Modal Logic and Game Theory

Abstract

In this paper, I demonstrate the fruitfulness of looking at modal logic from the perspective of game theory. In particular, I show how games in strategic form can be transformed into Kripke’s models for a multi-modal logic that combines the concepts of strategy profile, preference, and knowledge. The logic is sufficiently general to express solution concepts such as the best response, Nash Equilibrium, and Iterated Deletion of Strictly Dominated Strategies. Moreover, the logic allows us to derive the conditions on which these concepts are based.