The distribution of optimal strategies in symmetric zero-sum games

• 成果类型: Article
• 署名作者: Brandl, Florian
• 署名单位: Technical University of Munich
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2017.06.017
• 发表日期: 2017
• 页码: 674-680
• 关键词: Symmetric zero-sum games; maximin strategies; Random games; Uniqueness of Nash equilibria

摘要

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. (C) 2017 Elsevier Inc. All rights reserved.