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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167637715001406&_mathId=si1.gif&_user=111111111&_pii=S0167637715001406&_rdoc=1&_issn=01676377&md5=7afa369d77674e3fb399ae5d85f7c291" title="Click to view the MathML source">[0,1]ⁿclass="mathContainer hidden">class="mathCode">${[0,1]}^n$ is the projection of the set of mixed equilibria of a finite game with 2 actions per player on its first class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167637715001406&_mathId=si2.gif&_user=111111111&_pii=S0167637715001406&_rdoc=1&_issn=01676377&md5=0c83b8d455abbfe5e616451d02988205" title="Click to view the MathML source">nclass="mathContainer hidden">class="mathCode">$n$ coordinates. A similar result follows for sets of equilibrium payoffs. The proofs are constructive and elementary.