To achieve an optimal outcome in many situations, agents need to choose distinct actions from one another. This is the case notably in many resource allocation problems, where a single resource can only be used by one agent at a time. How shall a designer of a multi-agent system program its identical agents to behave each in a different way?
From a game theoretic perspective, such situations lead to undesirable Nash equilibria. For example consider a resource allocation game in that 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 that 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 that converges in polynomial number of steps to a correlated equilibrium of a 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.