Game Theoretic Learning

We consider a networked multiagent system in which the objective of each decision-making agent depends on the actions of other agents in the network as well as on an objective relevant state of the environment. Game theory and game-theoretic solution concepts provide rational models of individual behavior in such systems. The general problem we address in this chapter is the design of out-of-equilibrium (bounded-rational) decision-making and information exchange rules that allow players to learn about both the objective relevant state of the environment and the behavior of other players in the network, and eventually act individually rational. After a brief overview of game theory and learning in games setup, we first introduce the network-based fictitious play algorithm for the complete information game setting where players know the state of the environment and try to learn the behavior of other players. Convergence properties of the algorithm are presented. We then consider the incomplete information setting in which players have differing information about the state of the environment. In this setting, we introduce a Bayesian learning model, and discuss its convergence and computational properties. The high computational demand of Bayesian learning motivates us to present a network-based fictitious play algorithm that is tailored for incomplete information games.