Large Supports are Required for Well-Supported Nash Equilibria
نویسندگان
چکیده
We prove that for any constant k and any < 1, there exist bimatrix win-lose games for which every -WSNE requires supports of cardinality greater than k. To do this, we provide a graphtheoretic characterization of win-lose games that possess -WSNE with constant cardinality supports. We then apply a result in additive number theory of Haight [8] to construct win-lose games that do not satisfy the requirements of the characterization. These constructions disprove graph theoretic conjectures of Daskalakis, Mehta and Papadimitriou [7] and Myers [13].
منابع مشابه
Polylogarithmic Supports Are Required for Approximate Well-Supported Nash Equilibria below 2/3
In an -approximate Nash equilibrium, a player can gain at most in expectation by unilateral deviation. An -well-supported approximate Nash equilibrium has the stronger requirement that every pure strategy used with positive probability must have payoff within of the best response payoff. Daskalakis, Mehta and Papadimitriou [8] conjectured that every win-lose bimatrix game has a 2 3 -well-suppor...
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We prove that for any constant k and any ǫ < 1, there exist bimatrix win-lose games for which every ǫ-WSNE requires supports of cardinality greater than k. To do this, we provide a graphtheoretic characterization of win-lose games that possess ǫ-WSNE with constant cardinality supports. We then apply a result in additive number theory of Haight [8] to construct win-lose games that do not satisfy...
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