Costly search with adverse selection: solicitation curse versus acceleration blessing

• Author: Kyungmin Kim,Marilyn Pease
• Published date: 01 May 2017
• DOI: http://doi.org/10.1111/1756-2171.12185
• Date: 01 May 2017

RAND Journal of Economics

Vol.48, No. 2, Summer 2017

pp. 526–553

Costly search with adverse selection:

solicitation curse versus acceleration blessing

Kyungmin Kim∗

and

Marilyn Pease∗∗

We analyze a dynamic trading model of adverse selection where a seller can increase the fre-

quency of strategic price quotes. A low-quality seller benefits more from trade and, therefore,

searches more intensively than a high-quality seller. This makes a seller’s contact carry negative

information but a seller’s availability become a stronger indicator of high quality. In the station-

ary environment, the two effects exactly offset each other, and reducing search costs is weakly

beneficial to the seller. In the nonstationary environment, the relative strengths of the two effects

vary over time, and reducing search costs can be detrimental to the seller.

1. Introduction

We study a dynamic trading model in which a seller, with an indivisible object to sell,

receives strategic price quotes from a sequence of randomly arriving buyers. We introduce two

key features into this canonical trading environment. First, as in Akerlof (1970), the seller has

private information about the quality of the object, where a high-quality unit is more valuable to

both the seller and buyers than a low-quality unit. Second, the seller chooses the frequency of

price quotes (i.e., the arrival rate of buyers) at an increasing cost. The cost can be interpreted as

advertising expenditure (as in, e.g., Butters, 1977; Grossman and Shaprio, 1984) or search effort

(as in, e.g., Burdett and Judd, 1983; Mortensen, 1986).

Our goal is to understand the joint effects of adverse selection and endogenous search

(advertising) intensity in dynamic trading environments. A low-quality seller, due to her lower

reservation value, enjoys more trade surplus and, therefore, has a stronger incentive to speed up

trade than a high-quality seller. This affects buyers’ inferences regarding the seller’s underlying

type and, therefore, their trading behavior, which in turn influences the seller’s trading and

∗University of Miami; teddy.kyungmin.kim@gmail.com.

∗∗University of Iowa; marilyn-pease@uiowa.edu.

We thank the Editor and two anonymous referees for various valuable comments and suggestions. We are grateful to

Yeon-Koo Che, Michael Choi, Martin Gervais, Ilwoo Hwang, Ayca Kaya, Duk Gyoo Kim, Jinwoo Kim, and seminar

audiences at various places for many helpful comments and suggestions.

526 C2017, The RAND Corporation.

KIM AND PEASE / 527

search behavior. We formalize such inference problems of buyers and investigate equilibrium

implications for market outcomes.1

We identify the following two opposing effects, both of which stem from the fact that a

low-quality seller chooses a higher search intensity than a high-quality seller. First, a seller who

successfully finds a buyer is more likelyto possess a low-quality unit. In other words, the very fact

that a buyer has met a seller conveys bad newsabout the seller’s type.2FollowingLauer mann and

Wolinsky (2013), we call this effect the “solicitation curse.” Second, a seller who has not traded

yet is more likely to possess a high-quality unit. In other words,the fact that a unit is still available

is good news about its quality. Note that even without endogenous intensity, a low-quality seller

trades faster than a high-quality seller, because of the difference in reservation prices. Endogenous

intensity makes a low-quality seller trade even faster than a high-quality seller. For this reason,

we call this effect the “acceleration blessing.”

To be formal, refer to the probability that the seller who remains in the game is the high

type as buyers’ unconditional beliefs, and the corresponding probability when a buyer actually

faces the seller as buyers’ conditional beliefs. These two values are identical if both seller types

have the same search intensity. In our model, the low-type seller chooses a higher search intensity

than the high-type seller, and thus buyers’ conditional beliefs fall short of their unconditional

beliefs. The solicitation curse refers to this downward adjustment from buyers’ unconditional

beliefs to conditional beliefs. Meanwhile, the difference in search intensities drives up buyers’

unconditional beliefs beyond the level that is induced onlyby the difference in reservation prices.

This additional increase of buyers’ unconditional beliefs is the acceleration blessing. We study

how these two effects manifest themselves and interact with each other in both stationary and

nonstationary environments.

In Section 3, we consider an opaque trading environment where buyers do not receive any

information about the seller’strading history. In this case, all buyershave the same beliefs about the

seller’s type and, therefore, play identical offer strategies.The environment is stationary from the

seller’s viewpoint and,therefore, each seller type’soptimal search intensity is time-invariant. In this

case, the aforementioned two effects takesimple for ms. We quantify the two effects and showthat

their magnitudes are identical for any strategy profile. In other words, environmental stationarity

implies that the two effects exactly offset each other, and the difference in search intensities does

not directly affect buyers’ conditional beliefs. Nevertheless, endogenous search intensity still

influences the players’ equilibrium strategies. We provide a full-equilibrium characterization and

explain the effects of endogenous search intensity on market outcomes.

In Section 4, we examine a nonstationary version of the model. Specifically, we consider the

case in which buyers observe the seller’s time-on-the-market (i.e., how long the seller has been

on the market). The observability assumption allows us to study how the seller’s optimal search

intensity and buyers’ unconditional and conditional beliefs evolve over time. In this nonstationary

model, the players’ strategies and beliefs depend on the seller’s time-on-the-market, and thus

the solicitation curse and the acceleration blessing take more complex forms. The acceleration

blessing induces buyers’ (both unconditional and conditional) beliefs to converge to 1, which

is in stark contrast to a common result in the literature that buyers’ beliefs stay bounded away

from 1. As in the stationary model, the solicitation curse brings down buyers’ conditional beliefs

relative to their unconditional beliefs. Unlike in the stationary model, its strength relative to the

acceleration blessing changes over time. In particular, it outweighs the acceleration blessing for

a certain length of time, which leads to nonmonotonicity of buyers’ conditional beliefs. Wes how

1Our investigation is related to the literature on uninformative advertisements, which explains how they can be

used to signal product quality. Signalling playsno role in our model, because the seller has only one unit to sell (i.e., no

repeat purchases) and her search intensity is not observable by buyers (i.e., no credible signal).

2It is noteworthy that, although weobtain this effect in a fully rational framework, there is both experimental and

empirical evidence about this phenomenon. See, for example, Kirmani (1990, 1997), Kirmani and Wright (1989), and

Kwoka (1984).

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