Optimal Efficient Learning Equilibrium: Imperfect monitoring in symmetric games

Efficient Learning Equilibrium (ELE) is a natural solution concept for multi-agent encounters with incomplete information. It requires the learning algorithms themselves to be in equilibrium for any game selected from a set of (initially unknown) games. In an optimal ELE, the learning algorithms would efficiently obtain the surplus the agents would obtain in an optimal Nash equilibrium of the initially unknown game which is played. The crucial part is that in an ELE deviations from the learning algorithms would become non-beneficial after polynomial time, although the game played is initially unknown. While appealing conceptually, the main challenge for establishing learning algorithms based on this concept is to isolate general classes of games where an ELE exists. Unfortunately, it has been shown that while an ELE exists for the setting in which each agent can observe all other agents' actions and payoffs, an ELE does not exist in general when the other agents' payoffs cannot be observed. In this paper we provide the first positive results on this problem, constructively proving the existence of an optimal ELE for the class of symmetric games where an agent can not observe other agents' payoffs.