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Information in Contests

Paper Session

Sunday, Jan. 5, 2020 1:00 PM - 3:00 PM (PDT)

Marriott Marquis, Newport Beach
Hosted By: Econometric Society
  • Chair: Philipp Strack, Yale University

Optimal Disclosure of Value Distribution Information in All Pay Auction

Jingfeng Lu
,
National University of Singapore
Zijia Wang
,
National University of Singapore

Abstract

In this paper, we follow a Bayesian Persuasion approach to study
the auction organizer’s optimal disclosure of information about players’ value
distribution in a two-player all-pay auction setting. Players’ private values
(either high vh or low vl) are independently and identically distributed. There
are two possible value distributions (i.e., two possible states), and none of the
players knows the actual distribution. Before the auction starts, the organizer
pre-commits to a public signal to reveal information about the prevailing
value distribution. We find that there exists a cutoff for value ratio v = v_h/v_l,
above which a monotone equilibrium arises under any prior belief about the
state. In this circumstance, no disclosure is optimal. When value ratio v is
below the cutoff, there exist exactly two threshold beliefs about the state that
separate prior beliefs generating monotone and non-monotone equilibria. A prior belief would lead to a non-monotone equilibrium if and only if it lies in between. If the original prior leads to a monotone equilibrium, then still no disclosure is optimal; otherwise, a partial disclosure, which generates a posterior distribution over the two threshold beliefs, is optimal.

The Secret behind The Tortoise and the Hare: Information Design in Contests

Alejandro Melo Ponce
,
Nazarbayev University

Abstract

I analyze the optimal information disclosure problem under commitment of a “contest designer” in a class of binary action contests with incomplete information about the abilities of the players. If the contest designer wants to incentivize the players to play in equilibrium a particular strategy profile, she can design an information disclosure rule, formally a stochastic communication mechanism, to which she will commit and then use to “talk” with the players. The main tool to carry out the analysis is the concept of Bayes Correlated Equilibrium recently introduced in the literature. I find that the optimal information disclosure rules involve private information revelation (manipulation), which is also cost-effective for the designer. Furthermore, the optimal disclosure rule involves asymmetric and in most cases correlated signals that convey only partial information about the abilities of the players.

Information Disclosure in Contests: Private Versus Public Signals

Zhuoqiong Chen
,
Harbin Institute of Technology-Shenzhen

Abstract

Two players compete for a prize in an all-pay auction where their private binary valuations are independent from each other. A contest organizer commits to disclose additional information about the opponent’s valuation to each player – privately or publicly – to maximize either players’ expected payoff or total expected effort. I characterize the unique equilibrium of the contest when the organizer discloses a public signal to all players and a symmetric equilibrium when he discloses a private signal to each. When the organizer discloses privately, I show that any partially informative private signals induce higher expected payoffs for players and lower total expected effort than when no signal is disclosed. When the organizer discloses publicly, I characterize a public disclosure policy that induces higher total expected effort than when no signal is disclosed. I also characterize optimal public signals that maximize players’ expected payoff. Finally, the ranking between private and public signals in terms of maximizing players’ expected payoff is indeterministic. In terms of revenue ranking, the all-pay auction with the public disclosure policy dominates the first- and the second-price auctions with binary independent private valuation regardless of whether private or public disclosure is used in these winner-pay auctions.
JEL Classifications
  • C7 - Game Theory and Bargaining Theory
  • D4 - Market Structure, Pricing, and Design