The distribution of optimal strategies in symmetric zero-sum games

Florian Brandl

Games and Economic Behavior, 2017, vol. 104, issue C, 674-680

Abstract: Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is given by the corresponding matrix entry, the column player receives the negative of the row player. A randomized strategy is optimal if it guarantees an expected payoff of at least 0 for a player independently of the strategy of the other player. We determine the probability that an optimal strategy randomizes over a given set of actions when the game is drawn from a distribution that satisfies certain regularity conditions. The regularity conditions are quite general and apply to a wide range of natural distributions.

Keywords: Symmetric zero-sum games; Maximin strategies; Random games; Uniqueness of Nash equilibria (search for similar items in EconPapers)
JEL-codes: C62 C72 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:104:y:2017:i:c:p:674-680

DOI: 10.1016/j.geb.2017.06.017

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