Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2004-004 (April 15, 2004)

Robust Nash Equilibria and Second-Order Cone Complementarity Problems
by Shunsuke Hayashi, Nobuo Yamashita and Masao Fukushima

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In this paper we consider a bimatrix game in which the players can neither evaluate their cost functions exactly nor estimate their opponents' strategies accurately. To formulate such a game, we introduce the concept of robust Nash equilibrium that results from robust optimization by each player, and prove its existence under some mild conditions. Moreover, we show that a robust Nash equilibrium in the bimatrix game can be characterized as a solution of a second-order cone complementarity problem (SOCCP). Some numerical results are presented to illustrate the behavior of robust Nash equilibria.