Local search techniques for computing equilibria in two-player general-sum strategic-form games

The computation of a Nash equilibrium in a game is a challenging problem in artificial intelligence. This is because the computational time of the algorithms provided by the literature is, in the worst case, exponential in the size of the game. To deal with this problem, it is common the resort to concepts of approximate equilibrium. In this paper, we follow a different route, presenting, to the best of our knowledge, the first algorithm based on the combination of support enumeration methods and local search techniques to find an exact Nash equilibrium in two-player general-sum games and, in the case no equilibrium is found within a given deadline, to provide an approximate equilibrium. We design some dimensions for our algorithm and we experimentally evaluate them with games that are unsolvable with the algorithms known in the literature within a reasonable time. Our preliminary results are promising, showing that our techniques can allow one to solve hard games in a short time.