Logic and Game Theory

Abstract

Johan van Benthem has highlighted in his work that many questions arising in the analysis of strategic interaction call for logical and computational analysis. These questions lead to both formal and conceptually illuminating answers, in that they contribute to clarifying some of the underlying assumptions behind certain aspects of game-theoretical reasoning. We focus on the insights of a part of the literature at the interface of game theory and mathematical logic that gravitates around van Benthem’s work. We discuss the formal questions raised by the perspective consisting in taking games as models for formal languages, in particular modal languages, and how eliminative reasoning processes and solution algorithms can be analyzed logically as epistemic dynamics, and discuss the role played by beliefs in game-theoretical analysis and how they should be modeled from a logical point of view. We give many pointers to the literature throughout the chapter.