Nash convergence of gradient dynamics in general-sum games

Abstract

Multi-agent games are becoming an increasingly prevalent formalism for the study of electronic commerce and auctions. The speed at which transactions can take place and the growing complexity of electronic marketplaces makes the study of computationally simple agents an appealing direction. In this work, we analyze the behavior of agents that incrementally adapt their strategy through gradient ascent on expected payoff, in the simple setting of two-player, two-action, iterated general-sum games, and present a surprising result. We show that either the agents will converge to a Nash equilibrium, or if the strategies themselves do not converge, then their average payoffs will nevertheless converge to the payoffs of a Nash equilibrium. 1 Introduction It is widely expected that in the near future, software agents will act on behalf of humans in many electronic marketplaces based on auctions, barter, and other forms of trading. This makes multi-agent game theory (Owen, 199...