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Advances in Contest Theory

Paper Session

Sunday, Jan. 7, 2018 8:00 AM - 10:00 AM

Marriott Philadelphia Downtown, Meeting Room 406
Hosted By: Econometric Society
  • Chair: Rakesh Vohra, University of Pennsylvania

Risk-taking in Contests: The Impact of Fund-manager Compensation on Investor Welfare

Philipp Strack
,
University of California-Berkeley

Abstract

We provide a tractable model of competition in rank-order contests with general prize structures. A leading example of such a situation is the competition between fund managers whose compensation depends on how well they performed relative to their peers. We analyze their trading behavior in a dynamic financial market model à la Black Scholes. In the unique symmetric equilibrium, fund managers use randomized trading strategies which endogenously create risk. This risk is unrelated to the uncertainty generated by the assets traded in the underlying financial market. Furthermore, this risk is excessive as there exists a trading strategy that dominates the equilibrium return distribution in the sense of second-order stochastic dominance. This trading strategy takes the form of a simple index strategy.

Excessive risk-taking of fund managers leads to welfare losses if investors are risk-averse. Numerical examples indicate that welfare losses are substantial. Finally, we show that fund managers use more risky strategies, in the sense of second-order stochastic dominance, when competition between the agents increases.

Performance-Maximizing Contests

Wojciech Olszewski
,
Northwestern University
Ron Siegel
,
Pennsylvania State University

Abstract

Many sales, sports, and research contests are put in place to maximize contestants' performance. We investigate and provide a complete characterization of the prize structures that achieve this objective in settings with many contestants. The contestants may be ex-ante asymmetric in their abilities and prize valuations, and there may be complete or incomplete information about these parameters. The contestants may be risk neutral, risk averse, or risk seeking, and their performance cost may be linear, concave, or convex. A main takeaway is that awarding numerous prizes whose values gradually decline with contestants' ranking is optimal in the typical case of risk averse contestants that have a convex cost of performance.

Segmented Equilibria in the N-player Colonel Blotto Game

Dan Kovenock
,
Chapman University
Brian Roberson
,
Purdue University

Abstract

We extend the analysis of the classic Colonel Blotto game to the case of an arbitrary number of players. In equilibrium, the players (even symmetric players) may endogenously partition themselves into subsets of battlefields within which they compete rather than engaging in an all versus all competition in each and every battlefield. Our results shed light on the intricate interactions that arise when multiple players compete across multiple dimensions. Our entirely new method of constructing the equilibrium joint distributions also provides a framework for examining extensions of the n-player Colonel Blotto game.

Spying in Contests

Zhuoqiong Charlie Chen
,
Harbin Institute of Technology-Shenzhen

Abstract

Two players compete for a prize and their valuations are private information. Before the contest, each player can acquire a costly, noisy and private signal regarding the opponent's valuation. In equilibrium, each player's effort is non-decreasing in the posterior probability that the opponent has the same valuation. Accounting for the cost of spying, players are strictly better off spying when the spying technology is partially but not perfectly informative. Suppose instead that each player can, at no cost, ex ante commit to disclose a signal about her valuation to the opponent, but cannot observe realizations of the signal. Then every equilibrium involves non-disclosure by at least one player, even though some disclosure by each player would benefit both.
Discussant(s)
Johannes Horner
,
Yale University
Philip J. Reny
,
University of Chicago
Sandro Brusco
,
State University of New York-Stony Brook
John Morgan
,
University of California-Berkeley
JEL Classifications
  • A1 - General Economics