Abstract: Nash Equilibria computing is one of the most important problems in noncooperative games. In this paper, we give a searching algorithm for finding a simple Nash equilibrium in twoplayer games. We limit the searching strategy space according to rank and the conditionally dominant rows of the payoff matrix, order the space, and seach the limited and ordered strategy space for finding a simple Nash equilibrium.

Key words: twoplayer games, Nash equilibrium, support set, conditionally dominant