Equilibrium play in matches: Binary Markov games

• 成果类型: Article
• 署名作者: Walker, Mark; Wooders, John; Amir, Rabah
• 署名单位: University of Arizona
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2010.04.011
• 发表日期: 2011
• 页码: 487-502
• 关键词: Stochastic games; Minimax; Strictly competitive games; Game theory and sports; Tennis

摘要

We study two-person extensive form games, or matches, in which the only possible outcomes (if the game terminates) are that one player or the other is declared the winner. The winner of the match is determined by the winning of points, in point games. We call these matches binary Markov games. We show that if a simple monotonicity condition is satisfied, then (a) it is a Nash equilibrium of the match for the players, at each point, to play a Nash equilibrium of the point game; (b) it is a minimax behavior strategy in the match for a player to play minimax in each point game; and (c) when the point games all have unique Nash equilibria, the only Nash equilibrium of the binary Markov game consists of minimax play at each point. An application to tennis is provided. (C) 2010 Elsevier Inc. All rights reserved.