COMMITMENT AND COSTLY SIGNALING IN DECENTRALIZED MARKETS

• Author: Derek Stacey
• Published date: 01 November 2016
• DOI: http://doi.org/10.1111/iere.12206
• Date: 01 November 2016

INTERNATIONAL ECONOMIC REVIEW

Vol. 57, No. 4, November 2016

COMMITMENT AND COSTLY SIGNALING IN DECENTRALIZED MARKETS∗

BYDEREK STACEY1

Ryerson University, Canada

I propose a search model of a decentralized market with asymmetric information in which sellers are unable to

commit to asking prices announced ex ante. Relaxing the commitment assumption prevents sellers from using price

posting as a signaling device to direct buyers’ search. Private information about the gains from trade and inefficient

entry on the demand side then contribute to market illiquidity. Endogenous sorting among costly marketing platforms

can facilitate the search process by segmenting the market to alleviate information frictions. Seemingly irrelevant but

incentive compatible listing fees are implementable provided that the market is not already sufficiently active.

1. INTRODUCTION

In this article, I develop a directed search model of a decentralized market with private infor-

mation in which sellers lack the ability to commit to asking prices. Under certain assumptions

about the matching process and the method of price determination, the absence of commitment

precludes asking prices as an effective means of disclosing sellers’ unobservable reservation

values to appropriately direct buyers’ search. Instead, the net social surplus from market trans-

actions is adversely affected by information frictions and inefficient entry of buyers. In some

circumstances, however, sellers of different types can reveal their willingness to sell and attract

the appropriate number of buyers by sorting endogenously among costly marketing platforms.

Otherwise wasteful listing fees can therefore play a role in overcoming information frictions

and improving market efficiency.

I consider a decentralized market in which sellers advertise a single indivisible and homo-

geneous item for sale to attract buyers. Each buyer can incur a cost to visit a seller, but the

matching process is subject to search or coordination frictions resulting in instances where mul-

tiple buyers visit the same seller. Prices are determined by the equilibrium bidding strategies of

buyers when the number of competing bidders in a match is observable. A seller’s reservation

value is the crucial source of private information. I show that nonbinding list prices as cheap

talk are uninformative. Sellers with high reservation values mimic sellers with low reservations

values in order to drive up the final sale price by increasing the probability of a bidding war.

This result relies on the inability to commit to ex ante prices and, to some extent, the particulars

of the matching process and pricing protocol. The intuition is as follows: The appeal of a higher

expected selling price in multiple offer situations is offset by the possibility of a single low offer

in a bilateral match. Without commitment to an asking price, however, a seller is free to reject

any unacceptable offer and is therefore primarily concerned about increasing the expected

number of buyer visits, regardless of her reservation value.

∗Manuscript received December 2013; revised December 2014.

1This article is based on a chapter of my 2012 doctoral dissertation at Queen’s University. I thank my advisors,

Allen Head and Huw Lloyd-Ellis, for their help and support. The editor, Guido Menzio, and two anonymous referees

provided suggestions that substantially improved the article. Valuable comments were also received from confer-

ence/seminar participants at various institutions. The article was previously circulated under the title “Information,

Commitment, and Separation in Illiquid Housing Markets.” All errors are my own. Please address correspondence to:

Derek Stacey, Department of Economics, Ryerson University, 350 Victoria Street, Toronto, ON M5B 2K3, Canada.

E-mail: dstacey@economics.ryerson.ca.

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C

(2016) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1508 STACEY

I propose a costly signaling mechanism for market separation: If sellers can sort endogenously

among costly marketing platforms, I find that in some circumstances multiple platforms are

incentive compatible and implement a separating directed search equilibrium. This alleviates

the information problem and increases activity in the market. Even though marketing costs in

the form of listing fees provide no technological advantage in the matching process, incentive

compatible market separation is achievable as long as search costs are high enough that the

market would otherwise be sufficiently inactive. In high-demand settings, on the other hand,

motivated/anxious sellers cannot justify allocating resources to a costly signaling technology to

further increase the expected number of buyer visits.

Endogenous sorting among costly platforms is shaped by anxious sellers’ pre- and postmatch

incentives to separate. Ex ante, anxious sellers might be willing to pay a listing fee if it attracts

more buyers (in expectation) by signaling a higher surplus from trade. Since sellers respond

differently to changes in the expected number of buyer visits, which in turn is related to the

endogenous composition of sellers on a particular platform, it can be self-fulfilling for anxious

sellers to advertise on a platform that is costly enough to discourage mimicking by less motivated

sellers. Ex post, however, sellers with low reservation values prefer situations with private

information because, in a bilateral match, the buyer submits a better offer if his beliefs assign

a sufficiently high probability to the possibility that the seller’s reservation value is high. In

general, the first effect dominates, and market separation emerges as buyers become scarce,

that is, as search costs increase and fewer buyers choose to participate in the market.

This article is part of the search literature and in particular contributes to the study of markets

with search frictions and private information. In contrast to existing theories of competitive

or directed search with private information that rely on strong commitment assumptions,2

relaxing the assumption of full commitment to the announced terms of trade is an important

element in this article. A related paper by Kim (2012) shows that nonbinding messages can

support a partially separating equilibrium in a decentralized asset market when there is private

information about the quality of the asset. Nonbinding list prices are ineffective here because it

is the seller’s reservation value that is private information, which is independent of the buyer’s

valuation. Menzio (2007) relaxes the commitment assumption in a model of the labor market and

shows that cheap talk can sometimes credibly convey information when wages are determined

through bargaining. In a partially directed search equilibrium, a deviation from truth-telling

that improves the matching probability will result in a lower negotiated share of the surplus.

In an environment with auctions, in contrast, the transaction price increases with the number

of buyers in a match.3Without commitment to an asking price, sustaining a fully revealing

and constrained efficient equilibrium requires a trading protocol that does not generate too

much price dispersion (Kim and Kircher, 2014). Otherwise, the absence of commitment hinders

truth-telling and unravels market separation, as I show in the version of the model without

marketing platforms that charge listing fees.

Costly signaling has been studied extensively in the literature without search frictions. In

Spence’s (1973) canonical model of labor market signaling, a productive worker undertakes a

costly activity such as acquiring education to distinguish himself from a less-productive worker.

A crucial assumption is that the worker’s cost of undertaking the signaling activity is negatively

correlated with his unobservable productivity so that signaling can be an effective way to

distinguish worker types. This type of single-crossing property isoftenassumedinsignaling

theory. Fang (2001) constructs a signaling model that generates an endogenous single-crossing

property by allowing uninformed firms to give preferential treatment to and form different

2Recent papers in this literature include Guerrieri et al. (2010) and Delacroix and Shi (2013), to name a few. Guerrieri

et al. (2010) present a search environment with adverse selection and show that screening results in a fully revealing

competitive search equilibrium when the uninformed party can commit to a take-it-or-leave-it trading mechanism.

Delacroix and Shi (2013) study a model with adverse selection where sellers can post nonnegotiable prices as a means

of directing search and also as a signal of the quality of their asset.

3Julien et al. (2006) highlight the implications of this type of setup for residual price dispersion in a theory of the

labor market with full information.