Multi-player Approximate Nash Equilibria

Artur Czumaj, Michail Fasoulakis, Marcin Jurdzinski

Abstract: In this paper we study the complexity of finding approximate Nash equilibria in multi-player normal-form games. First, for any constant number m, we present a polynomial-time algorithm for computing a relative (1 - 1(1+(m-1)m))-Nash equilibrium in arbitrary m-player games and a relative (1 - 1(1+(m-1)m))-Nash equilibrium in symmetric m-player games. Next, we show that there is an additive ε-well-supported Nash equilibrium, for any ε>0, with support equal to O(ln(m n/ε)/ε2), where n is the number of pure strategies. Finally, we prove that finding additive approximate Nash equilibria is easy in random multi-player games.