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
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.