Epistemic Logic and the Foundations of Decision and Game Theory

This paper reviews a number of foundational results at the intersection of epistemic logic, decision and game theory. It first presents a decisiontheoretic underpinning of epistemic analysis in terms of modal operators. Then it moves to the theory of strategic interaction, and show how this kind of epistemic analysis sheds light on the assumptions underlying wellknown solution concepts, both for normal and extensive form games. Foundational work in decision and game theory aims at making explicit the assumptions that underlie the basic concepts in these disciplines. Decision theory and game theory are two sub-fields of micro-economics, concerned with the question of rational decision making by individual agents. Decision theory is the study of individual decision making under uncertainty, while game theory looks at situations of strategic interaction. Epistemic assumptions occupy a central place in the foundations of both decision theory and game theory. “Epistemic” is here understood in a broad sense, as encompassing a whole array of informational attitudes: beliefs, knowledge, assumptions, acceptances, and so on. Foundational work asks, on the one hand, about the conditions under which one can assume that the attitudes of the decision maker satisfy certain constraints and, on the other hand, what kind of assumptions about the content of such attitudes lead to certain patterns of (rational) behaviour. Epistemic and dynamic epistemic logic have become important qualitative tools in this foundational endeavour. One uses both the semantics and the syntax of these modal system to formalize some aspects of the informational attitudes under examination, as well as to study the interplay between information, preferences and decisions. ∗I am grateful to Richard Bradley, Boudewijn de Bruin, Martin van Hees, Jan-Willem van de Rijt, Peter Timmerman, Lieuwe Zijlstra, Giacomo Bonanno and the anonymous referee of the IJCPR for helpful comments and suggestions. Parts of Section 2.2 stem from joint work with Eric Pacuit (Tilburg University), to whom I am very grateful as well.