Semi-algebraic sets and equilibria of binary games

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• 作者：Guillaume Vigeral ; ^{vigeral@ceremade.dauphine.fr" class="auth_mail" title="E-mail the corresponding author} ; Yannick Viossat ^{viossat@ceremade.dauphine.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Semi-algebraic sets ; Nash equilibria ; Equilibrium payoffs ; Binary games
• 刊名：Operations Research Letters
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：44
• 期：1
• 页码：19-24
• 全文大小：381 K

文摘

Any nonempty, compact, semi-algebraic set in [0,1]ⁿ${[0,1]}^n$ is the projection of the set of mixed equilibria of a finite game with 2 actions per player on its first n$n$ coordinates. A similar result follows for sets of equilibrium payoffs. The proofs are constructive and elementary.