An offer you can't refuse: early contracting with endogenous threat

• Author: Jerome Pouyet,Bruno Jullien,Wilfried Sand‐Zantman
• DOI: http://doi.org/10.1111/1756-2171.12196
• Published date: 01 August 2017
• Date: 01 August 2017

RAND Journal of Economics

Vol.48, No. 3, Fall 2017

pp. 733–748

An offer you can’t refuse: early contracting

with endogenous threat

Bruno Jullien∗

Jerome Pouyet∗∗

and

Wilfried Sand-Zantman∗∗∗

A seller has private information on the future gains fromtrade with a buyer, but the buyer has the

option to invest to produce the good internally. Both the buyer and the seller can efficiently trade

ex post under complete information. Despite the lack of information, the buyer sometimes gains

by making an early contract offer to the seller. The early contract divides the different types of

sellers according to their information, which renders the threat of producing the good in-house

credible and enablesthe buyer to extract a larger share of the gains fromtrade. Several extensions

are investigated.

1. Introduction

Although asymmetric information has been recognized as a major impediment to efficient

trade, much less is known about its impact on the bargaining positions of the trading parties.1We

show in this article that asymmetric information allows the uninformed party to use threats that

would not otherwise be credible, thereby providing the uninformed party with a larger share of

the trade surplus.

As an illustration, consider the following situation: a Chief Executive Officer (CEO) must

decide between using an external specialist for performing repairs or maintenance on her

∗Toulouse School of Economics, CNRS, Universityof Toulouse Capitole; bruno.jullien@tse-fr.eu.

∗∗Paris School of Economics – CNRS and ENS; jerome.pouyet@ens.fr.

∗∗∗Toulouse School of Economics, University of Toulouse Capitole; wsandz@tse-fr.eu.

This article supersedes the Working Paper “Divide and Learn: Early Contracting with Endogenous Threat.” We have

benefited from the detailed comments of J.E. de Bettignies, G. Celik, O. Compte, B.MacLeod, D. Martimort, M. Peitz,

J. Swinkels, T. Valletti, and seminar participants at Paris School of Economics (2011), 2011 CSIO/IDEI conference,

T´

el´

ecom ParisTech (2011), the Universityof Besanc¸on (2011), the ENTER Jamboree (UAB, 2012), University College

London (2012), Thema (2013), Toulouse Business School (2013), Imperial College London (2013), and at the EARIE

2012 conference in Roma. We are indebted to the Editor, Benjamin Hermalin, and two referees for useful remarks on

a previous draft. We also gratefully acknowledge Orange for its financial support. This work was supported by a grant

overseen by the FrenchNational Research Agency (ANR-12-BSH1-0009).

1See Laffont and Martimort (2002) for the consequences of incomplete information and the design of constrained

optimal contracts.

C2017, The RAND Corporation. 733

734 / THE RAND JOURNAL OF ECONOMICS

infrastructure or performing these tasks in-house. The likelihood of repairs depends on vari-

ous elements that only this specialist may know well, in particular when the CEO has been newly

appointed and therefore has poor information on the likelihood of requiring the specialist’sskills

or when the service is related to a new project.2

From an organizational perspective, the CEO has three options. The first is to wait and

employ the specialist when needed, an ex post transaction that is assumed to take place under

complete information. Another option is to produce the service internally, perhaps by dedicating

resources to train a team within the firm; this is a profitable option only when the likelihood of

needing the service is sufficiently high. The last option is to propose a contract to the specialist

ex ante, before the realization of the firm’s need, to specify a price when the specialist’s service

is needed. Such a contract takes place under asymmetric information between the firm and the

provider, and the CEO cannot commit to the action chosen were the specialist to refuse that

contract.

Our analysis reveals that the CEO may choose the last option and use the threat to rely on

in-house supply as a tool to reduce the price paid to the specialist, despite the CEO’s inability

to commit to using this threat. Specifically, being at an informational disadvantage may increase

the credibility of the option to produce the service internally, thereby providing the CEO with

a stronger ex ante bargaining position vis-`

a-vis the specialist. When this is indeed the case, the

CEO gains more by proposing an ex ante contract under asymmetric information than by relying

on ex post supply under complete information.

This ex ante contract exploits the heterogeneity among the different types of specialists;

that is, some types know that the likelihood of repair is low, whereas other types know that it is

high. Suppose that the CEO proposes a contract to the specialist. When the likelihood of the firm

needing the specialist’s services is low enough, the specialist accepts that contract because his

expected gain from an ex post trade is low. Following a refusal, the CEO must therefore infer that

likelihood is high, making the option of producing the service internally more profitable. This

deters a specialist who knows that the likelihood is high from refusing the contract. There is thus

an information trap whereby acceptance by certain types of specialists forces acceptance by the

other types, even when the offer is less profitablefor some specialists than their gain from ex post

trade.

Tomake this point in the most transparent way, wemodel the relationship between a potential

buyer (she—the CEO in the above illustration) and a seller (he—the specialist). The buyer will

have unit demand with some probability θthat is privatelyknown to the seller. Conditional on the

demand being positive, the reservation utility of the buyer is fixed at a commonly known value.

In this case, gains from trade are always realized ex post, and the only question is the division

of the surplus between the buyer and the seller. Our model involves two periods, and demand is

realized in the second period (ex post).

Faced with uncertainty, the buyer can wait until the demand is realized. In this case, there

is a negotiation in the second period between the seller and the buyer, and the good is traded if

demand is positive. During the first period, the buyermay instead decide to invest to produce the

good in-house; such an investment is referred to as “bypass.” Prior to that decision, the buyer can

also propose a contract to the seller that specifies the future terms of trade. A feature that makes

the contracting problem interesting and novel is the inability of both parties to commit to future

actions in the absence of a contract.

To highlight the strength of our mechanism, we assume that, based on her prior beliefs

regarding θ, the buyer does not find it profitable to produce the good in-house. This means that,

absent additional information, the buyer cannot credibly use her ability to invest as a threat to

reduce the price paid ex ante. When the seller has no superior information with respect to the

buyer, the only outcome is then that the buyer waits and trades ex post if the demand is positive.

Weshow that, instead, if the seller privately knows θin the first period and the buyer’s investment

2In the conclusion, we suggest several other applications with similar features.

C

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