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| Volume 5, Number 2, May 2009, pp. 237-259 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Ryoichi Nishimura, Shunsuke Hayashi and Masao Fukushima | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Key words: | ||||||||||||||||||||||||||||||||||||||||||||||||||
| N-person non-cooperative game, incomplete information, robust Nash equilibrium, robust optimization, complementarity problem | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Mathematices Subject Classification: 91A06, 91A10, 90C33 | ||||||||||||||||||||||||||||||||||||||||||||||||||
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| Abstract: | |||
| 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. | |||
| Robust Nash equilibria in N-person non-cooperative games: Uniqueness and reformulation | ||