On Nash-Equilibria of Approximation-Stable Games

Abstract. One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ǫ-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ǫapproximate equilibria are contained inside a small ball of radius ∆ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximationstable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ǫ, ∆) approximation-stable games must have an ǫ-equilibrium of support O(∆2−...

• Type: Journal
• Year: 2010
• Where: SAGT
• Authors: Pranjal Awasthi, Maria-Florina Balcan, Avrim Blum, Or Sheffet, Santosh Vempala
• Keywords: Game Theory, Nash Equilibrium, Nash Equilibrium Strategies, SAGT 2010, True Equilibrium