Abstract. In view of the intractability of finding a Nash equilibrium, it is important to understand the limits of approximation in this context. A subexponential approximation scheme is known [LMM03], and no approximation better than is possible by any algorithm that examines equilibria involving fewer than log n strategies [Alt94]. We give a simple, linear-time algorithm examining just two strategies per player and resulting in a 1 2 -approximate Nash equilibrium in any 2-player game. For the more demanding notion of well-supported approximate equilibrium due to [DGP06] no nontrivial bound is known; we show that the problem can be reduced to the case of win-lose games (games with all utilities 0 − 1), and that an approximation of is possible contingent upon a graph-theoretic conjecture.
As for polynomial time algorithms, it is fairly simple to obtain a 3 4 -approximation and even better a 1 2 -approximation REF .
A note on approximate Nash equilibria
IN WINE ’06
Mathematics Computer Science