A second-order cone programming formulation for two player zero-sum games with chance constraints

Abstract

We consider a two player finite strategic zero-sum game where each player has stochastic linear constraints. We formulate the stochastic constraints of each player as chance constraints. We show the existence of a saddle point equilibrium in mixed strategies if the row vectors of the random matrices defining the stochastic constraints are elliptically symmetric distributed random vectors. We further show that a saddle point equilibrium can be obtained from the optimal solutions of a primal-dual pair of second-order cone programs.