The epistemic structure of a theory of a game
 Michael Bacharach
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This paper is a contribution to the systematic study of alternative axiomsets for theories of (normalform, completeinformation) 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.
 Title
 The epistemic structure of a theory of a game
 Journal

Theory and Decision
Volume 37, Issue 1 , pp 748
 Cover Date
 199407
 DOI
 10.1007/BF01079204
 Print ISSN
 00405833
 Online ISSN
 15737187
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 epistemic logic
 game theory
 formal theory of rational play
 logical omniscience
 impossible world
 default
 autoepistemic logic
 groundedness
 Industry Sectors
 Authors

 Michael Bacharach ^{(1)}
 Author Affiliations

 1. Institute of Economics and Statistics, St. Cross Building, Manor Road, OX1 3UL, Oxford, UK