reaching correlated equilibria through multi-agent learning
Many games have undesirable Nash equilibria. For example consider a resource allocation game in which two players compete for an exclusive access to a single resource. It has three Nash equilibria. The two pure-strategy NE are efficient, but not fair. The one mixed-strategy NE is fair, but not efficient. Aumann's notion of correlated equilibrium fixes this problem: It assumes a correlation device which suggests each agent an action to take. However, such a "smart" coordination device might not be available. We propose using a randomly chosen, "stupid" integer coordination signal. "Smart" agents learn which action they should use for each value of the coordination signal. We present a multi-agent learning algorithm which converges in polynomial number of steps to a correlated equilibrium of a wireless channel allocation game, a variant of the resource allocation game. We show that the agents learn to play for each coordination signal value a randomly chosen pure-strategy Nash equilibrium of the game. Therefore, the outcome is an efficient correlated equilibrium. This CE becomes more fair as the number of the available coordination signal values increases. We believe that a similar approach can be used to reach efficient and fair correlated equilibria in a wider set of games, such as potential games.
coordination multiagent learning game theory