Signaling in a Rent‐Seeking Contest with One‐Sided Asymmetric Information

• Published date: 01 April 2017
• Author: PIM HEIJNEN,LAMBERT SCHOONBEEK
• DOI: http://doi.org/10.1111/jpet.12171
• Date: 01 April 2017

SIGNALING IN A RENT-SEEKING CONTEST WITH ONE-SIDED

ASYMMETRIC INFORMATION

PIM HEIJNEN

University of Groningen

LAMBERT SCHOONBEEK

University of Groningen

Abstract

We consider a two-player rent-seeking Tullock contest where one player

has private information about his valuation of the prize, which can be

high or low. This player can send a costly signal to his opponent, i.e.,

he can commit to reduce the prize either by some absolute amount

of money or proportionally, conditional on winning it. We show that

both kinds of signaling imply completely opposite results for separating

equilibria, both in terms of conditions for existence and the type of

player who sends the costly signal.

1. Introduction

In practice, we encounter many instances where two players compete for a single prize.

In such cases, we observe now and again that a player commits to give up part of the

prize conditional on winning it. For example, take two rival contractors who lobby of-

ficials to obtain a building contract. It then may happen that one of them commits to

organize an (excessively) expensive feast to celebrate the completion of the project, if

the contract will be awarded to him.1Next, consider the take-over contest for the Dutch

bank ABN-AMRO in 2007 between the British bank Barclays and a consortium of the

Royal Bank of Scotland, Fortis, and Santander. Barclays committed to invest 20 million

Euros in the Amsterdam Business School of the University of Amsterdam conditional on

winning the contest. Or, in litigation, we sometimes see that a celebrity commits to give

1A committee of the Dutch parliament, investigating possible bribing of government officials by con-

tractors, observes that such feasts occurred in the Dutch construction sector (Tweede Kamer 2003).

Pim Heijnen, Department of Economics, Econometrics and Finance, Faculty of Economics and Busi-

ness, University of Groningen, P.O.Box 800, 9700 AV Groningen, The Netherlands (p.heijnen@rug.nl).

Lambert Schoonbeek, Department of Economics, Econometrics and Finance, Faculty of Economics

and Business, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands

(l.schoonbeek@rug.nl).

We thank the associate editor and two anonymous referees for very helpful suggestions that improved

the paper substantially. We also thank Allard van der Made and seminar participants at the University

of Nottingham, the 4th World Congress of the Game Theory Society in Istanbul, the European Public

Choice Society Meeting in Zurich, and EEA 2014 in Toulouse for useful discussions.

Received April 29, 2013; Accepted July 11, 2015.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 19 (2), 2017, pp. 548–564.

548

Signaling in a Rent-Seeking Contest 549

away part of his indemnity (e.g., as a donation to charity) if he wins the lawsuit from the

defendant.2Finally, consider two politicians running for election. Then, one of them

might commit to reward specific individuals or organizations, regardless of their merit,

in case he is elected.3,4

We argue that sacrificing part of the prize conditional on winning can be rational-

ized as a strategic choice in a signaling game, used in order to induce less aggressive

behavior of the opponent. We investigate this possibility in the context of the two-player

rent-seeking contest of Tullock (1980). The game has many applications, e.g., in terms

of lobbying, rent-seeking, litigation, and political campaigning (Nitzan 1994; Lockard

and Tullock 2001; Congleton, Hillman, and Konrad 2008; Konrad 2009). In the stan-

dard contest, the players have complete information about their valuations of the prize.

However, we examine the case with asymmetric information, where one player has pri-

vate information regarding his valuation, which can be either high or low with given

probabilities. The valuation by the other player is publicly known. In this setup, we in-

troduce the option of costly signaling.

We analyze the following three-stage game. In stage 1, the privately informed player

(referred to as the informed player) learns his type, i.e., his true valuation of the prize.

The opponent (the uninformed player) only knows the distribution. In stage 2, the

informed player can send an observable costly signal to the uninformed player by com-

mitting to give up part of the prize conditional on winning. In stage 3, the players play

the actual contest. We consider two simple variants of signaling in stage 2. In the first

variant, the informed player can commit to reduce his prize by some absolute amount of

money (e.g., 100,000 euros) conditional on winning. We call this absolute signaling. In

the second variant, the informed player can commit to lower his prize proportionally to

some fraction (e.g., 90%) of its initial value contingent on winning. We call this propor-

tional signaling. For both variants of signaling, we derive the necessary and sufficient

condition for the existence of separating equilibria. In such equilibria, the informed

player strategically reveals his type to his opponent through his decision in stage 2

(Fudenberg and Tirole 1991).

Signaling has a direct negative effect on the payoff of the player who sends the

signal, since it reduces the size of his prize contingent on winning. In addition, sig-

naling has an indirect effect on this player’s payoff because it influences the efforts

subsequently chosen by the players in the contest. Importantly, the indirect effect is

positive if it entails a reduction of the effort of the opponent. The interplay of the

direct and indirect effect determines the conditions for the existence of separating

equilibria. We find that the game with absolute signaling has separating equilibria if

and only if the informed player is relatively strong (in a sense to be specified below).

In such equilibria, the high type informed player is willing to send a costly absolute

2This type of behavior is especially prevalent in U.K. libel cases, where celebrities sue newspapers and

magazines over the publication of allegedly defamatory stories. For instance, in 2007, Kate Winslet sued

Grazia, a weekly women’s magazine, for publishing a story that claimed she had sought medical help

for weight loss. She promised that the indemnity would be donated to charities, which combat eating

disorders. After winning the court case, she indeed donated the money.

3For example, take any country in which nepotism and rent-seeking are prevalent. A presidential can-

didate, who is open about his intention to appoint clearly incompetent family members as government

officials, is reducing the rent from office.

4In the examples above, the relevant player makes a public announcement and he or she does not

renege on this announcement for fear of tarnishing his or her reputation. In that sense, the player

commits to giving up part of the prize conditional on winning it.