On Learning Algorithms for Nash Equilibria

Can learning algorithms find a Nash equilibrium? This is a natural question for several reasons. Learning algorithms resemble the behavior of players in many naturally arising games, and thus results on the convergence or nonconvergence properties of such dynamics may inform our understanding of the applicability of Nash equilibria as a plausible solution concept in some settings. A second reason for asking this question is in the hope of being able to prove an impossibility result, not dependent on complexity assumptions, for computing Nash equilibria via a restricted class of reasonable algorithms. In this work, we begin to answer this question by considering the dynamics of the standard multiplicative weights update learning algorithms (which are known to converge to a Nash equilibrium for zero-sum games). We revisit a 3×3 game defined by Shapley [10] in the 1950s in order to establish that fictitious play does not converge in general games. For this simple game, we show via a p...

• Type: Journal
• Year: 2010
• Where: SAGT
• Authors: Constantinos Daskalakis, Rafael Frongillo, Christos H. Papadimitriou, George Pierrakos, Gregory Valiant
• Keywords: Algorithm, Game Theory, Nash Equilibria, Nash Equilibrium, SAGT 2010