Information Acquisition and the Equilibrium Incentive Problem

• Date: 01 February 2017
• DOI: http://doi.org/10.1111/jems.12175
• Author: Alice Peng‐Ju Su
• Published date: 01 February 2017

Information Acquisition and the Equilibrium

Incentive Problem

ALICE PENG-JUSU

Department of Economics, National TaipeiUniversity

New TaipeiCity 237 Taiwan

apjs@mail.ntpu.edu.tw

I study the optimal incentive provision in a principal–agent relationship with costly information

acquisition by the agent. I emphasize that adverse selection or moral hazard is the principal’s

endogenous choice by inducing or deterring information acquisition. The principal designs the

contract not only to address an existing incentive problem but also to implement its presence.

Implementation of adverse selection relies on a steeper information rent to the agent than the

standard menu, such that the agent is motivated to distinguish the efficient state of nature from

the inefficient. Moral hazard is implemented by replacing the benchmark debt contract with a

debt-with-equity-share contract, such that the agent does not attempt to acquire information to

either avoid debt or to extract rent.

1. Introduction

Incentive problems, that is, adverse selection and moral hazard, have been the essence of

standard agency theories, in which either or both are exogenously present. The exogene-

ity of incentive problems is attributed to the assumption that productive information

structures are exogenous.1Information is, however,often realized as a result of endoge-

nous and costly acquisition activities, as enunciated by Arrow:

A key characteristic of information costs is that...they typically represent an irre-

versible investment...I am thinking of the need for having made an adequate invest-

ment of time and effort to be able to distinguish one signal from another. (Arrow,

1974 : 39)

As the information structure is endogenous, so is the underlying incentive prob-

lem in the principal–agent relationship. Consider a principal contracting with an agent

protected by limited liability, and both players are risk neutral. The principal’s revenue

An earlier version of this paper was part of my dissertation at the Department of Economics, University

of Washington. I am grateful to Fahad Khalil and Jacques Lawarr´

ee for their advice. The editor, coeditor,

and two anonymous referees have provided valuable comments and suggestions that greatly improved the

initial work. I would also like to thank Philip Brock, Charles Hill, Ben Keefer,Doyoung Kim, Meng-Yu Liang,

Dennis O’Dea, Xu Tan, Quan Wen, Ho-Po Crystal Wong, and Tak-Yuen Wong for their helpful comments.

Appreciation also goes to seminar participants at the University of Washington, National Taipei University,

Academia Sinica, and National Chungcheng University, as well as to the 25th International Conference on

Game Theory, and the 8th Japan-Taiwan-Hong Kong Contract Theory Conference. Any remaining errors are

mine.

1. Consider a principal contracting with an agent to execute a project that yields output to the principal,

which depends on the agent’s private productive effort and stochastic productive state of nature. Adverse

selection arises when the agent has private information on the productive state of nature, whereas the prin-

cipal observes only its stochastic distribution. The agent then manipulates output through private effort to

communicate such information to the principal. Moral hazard arises when the productive effort is imperfectly

measured by the output as the productive state of nature is imperfectly and symmetrically observed.

C2016 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume26, Number 1, Spring 2017, 231–256

232 Journal of Economics & Management Strategy

is generated by the agent’s hidden productive effort, and his productivity depends on

the stochastic state of nature. The agent can acquire information on the realized state of

nature but only at a sunk cost. The principal may thus implement adverse selection with

a contract that induces the agent to acquire information, so that information is asym-

metric and the agent manipulates the output with productive effort to communicate

the state of nature to the principal. The principal may also implement moral hazard

with a contract that deters the agent from acquiring information, in which scenario the

principal and the agent are symmetrically informed, and the publicly observed output

is an imperfect measure of the agent’s private effort. Conventional incentive theories

have previously discussed optimal contracts to cope with an existing incentive problem.

I study how such a contract is designed to implement the presence of the incentive

problem.

The emergence of the incentive problem and its interaction with the principal’s

information management has only received attention at one end: endogenous informa-

tion acquisition that generates adverse selection.2To the best of my knowledge, moral

hazard as a consequence of deterrence of information acquisition has not yet been ad-

dressed in contract theory. I fill this gap by investigating how information management

interacts with the equilibrium incentive problem and how the optimal contract is mod-

ified from the benchmark second best in response to such interaction.

To implement adverse selection by inducing perfect information acquisition, the

principal offers a menu contract that motivates the agent to distinguish efficient from

inefficient states of nature and to reveal the truth. I discuss two possible ways for

the principal to induce information acquisition. The first is to offer a contract with

continuous transfer, in which a higher (lower) output than the second best is specified

for a sufficiently efficient (inefficient) state of nature to implement a steeper rent than

its second-best counterpart. This method is a simple replication of Cr´

emer, Khalil, and

Rochet (1998a).

Alternatively, the principal can use the fact that the agent can only determine

productive effort but not realized output when the agent has not acquired information.

The principal can commit to pay a zero transfer over the set of outputs that an uninformed

agent generates with probability 1; the proposed candidate in this paper is the set of

rational numbers. The principal gains from this contract because it allows her to detect an

uninformed agent with probability 1, which relaxes the constraint to induce information

acquisition. The loss from this contract is that it relies on some pooling over some states

of nature to have the output rational on the equilibrium path. Due to continuity of the

model, there is an arbitrarily close rational output for any irrational output, and the loss

from pooling is only of second order and is outweighed by the first-order gain. Relying

on the rational output to screen the informed agent from the uninformed, the contract

restores output (at least weakly) toward efficiency for any state of nature to prescribe

an expected information rent to the agent that covers the cost of information acquisition

exactly.

I extend Poblete and Spulber (2012) to study the principal’s implementation of

moral hazard by deterring information acquisition. Under the conditions introduced by

Poblete and Spulber,the second-best contract with the presence of moral hazard is a debt

contract that prescribes a debt paid to the principal, leaving the agent the claimant of the

residual output. To deter information acquisition, the principal must deter the agent’s

2. Please refer to Lewis and Sappington (1997), Cr´

emer et al. (1998a), and Terstiege(2012) in the literature

review for more details.