A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty

Authors:
V. Jeyakumar;G. Y. Li;G. M. Lee
Affiliations:
Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia;Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia;Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea
Venue:
Operations Research Letters
Year:
2011

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Abstract

The celebrated von Neumann minimax theorem is a fundamental theorem in two-person zero-sum games. In this paper, we present a generalization of the von Neumann minimax theorem, called robust von Neumann minimax theorem, in the face of data uncertainty in the payoff matrix via robust optimization approach. We establish that the robust von Neumann minimax theorem is guaranteed for various classes of bounded uncertainties, including the matrix 1-norm uncertainty, the rank-1 uncertainty and the columnwise affine parameter uncertainty.