JULIUS SENSAT GAME THEORY AND RATIONAL DECISION ∗ ABSTRACT. In its classical conception, game theory aspires to be a determinate decision theory for games, understood as elements of a structurally specified domain. Its aim is to determine for each game in the domain a complete solution to each player’s decision problem, a solution valid for all real-world instantiations, regardless of context. “Permis- siveness” would constrain the theory to designate as admissible for a player any conjecture consistent with the function’s designation of admissible strategies for the other players. Given permissiveness and other appropriate constraints, solution sets must contain only Nash equilibria and at least one pure-strategy equilibrium, and there is no solution to games in which no symmetry invariant set of pure-strategy equilibria forms a Cartesian product. These results imply that the classical program is unrealizable. Moreover, the program is implicitly committed to permissiveness, through its common-knowledge assumptions and its commitment to equilibrium. The resulting incoherence deeply undermines the classical conception in a way that consolidates a long series of contextualist criticisms. 1. INTRODUCTION In the classical conception of game theory, a game is an element in a structurally defined domain of multi-agent decision situations, and game theory is its decision theory. The theory aims at a complete solution for each game in the domain: for each player, a set of alternative actions each of which would count as a fully rational strategy, given his concern to promote his outcome values. Were this ideal to be achieved, then in any real-world instantiation of the game, regardless of the circumstances not reflected in the game’s structure, a player could rationally choose any of his specified solution strategies. Though game theory is currently thriving in its applications and in- terdisciplinary forays, this founding conception is problematic. Serious conceptual and intuitive difficulties began accumulating as early as the seminal contributions of von Neumann and Morgenstern (1953 [1944]) and Nash (1951), and there have been forceful systematic critiques (e.g. Schelling (1960), Aumann (1974) and Spohn (1982)). Nonetheless, there are still strong proponents (e.g. Harsanyi and Selten (1988)), and matters remain unresolved. Erkenntnis 47: 379–410, 1998. © 1998 Kluwer Academic Publishers. Printed in the Netherlands.