Using tabu best-response search to find pure strategy nash equilibria in normal form games

We present a new method for computing pure strategy Nash equilibria for a class of n-person games where it is computationally expensive to compute the payoffs of the players as a result of the joint actions. Previous algorithms to compute Nash equilibria are based on mathematical programming and analytical derivation, and require a complete payoff matrix as input. However, determining a payoff matrix can itself be computationally intensive, as is the case with combinatorial auctions. This paper proposes an approach, based on best-response dynamics and tabu search, that avoids the requirement that we have a complete payoff matrix upfront, and instead computes the payoffs only as they become relevant to the search. The tabu features help break best-response cycles, and allow the algorithm to find pure strategy Nash equilibria in multiplayer games where best-response would typically fail. We test the algorithm on several classes of standard and random games, and present empirical results that show the algorithm performs well and gives the designer control over the tradeoffs between search time and completeness.