A Language for Descriptive Decision and Game Theory

In descriptive decision and game theory, one specifies a model of a situation faced by agents and uses the model to predict or explain their behavior. We present Influence Diagram Networks, a language for descriptive decision and game theory that is based on graphical models. Our language relaxes the assumption traditionally used in economics that beliefs of agents are consistent, i.e. conditioned on a common prior distribution. In the single-agent case one can model situations in which the agent has an incorrect model of the way the world works, or in which a modeler has uncertainty about the agent's model. In the multi-agent case, one can 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.Engineering and Applied Science