A. Lisser, V. Singh, O. Jouini
We consider a two player bimatrix game where the entries of each player’s payoff matrix are independent random variables following a certain distribution. We formulate this as a chance-constrained game by considering that the payoff of each player is defined by using a chance-constraint. We consider the case of normal and Cauchy distributions. We show that a Nash equilibrium of the chance-constrained game corresponding to normal distribution can be obtained by solving an equivalent nonlinear complementarity problem. Further if the entries of the payoff matrices are also identically distributed with non-negative mean, we show that a strategy pair, where each player’s strategy is the uniform distribution on his action set, is a Nash equilibrium of the chance-constrained game. We show that a Nash equilibrium of the chance-constrained game corresponding to Cauchy distribution can be obtained by solving an equivalent linear complementarity problem.
Keywords: Chance-Constrained Game, Nash Equilibrium, Normal Distribution, Cauchy Distribution, Nonlinear Complementarity Problem, Linear Complementarity Problem.
Scheduled
WE2 Game Theory and equilibrium models
June 1, 2016 4:30 PM
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