Playing large games using simple strategies

We prove the existence of -Nash equilibrium strategies with support logarithmic in the number of pure strategies. We also show that the payoffs to all players in any (exact) Nash equilibrium can be -approximated by the payoffs to the players in some such logarithmic support -Nash equilibrium. These strategies are also uniform on a multiset of logarithmic size and therefore this leads to a quasi-polynomial algorithm for computing an -Nash equilibrium. To our knowledge this is the first subexponential algorithm for finding an -Nash equilibrium. Our results hold for any multiple-player game as long as the number of players is a constant (i.e., it is independent of the number of pure strategies). A similar argument also proves that for a fixed number of players m, the payoffs to all players in any m-tuple of mixed strategies can be -approximated by the payoffs in some m-tuple of constant support strategies. We also prove that if the payoff matrices of a two person game have low ra...

• Type: Conference
• Year: 2003
• Where: SIGECOM
• Authors: Richard J. Lipton, Evangelos Markakis, Aranyak Mehta
• Keywords: -Nash Equilibrium, Exact Nash Equilibrium, Payoff Matrices, SIGECOM 2003