A Language for Opponent Modeling in Repeated Games

Traditional game-theoretic formalisms, commonly used in multi-agent systems, invoke the assumption of common knowledge of rationality to justify a Nash equilibrium solution. It is assumed that all agents know a correct model of the game and are completely rational, and that this is common knowledge. However, real-life agents are partially irrational, they may use models other than the real world to make decisions, and they may be uncertain about their opponents’ decision making processes. For modeling boundedly-rational agents, a descriptive approach to game theory is needed, in which agents model their opponents and attempt to predict their behavior using their model. We present Networks of Influence Diagrams (NIDs), a language for descriptive decision and game theory that is based on graphical models. This paper describes NIDs and their syntax, and provides algorithms for solving NIDs and learning NID parameters. We also show that NIDs provide an elegant framework for opponent modeling that is more expressive than current approaches, leads to a better outcome than the Nash equilibrium strategy and is able to capture non-stationary distributions of opponents.