

Economic theory predicts that, at a minimum, participants in a mechanism design problem 

will rationally select bidding strategies that are sustainable as Nash equilibrium outcomes. In the 

context of a spectrum auction, a Nash equilibrium represents a set of bidding strategies such that 

no bidder can expect to increase his or her payoff by following a different bidding strategy, 

assuming that every other bidder continues to play their equilibrium strategy. In the absence of a 

strictly dominant strategy for each bidder, there can in general be a large number of Nash 

equilibria. A full description of these equilibria depends on a detailed description of the 

information available to each bidder about the auction mechanism itself and each bidder’s beliefs 

about the private valuations of all rival bidders. In a set of auction experiments to be described 

later, experimental subjects were told the rules of the auction and their individual assigned 

valuations, but were given no information about other subject’s valuations other than the total 

number of subjects participating. Suppose, contrary to this experimental setup, that each bidder 

has complete information about the number of other bidders, the type (i.e. licensed/unlicensed) 

of each bidder, and each bidder’s true valuation. In the remainder of this section we will show 

that under these assumptions it is possible to enumerate the full set of Nash equilibrium 

outcomes. 

30 Experimental evidence indicates that the “give back” option has the effect of increasing contribution rates in some 

public good environments. See Isaac, M, D. Schmidtz, and J. Walker (1989) “The Assurance Problem in a 

Laboratory Market,” Public Choice, 62, 217-236.

31 See Isaac, Schmidtz, and Walker (1989) op cit.
18

In the experiments, the auction was conducted as a particular type of “clock auction” as 

described above. The tested clock auction can be shown to be strategically equivalent to a sealed 

bid auction in which each bidder submits two bids – one for the first unit of spectrum acquired 

and a different bid for the second unit. In the experimental set up, the clock price started at 10 

and advanced in units of 10. In order to simplify the present analysis it will be assumed that bids 

can be submitted in any integer units, so that the minimum bid increment is equal to 1. As in the 

experiment, the market clearing price is equal to either the highest rejected bid for licensed use 

or the highest rejected aggregate bid for unlicensed use, whichever is the highest. Winning 

licensed bidders pay this price, while each winning unlicensed bidder pays an amount 

proportional to his actual bid, such that the sum of the unlicensed prices add up to the market 

clearing price. The values assigned in Session 1 of the experiments are shown in Figure 2 above 

and Table 1 below. 

Table 1: Assigned Valuations in Session 1 of the Experiment

Bidder Subject Type (L/U) Value Unit 1 Value Unit 2

A L 400 250

B L 300 200

C U 120 80

D U 120 80

E U 60 40

F U 60 40

G U 40 20

H U 40 20

Sum C – H 440 280

Assuming complete information, there are a large number of Nash equilibria in the auction 

game, one of which is shown in Table 2. In this equilibrium, licensed bidders submit winning

bids for three of the four licenses, and the remaining block of spectrum is awarded to unlicensed 

bidders collectively. The market price is determined by the highest rejected bid, which in this 

case is made by both licensed bidder B and collectively by unlicensed bidders C through H.32

32 We will demonstrate later that the efficient allocation cannot be sustained as a Nash equilibrium if all bidders bid 

their true values. However, it will also be shown that the efficient allocation can be sustained as an equilibrium with 

different bidding strategies.
19

Table 2: An Example of Nash Equilibrium

Bidder Bid 1 Bid 2 Price Surplus

A 400 250 200 250

B 300 200 200 100

C 56 55 55.72 64.28

D 55 55 54.73 65.27

E 27 27 26.87 33.13

F 27 27 26.87 33.13

G 18 18 17.91 22.09

H 18 18 17.91 22.09

Sum C – H 201 200 200 240

To verify that the bidding strategies shown in Table 2 represent a Nash equilibrium, one 

needs to show that no bidder can unilaterally benefit by changing either one of its bids. Given 

the bids in Table 2, bidder A wins 2 units; bidder B wins 1 unit; and the unlicensed bidders 

together win 1 unit. Bidder B’s bid for a second unit and the combined bids of bidders C – H for 

a second unit tie as extra-marginal (rejected) bids equal to 200. These bids establish the market 

clearing price. No winning bidder can gain by either increasing its bid for the first unit of 

spectrum (since it is already winning and the market price is determined by the tie bids for a 

second unit of spectrum) or reducing his/her bid for that unit (since each bidder gets positive 

surplus for each unit won, and reducing a bid can only result in the loss of that surplus). If 

bidder B increases its bid for the second unit to 202 or greater, it will become a winning bidder, 

but it will have bid above its true valuation, and will therefore be worse off.33 Since bidder B’s 

second bid is tied with the second aggregate bid of C – H, bidder B cannot change the market 

price by reducing its bid for a second unit of spectrum, and therefore cannot increase the surplus 

attained for the first unit. 

None of the unlicensed bidders C – H can benefit by unilaterally reducing their bid for the 

first unit of spectrum, since doing so would convert their collective bid into a losing bid (or tie 

for losing) which would result in forfeiting the surplus each bidder obtains. Similarly, none of 

the unlicensed bidders C – H can benefit by unilaterally increasing their bid for a second unit of 

spectrum. In order to displace bidder A’s winning bid for a second unit and, in so doing, obtain a 

second block of spectrum for unlicensed designation, the unlicensed bidders must increase their 

aggregate bid to 251 or more. Such a bid would increase the market clearing price to 250, 

33 If B bids 201 for a second unit it will win with a 50% probability assuming that ties are settled by a coin toss, and 

this will also result in a loss of surplus.
20

thereby reducing by 50 the surplus that any individual bidder obtains on their first block of 

spectrum. This reduction in surplus exceeds the 30 units of surplus (i.e., 280 – 250) such bidders 

collectively would obtain from having a second block of spectrum designated to unlicensed 

operations. 

There are a large number of Nash equilibria for the auction game described in Table 1. 

These equilibria can be sorted into three different “Types” according to the number of blocks of 

spectrum which are won collectively by the unlicensed bidders. A “Type 1” equilibrium, as 

represented in Table 2, results in three blocks of spectrum being designated to licensed 

operations and one block to unlicensed operations. While their quantitative bids may differ 

significantly, all Type 1 equilibrium strategies have the following characteristics.

1. Bidder A bids an amount for both units 1 and 2 of spectrum that is large enough such that 

no unlicensed bidder has an incentive to raise his/her bid for a second unit.

2. Bidder B bids an amount for the first unit that is large enough such that no unlicensed 

bidder has an incentive to raise his/her bid for a second unit. Bidder B bids exactly 200 

for the second unit.

3. The six unlicensed bidders place bids for a first unit that sum to exactly 201, and bids for 

a second unit that sum to exactly 200. 34

4. Total surplus for licensed bidders A and B is 250 and 100 respectively. Collective total 

surplus for bidders C through H is equal to 240.

5. Auction revenue is equal to 800 (i.e., 4 x 200).

6. Total surplus is equal to 1390.

In a Type 2 Nash equilibrium, the two licensed bidders win all four blocks of available 

spectrum. In this case, each of the unlicensed bidders individually attempts to free ride, with the 

result that no spectrum is allocated to their use in spite of their high collective value for it. 

Suppose, for example, that each unlicensed bidder places a bid equal to zero. The licensed 

bidders could then place any bids greater than or equal to 120 (the highest valuation of an 

34 Since bidder B and the unlicensed bidders C – H both win one unit of spectrum, the market price is determined by 

the higher of their bids for the second unit. If these bids are not identical, then the bidder placing the higher bid 

would prefer to reduce that bid by a small amount in order to reduce the market price. If these bids are equal and 

less than 200, it follows that any unlicensed bidder could have increased surplus by reducing its bid for their first 

unit of spectrum, and bidder B could also benefit by increasing her bid for the second unit to any amount less than 

200. The smallest possible equilibrium bids by A and B in an equilibrium depend on the particular equilibrium bids 

of C – H for the second unit. If bidders C – H bid as shown in Table 2, then a simple algebraic argument shows 

each of these bids must be greater than 225 in order to prevent the highest value unlicensed bidders (C and D) from 

unilaterally increasing their bids in order to gain a second unit of spectrum for unlicensed use.
21

unlicensed bidder for a unit of spectrum) for both units of spectrum that they desire. In this case, 

the market price would be equal to zero, and no licensed or unlicensed bidder could unilaterally 

increase their surplus by changing their bid. As in the case of Type 1 equilibria, there are an 

large number of Type 2 equilibria, which all have the following characteristics.

1. Bidders C – H collectively bid an amount less that 200 (bidder B’s value for a second 

unit of spectrum) for each unit of spectrum. The losing bid for the first unit of spectrum 

determines the market price.

2. Bidders A and B bid an amount for both units of spectrum that is high enough to make it 

unprofitable for an unlicensed bidder to bid for a second unit.

3. Total surplus for licensed bidder A is 650 minus twice the market price, while total 

surplus for bidder B is 500 minus twice the market price. Collective total surplus for 

bidders C through H is equal to 0.

4. Auction revenue is equal to the highest collective bid of C – H multiplied by 4.

5. Total surplus is equal to 1150.

Finally, there exist Type 3 Nash equilibria which sustain the efficient allocation. That is, the 

two licensed bidders each win one block of spectrum, and two blocks of spectrum are designated 

to unlicensed operations. Unlike Type 1 and Type 2 equilibria, Type 3 equilibria require that 

some bidders bid above their true valuations.35 As an example, suppose that bidders A and B bid 

their true valuations for the first unit of spectrum, and that both bid 250 for the second unit of 

spectrum, which is equal to A’s true value and greater than B’s true value. Suppose in addition 

that the unlicensed bidders collectively bid 251 for both units of spectrum, with each bidder 

35 Suppose that unlicensed bidders C through H place winning bids for two units of spectrum and that the remaining 

two units are both won by licensed bidder A at bids less than or equal to A’s true value. Then bidder B must have 

placed bids such that the market price is less than or equal to 250 (bidder A’s value for the second unit). It then 

follows that the collective bids of C – H for both winning units must also be less than or equal to 251, since 

individually each bidder has an incentive to reduce its bid in order to reduce its share of the market price as long is 

the collective bid is still winning. But now, bidder B would prefer to increase its bid for the first unit to any amount 

greater than 251, which would allow B to win that unit at a market price that would remain less than or equal to 251. 

Now suppose that bidders A and B each win exactly one unit of spectrum. In this case, A and B must place 

identical bids for their second unit of spectrum, since otherwise, the bidder placing the higher bid would prefer to 

lower that bid in order to reduce the market price (and increase the surplus on the winning bid for the first unit of 

spectrum). If all bids are less than or equal to true values, the resulting market price must be less than or equal to 

200. As before, the unlicensed bidders must collectively bid an amount less than or equal to 201. In this case, 

bidder A would prefer to increase its bid to anything greater than 201, which would allow it to win a second unit at a 

market price less than or equal to 201.
22

bidding less than or equal to his or her value.36 Given these bids, neither A nor B would want to 

increase their bid for a second unit to an amount greater than 251, since doing so would result in 

winning at a market price greater than either bidder’s value. Similarly, neither A nor B can 

benefit by unilaterally reducing their bid for a second unit, since doing so would not change the 

market price. While these bids formally represent a Nash equilibrium, we note that we can find 

no compelling reason to believe that bidders A and B would choose to place bids for a second 

unit of spectrum in this manner. 37

All Type 3 equilibria have the following characteristics.

1. Bidders A and B bid any amount greater than 250 for the first unit of spectrum.

2. Bidders A and B place identical bids less than or equal to 250 for the second unit of 

spectrum. These bids determine the market price.

3. Bidders C through H collectively bid any amount greater than 250 for both units of 

spectrum.

4. Total surplus for bidder A is 400 minus the market price and for bidder B is 300 minus 

the market price. Collective total surplus for bidders C – H is equal to 720 minus twice 

the market price.

5. Auction revenue is equal to the market price multiplied by 4.

6. Total surplus is equal to 1420.

While each type of equilibrium permits a large number of equilibrium bidding strategies, the 

total surplus and the surplus for each bidder depend only on the bids of the extra-marginal 

bidders which determine the market price. These results are summarized in Table 4.

36 This is possible since the values for the second unit sum to 280.

37 It can be demonstrated that any strategy in which a player bids above her value is weakly dominated by an 

alternative strategy in which the bid is equal to the value. Weakly dominated strategies cannot be eliminated as 

equilibrium outcomes, but they are in some cases rejected by a process of iterative elimination of dominated 

strategies.
23

Table 4: Summary Results of Nash Equiliria for Session 1 Valuations

Market Price (P) A Surplus B Surplus C – H Surplus Total Surplus

Type 1 200 250 100 240 1390

Type 2 P < 200 650 – 2 P 500 – 2 P 0 1150

Type 3 P ≥ 250 400 – P 300 – P 720 – 2 P 1420

Given the substantial difference in total surplus across the three equilibrium types, an 

important question is which equilibrium type market participants will settle on. Note that 

licensed bidders A and B unambiguously prefer Type 2 equilibria while unlicensed bidders C –

H unambiguously prefer Type 1 equilibria.38 Nevertheless, game theory does not shed light on 

which type of equilibrium is most likely. In the following section we examine the equilibrium 

outcomes selected by market participants in two different experimental environments.

7 Economic Experiments

A series of 34 separate auction experiments were conducted, 13 of which were conducted 

under the Session One valuation set, while 21 were conducted under the Session Two valuation 

set. The information that subjects had regarding the economic environment was limited. Each 

of the subjects knew their own valuations, the total number of subjects in the experiment, the 

total number of available blocks of spectrum and that each subject had a demand for exactly two 

blocks. Subjects were unaware of the number of participants that preferred licensed versus 

unlicensed use, as well as the value each subject placed on having one or two blocks of spectrum 

designated to a given license regime. 

To induce behavior reminiscent of the naturally occurring environment, subjects earned 

profits based on their performance in the experiment. In particular, subjects were paid an 

amount that is equal to the difference between the value they placed on having spectrum 

allocated to their preferred use minus the price they paid to access spectrum on that basis. 

Therefore, continuing the example of section 5.2 (which assumes truthful bidding), Bidder C 

would earn 51.8 (i.e., 120-68.2) from having one block of spectrum designated to unlicensed 

operations, and would earn an additional 8.6 (i.e., 80 – 71.4) from having a second block of 

spectrum allocated to unlicensed operations. Importantly, in the experimental framework, a UType bidder has the option to bid less than his or her value, or even to not submit a bid in the 

38 No bidder prefers a Type 3 equilibrium. Auction revenue and total surplus are highest in this type.
24

auction, deciding instead to simply free-ride off the bids submitted by other U-Type bidders. In 

such a circumstance, if the spectrum is allocated to unlicensed operations, the bidder is not 

allocated a cost share and thus, earns an amount equal to his/her assigned valuation for that 

spectrum block. 

The experimental results reveal that the Type 1 equilibria are approximately attained in a 

large number of experimental sessions. In one session, the final experimental bids are shown in 

Table 5 along with the prices paid and surplus earned by each subject. While the unlicensed 

bidders somewhat overbid for the first unit of spectrum, by collectively bidding 260 instead of 

201, in all other respects, the experimental bidding conforms exactly to a Type 1 equilibrium.

Table 5: Bids Submitted in Session 1 of the Experiment

Bidder Bid 1 Bid 2 Price Surplus

A 460 240 200 250

B 300 200 200 100

C 80 80 61.54 58.46

D 100 60 76.92 43.08

E 20 20 15.38 44.62

F 10 10 7.69 52.31

G 20 10 15.38 24.62

H 30 20 23.08 16.92

Sum C – H 260 200 200 240

Summary results for all experimental sessions are shown in Table 6. These results show 

that Type 1 equilibria were obtained in the vast majority of experimental auctions. For example, 

in 28 of the 34 auctions (i.e., 82%), the competitive process resulted in one spectrum block being 

designated to unlicensed use. In comparison, in only two out of the 34 auctions (i.e., 6%) did the 

competitive process lead to all four blocks being designated to licensed operations (Type 2 

equilibria). Finally, in four out of the 34 auctions (i.e., 12%), two spectrum blocks were 

designated to unlicensed use, which was the efficient allocation. 

Consistent with the observation that Session 2 valuations presented a greater coordination 

challenge for U-Type bidders than Session 1 valuations, U-Type bidders were always able to 

coordinate their bids in the Session 1 valuation environment so that at least one block of 

spectrum was allocated to unlicensed operations. In contrast, there were two instances in which 

U-Type bidders were unable to coordinate their bids under the Session 2 valuation environment 

so that no blocks were allocated to unlicensed operations. 
25

Table 6: Experimental Results

Number of Blocks Designated to 

Unlicensed Operations

(Efficiency)

Total 

Number of 

Auctions

Average 

Efficiency

0 Blocks 1 Block 2 Blocks

Session 1 0.95 0

(.82)

11

(.98)

2

(1.0) 13

Session 2 0.95 2

(.80)

17

(.99)

2

(1.0) 21

The inability of the mechanism to achieve a higher efficiency value is due, in part, to the 

incentive U-Type bidders have to strategically reduce their demands for the second block of 

spectrum. It is well known that in instances where bidders have multi-unit demands and a 

simultaneous ascending-bid auction with uniform pricing is employed to allocate items, bidders 

can find it in their mutual interest to reduce demand in an effort to maximize their profits.39

Such “demand reduction” would be profitable if the gain from a lower price for the buyer’s “n”-

infra-marginal units is greater than the profit it would earn from “n+1” infra-marginal units. In 

the current example, U-Type bidders would earn greater profits if they collectively failed to bid 

for a second block of spectrum electing, instead, to have the market generate a lower market 

clearing price.

The average efficiency obtained under each session valuation environment was 95%. In 

evaluating the performance of the market, it is important to recognize that the lower bound for 

the assignment efficiency is the level of efficiency obtained when zero blocks of spectrum are 

assigned to unlicensed operations. As shown, the efficiency of the market when zero blocks of 

spectrum are assigned to unlicensed operations is 82% under Session 1, and 80% under Session 

2. 

8 Concluding Comments

One of the more important spectrum management problems the FCC faces involves whether 

to designate spectrum to either licensed use or unlicensed operations. Spectrum designated to 

unlicensed use is made freely available for uses which comply with appropriate technical 

39 Such an effect is referred to as strategic demand reduction. For a discussion of strategic demand reduction in FCC 

spectrum auctions, see Weber, Robert, (1997) “Making More With Less,” Journal of Economics and Management 

Strategy, Vol. 6. pgs. 529-548. 
26

standards. Spectrum allocated to licensed use grants the owner of the license the right to exclude 

non-payers from using the spectrum and is generally awarded to private parties through an 

auction mechanism. The FCC and other regulatory bodies attempt to solve this problem through 

an administrative process. However, such a process has some important limitations, not the least 

of which is that it often is based on the reported needs of interested parties. One method of 

reducing the incentive that parties have to exaggerate the value they place on a given set of 

license rules involves creating a market for such rules in which participants bid to have their

license rule needs met. By reducing the incentive that interested parties have to misrepresent 

their economic interests, this approach may substantially improve the efficiency of the licensing 

process. 

We examine the feasibility of using a market mechanism (i.e., a “clock auction”) to 

determine, based on the bids submitted by market participants for the corresponding licensing 

rules, the efficient allocation of a given amount of spectrum between licensed and unlicensed 

operations. One general source of market failure is the unwillingness of bidders to reveal the 

true value they place on a particular license regime. A major cause of under revelation in the 

current instance is “free riding” behavior involving unlicensed operations. If a significant 

number of bidders that wish to see spectrum designated to unlicensed operations free ride on the 

bids made by other similarly-interested bidders, then the efficient designation of spectrum to 

licensed and unlicensed operations may not occur. 

This study created an economic model that was designed to stress test whether our market 

approach could achieve the efficient assignment of license rules to four spectrum blocks. 

Assuming complete information, analyses demonstrate that there are a large number of Nash 

equilibria in the auction game. Economic experiments were conducted to determine whether 

bidders had a tendency to settle on equilibria that achieve the efficient designation of spectrum to 

licensed and unlicensed operations. The results of the experiments show that in 28 of the 34 

auctions, the competitive process resulted in one spectrum block being designated to unlicensed 

operations. In addition, in four of the 34 auctions (i.e., 12%), two spectrum blocks were 

designated to unlicensed use, which was the efficient designation. The inability of the market 

mechanism to achieve a higher efficiency value is due, in part, to the incentive U-Type bidders 

have to strategically reduce their demands for the second block of spectrum. Indeed, in the 

current example, U-Type bidders would earn greater profits if they collectively failed to bid for a 
27

second block of spectrum electing, instead, to have the market generate a lower market clearing 

price.