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Robust Nash equilibria and second-order cone complementarity problems. (English) Zbl 1137.91310

Summary: 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.

MSC:

91A10 Noncooperative games
91A05 2-person games
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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