Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer

Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in... By P.-A. CHIAPPORI, S. LEVITT, The concept of mixed strategy is a fundamental component of game theory, and its normative importance is undisputed. However, its empirical relevance has sometimes been viewed with skepticism. The main concern over the practical usefulness of mixed strategies relates to the “indifference” property of a mixedstrategy equilibrium. In order to be willing to play a mixed strategy, an agent must be indifferent between each of the pure strategies that are played with positive probability in the mixed strategy, as well as any combination of those strategies. Given that the agent is indifferent across these many strategies, there is no benefit to selecting precisely the strategy that induces the opponent to be indifferent, as required for equilibrium. Why an agent would, in the absence of communication between players, choose exactly one particular randomization is not clear.1 Of course, whether agents, in real life, actually play Nash equilibrium mixed strategies is ultimately an empirical question. The evidence to date on this issue is based almost exclusively on laboratory experiments (e.g., Barry O’Neill, 1987; Amnon Rapoport and Richard B. Boebel, 1992; Dilip Mookherjee and Barry Sopher, AND T. GROSECLOSE* * Chiappori: Department of Economics, University of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png American Economic Review American Economic Association

Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer

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Publisher
American Economic Association
Copyright
Copyright © 2002 by the American Economic Association
Subject
Shorter Papers
ISSN
0002-8282
D.O.I.
10.1257/00028280260344678
Publisher site
See Article on Publisher Site

Abstract

By P.-A. CHIAPPORI, S. LEVITT, The concept of mixed strategy is a fundamental component of game theory, and its normative importance is undisputed. However, its empirical relevance has sometimes been viewed with skepticism. The main concern over the practical usefulness of mixed strategies relates to the “indifference” property of a mixedstrategy equilibrium. In order to be willing to play a mixed strategy, an agent must be indifferent between each of the pure strategies that are played with positive probability in the mixed strategy, as well as any combination of those strategies. Given that the agent is indifferent across these many strategies, there is no benefit to selecting precisely the strategy that induces the opponent to be indifferent, as required for equilibrium. Why an agent would, in the absence of communication between players, choose exactly one particular randomization is not clear.1 Of course, whether agents, in real life, actually play Nash equilibrium mixed strategies is ultimately an empirical question. The evidence to date on this issue is based almost exclusively on laboratory experiments (e.g., Barry O’Neill, 1987; Amnon Rapoport and Richard B. Boebel, 1992; Dilip Mookherjee and Barry Sopher, AND T. GROSECLOSE* * Chiappori: Department of Economics, University of

Journal

American Economic ReviewAmerican Economic Association

Published: Sep 1, 2002

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