When do auctions ensure the welfare‐maximizing allocation of scarce inputs?

• Author: John W. Mayo,David E.M. Sappington
• Date: 01 February 2016
• Published date: 01 February 2016
• DOI: http://doi.org/10.1111/1756-2171.12123

RAND Journal of Economics

Vol.47, No. 1, Spring 2016

pp. 186–206

When do auctions ensure

the welfare-maximizing allocation

of scarce inputs?

John W. Mayo∗

and

David E.M. Sappington∗∗

We determine when an unfettered auction will ensure the welfare-maximizing allocation of a

scarce input that enhances product quality and may reduce production costs. A supplier values

the input for this “use value” and for its “foreclosure value,” because once the input is acquired,

it is unavailable to rivals. An unfettered auction often ensures the welfare-maximizing allocation

of an input increment. However, it can fail to do so when the input would increase relatively

rapidly the competitive position of a rival with a moderate competitive disadvantage. Bidder

handicapping that ensures auctions generate welfare-maximizing input allocations differ from

standard handicapping policies.

1. Introduction

It is well known that a vertically integrated firm might seek to deny access to an upstream

input to foreclose downstream rivals from operating in lucrative retail markets. It is also well

known that a monopolist typically is willing to pay more than a potential entrant for an essential

input because, by foreclosing entry, the monopolist can secure its monopoly profit whereas an

entrant can gain at most its share of a smaller duopoly profit.1

Recently,foreclosure concer ns have expanded to the domain of auctions. For instance, some

have questioned whether leading suppliers of wireless communications services might outbid

smaller rivalsin auctions of scarce radio spectrum primarily to limit the ability of the smaller rivals

to develop into effective competitors (US Department of Justice, 2013). Similarly, the Supreme

∗Georgetown University; mayoj@georgetown.edu.

∗∗University of Florida; sapping@ufl.edu.

We are grateful for very helpful comments and suggestions to the coeditor, anonymousreferees, Evan Kwerel, Preston

McAfee, TimothyTardiff, and seminar participants at the Federal Communications Commission, the Center for Research

in Regulated Industries 2014 Eastern Conference, the Southern Economics Association 2014 Annual Meeting, and the

Allied Social Sciences Association 2015 Annual Meeting.

1Corresponding considerations explain why a monopolist may engage in preemptive patenting to exclude rivals

(e.g., Gilbert and Newbery,1982). Rey and Tirole (2007) provide a comprehensive review of the literature on foreclosure.

186 C2016, The RAND Corporation.

MAYO AND SAPPINGTON / 187

Court has considered the possibility of “predatory bidding,” whereby a firm intentionally bids

particularly aggressively for a scarce input to limit downstream competition from other potential

input purchasers.2Because auctions are commonly employedto allocate scarce inputs in practice,3

these considerations raise important public policy concerns.

Numerous authors have recognized that auctions do not always ensure the welfare-

maximizing allocation of scarce inputs.4However, to our knowledge, the literature does not

provide a clear delineation of the industry conditions under which unfettered input auctions—

auctions that allocate inputs to the bidders that value them most highly5—will, and will not,

ensure the welfare-maximizing allocation of inputs. The purpose of this research is to provide

such a delineation in the context of a common model of industry competition.

The bidders in our model engage in Hotelling price competition after the input auction

concludes. The input being auctioned enhances customer valuation of a firm’s product and can

reduce the firm’sproduction cost. To illustrate, the input might be spectrum that enables a supplier

of wireless communications service to increase the speed and reliability of its service, which can

reduce customer acquisition and retention costs. Each of the firms in our model has an initial

endowment of the input, and the incremental amount of the input that is being auctioned is

relatively small. Consequently, no firm can preclude the operation of its rivals even if it were to

acquire all of the available input.

Each firm in this setting derives a “use value” and a “foreclosure value” from the input.

The use value arises because the firm that acquires the input increment can employ it to enhance

its competitive position.6The foreclosure value arises because, by acquiring an increment of a

scarce input, a firm precludes its rivals from acquiring the increment.7Such preclusion does not

foreclose the rival in the traditional sense of driving the rival from the market, but rather in the

sense of preventing the rival from employing the increment to improve its competitive position.

A firm (“firm 1”) will value highly, and therefore bid aggressively for, an input increment

that will substantially enhance its competitive position. However, the firm’s rival will also bid

aggressively for the input in this case in an attempt to prevent firm 1 from acquiring the input

that will substantially enhance its competitive position. These offsetting valuations of the rate

at which the input increases the competitive positions of the duopolists ensure that the input

allocation is determined at auction by the relative levels of the firms’ competitive positions. The

firm with the strongest competitive position—and thus the largest market share—will win an

unfettered auction for the input increment.

2Weyerhauser Co. v. Ross-Simmons Hardwood Lumber Co. 127 S. Ct. 1069, 1078 (2007). Blair and Lopatka

(2008) provide an informative discussion of this issue.

3To illustrate, auctions havebeen employed to allocate billions of dollars of spectrum among suppliers of wireless

communications services since the mid-1990s. See McAfee and McMillan (1996), Kwerel and Rosston (2000), Hazlett

and Munoz (2009), and Cramton et al. (2011), for example. Timber harvesting and oil drilling rights also are typically

allocated to suppliers of wood and oil products via auction. See Hendricks, Porter,and Wilson (1994), Haile (2001), and

Athey,Coey, and Levin (2013), for example.

4To illustrate, Jehiel and Moldovanu(2003) obser vethat, “When the assets for sale ... are inputs that will subse-

quently be used by the successful bidders in imperfect competition with each other ... auctions can behavein sur prisingly

problematic ways.” Eso, Nocke, and White (2010) note that, “Allocating input(s) through efficient auctions may be

misguided when bidders are competing firms.”

5For example, first-price and second-price auctions with no bidder subsidies generally have this feature. The

unfettered input auctions that we analyze are isomorphic to the efficient capacity auctions that Eso, Nocke, and White

(2010) consider. The authors define an efficientcapacity auction to be one that allocates “each unit of capacity to the fir m

that values it the most.”

6Formally,a firm’s “competitiveposition” is the difference between the valuation that customers place on the firm’s

product and the firm’sunit cost of production.

7Cramton et al. (2011) note that auctions may fail to promote economic efficiency because “an incumbent will

include in its private valuenot only its use value of the [scarce input] but also the value of keeping [it] from a competitor.”

Our terminology parallels that of the US Department of Justice (2013) which, in the context of spectrum auctions,

observes, “the private value [of spectrum] for incumbents ... includes not only the revenuefrom use of the spectr um but

also any benefits gained by preventingrivals from improving their services and thereby eroding the incumbents’ existing

businesses. The latter might be called ‘foreclosure value’ as distinct from ‘use value.’”

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