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

Hayashi, Shunsuke; Yamashita, Nobuo; Fukushima, Masao

J. Nonlinear Convex Anal. 6, No. 2, 283-296 (2005).

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)