Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2008-003 (April 17, 2008)

Robust Nash equilibria in N-person non-cooperative games: Uniqueness and reformulation
by Ryoichi Nishimura, Shunsuke Hayashi and Masao Fukushima

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In this paper we propose a general framework of distribution-free models for N-person non-cooperative games with uncertain information. In the model, we assume that each player's cost function and/or the opponents' strategies belong to some uncertainty sets, and each player chooses his/her strategy according to the robust optimization policy. Under such assumptions, we define the robust Nash equilibrium for N-person games by extending some existing definitions. We present sufficient conditions for existence and uniqueness of a robust Nash equilibrium. In order to compute robust Nash equilibria, we reformulate certain classes of robust Nash equilibrium problems to second-order cone complementarity problems. We finally show some numerical results to discuss the behavior of robust Nash equilibria.