Modal logic and game theory: two alternative approaches

Two views of game theory are discussed: (1) game theory as a description of the behavior of rational individuals who recognize each other’s reationality and reasoning abilities, and (2) game theory as an internally consistent recommendation to individuals on how to act in interactive situations. It is shown that the same mathematical tool, namely modal logic, can be used to explicitly model both views. Game theory can be thought of as being composed of two separate modules. The first module consists of a formal language for the description of interactive situations, that is, situations where several individuals take actions that affect each other. This language provides alternative descriptions, from the more detailed one of extensive forms to the more condensed notions of strategic form and coalitional form. The language of game theory has proved to be useful in such diverse fields as economics, political science, military science, evolutionary biology, computer science, mathematical logic, experimental psychology, sociology and social philosophy. The unifying role of the game-theoretic language has been a major achievement in itself. The second module is represented by the collection of solution concepts. Each solution concept associates with every game in a given class an outcome or set of outcomes. Most of the debate in game theory has centered on this module, in particular on the rationale for, and interpretation of, various solution concepts. From a broader point of view, the issue of debate is what the role and aims of game theory are (or should be). In this respect one can distinguish at least four different views of game theory: 1. Game theory as a description of how rational individuals behave: Briefly put, game and economic theory are concerned with the interactive behavior of Homo rationalis ‐ rational man. Homo rationalis is the species that always acts both purposefully and logically, has well-defined goals, is motivated solely by the desire to approach these goals as closely as possible, and has the calculating ability required to do so. (Aumann, 1985, p. 35)