A Language for Modeling Agents' Decision Making Processes in Games

Multi-agent systems that use game-theoretic analysis for decision making traditionally take a normative approach, in which agents' decisions are derived rationally from the game description. This approach is insufficient to capture the decision making processes of real-life agents. Such agents may be 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. We present Networks of Influence Diagrams (NIDs), a language for descriptive decision and game theory that is based on graphical models. NIDs provide a framework for computing optimal decisions for agents that operate in an environment characterized by uncertainty, not only over states of knowledge but also over game mechanics and others' decision processes. NIDs allow the modeling of situations in which an agent has an incorrect model of the way the world works, or in which a modeler has uncertainty about the agent's model. One can also recursively model agents' uncertain beliefs about other agents' decision-making models. We present an algorithm that computes the actions of agents under the assumption that they are rational with respect to their own model, but not necessarily with respect to the real world. Applications of our language include determining the cost to an agent of using an incorrect model, opponent modeling in games, and modeling bounded rationality.