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Second-order cone programming formulation for two player zero-sum game with chance constraints

Vikas Vikram Singh(vikas.singh***at***lri.fr)
Abdel Lisser(abdel.lisser***at***lri.fr)

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 if the row vectors of the random matrices, defining the stochastic constraints of each player, 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.

Keywords: Stochastic programming, Chance constraints, Zero-sum game, Saddle point equilibrium, Second-order cone program.

Category 1: Stochastic Programming

Category 2: Other Topics (Game Theory )


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Entry Submitted: 12/20/2016
Entry Accepted: 12/20/2016
Entry Last Modified: 12/20/2016

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