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Vikas Vikram Singh (vikas.singhlri.fr) Abstract: We consider a two player bimatrix game where the entries of the payoff matrices are random variables. We formulate this problem as a chanceconstrained game by considering that the payoff of each player is defined using a chance constraint. We consider the case where the entries of the payoff matrices are independent normal/Cauchy random variables. We show a onetoone correspondence between a Nash equilibrium of a chanceconstrained game corresponding to normal distribution and a global maximum of a certain mathematical program. Further as a special case where the payoffs are independent and identically distributed normal random variables, we show that a strategy pair, where each player’s strategy is a uniform distribution over his action set, is a Nash equilibrium. We show a onetoone correspondence between a Nash equilibrium of a chanceconstrained game corresponding to Cauchy distribution and a global maximum of a certain quadratic program. Keywords: Chanceconstrained game, Nash equilibrium, Normal distribution, Cauchy distribution, Mathematical program, Quadratic program. Category 1: Stochastic Programming Category 2: Other Topics (Game Theory ) Citation: Download: [PDF] Entry Submitted: 12/31/2015 Modify/Update this entry  
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