Satisfaction Equilibrium: Achieving Cooperation in Incomplete Information Games

Abstract

So far, most equilibrium concepts in game theory require that the rewards and actions of the other agents are known and/or observed by all agents. However, in real life problems, agents are generally faced with situations where they only have partial or no knowledge about their environment and the other agents evolving in it. In this context, all an agent can do is reasoning about its own payoffs and consequently, cannot rely on classical equilibria through deliberation, which requires full knowledge and observability of the other agents. To palliate to this difficulty, we introduce the satisfaction principle from which an equilibrium can arise as the result of the agents’ individual learning experiences. We define such an equilibrium and then we present different algorithms that can be used to reach it. Finally, we present experimental results that show that using learning strategies based on this specific equilibrium, agents will generally coordinate themselves on a Pareto-optimal joint strategy, that is not always a Nash equilibrium, even though each agent is individually rational, in the sense that they try to maximize their own satisfaction.

This research was supported in part by the Natural Science and Engineering Council of Canada (NSERC).