THE EPISTEMIC STRUCTURE OF A THEORY OF A GAME

This paper is a contribution to the systematic study of alternative axiom-sets for theories of (normal-form, complete-information) games. It provides an introduction to epistemic logic, describes a formulation in epistemic logic of the structure of a theory of a game (the 'broad theory' of that game), and applies methods of epistemic logic to define strategies for dealing with two disturbing features of game theory, its hyperrationality assumptions and its indeterminacy. The analysis of these problems is conducted in terms of two principles which impregnate much game theory, Cleverness and Cloisteredness (the principles that players know respectively all, and only, the logical consequences of their assumed knowledge). Broad theories allow us to formulate and revise these principles despite their metatheoretical character. It is shown how Cleverness may be weakened by using logics which restrict the Rule of Epistemization, and Cloisteredness by using default logic or autoepistemic logic; the latter is used to characterize Nash equilibrium beliefs as parts of certain autoepistemic extensions of players' knowledge bases, but these particular extensions are rejected as ungrounded.