Epistemic Foundations of Game Theory

Foundational work in game theory aims at making explicit the assumptions that underlie the basic concepts of the discipline. Non-cooperative game theory is the study of individual, rational decision making in situations of strategic interaction. This entry presents the epistemic foundations of non-cooperative game theory (this area of research is called epistemic game theory). Epistemic game theory views rational decision making in games as something not essentially different from rational decision making under uncertainty. As in Decision Theory (Peterson, 2009), to choose rationally in a game is to select the “best” action in light of one’s beliefs or information. In a decision problem, the decision maker’s beliefs are about a passive state of nature, the state of which determines the consequences of her actions. In a game, the consequences of one’s decision depend on the choices of the other agents involved in the situation (and possibly the state of nature). Recognizing this—i.e., that one is interacting with other agents who try to choose the best course of action in the light of their own beliefs—brings higher-order information into the picture. The players’ beliefs are no longer about a passive or external environment. They concern the choices and the information of the other players. What one expects of one’s opponents depends on what one thinks the others expect from her, and what the others expect from a given player depends on what they think her expectations about them are. This entry provides an overview of the issues that arise when one takes this broadly decision-theoretic view on rational decision making in games. After some general comments about information in games, we present the formal tools developed in epistemic game theory and epistemic logic that have been used to understand the role of higher-order information in interactive decision making. We then show how these tools can be used to characterize known “solutions” of games in terms of rational decision making in specific informational contexts. Along the way, we highlight a number of philosophical issues that arise in this area.