The epistemic structure of a theory of a game
 Michael Bacharach
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
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.
 Aumann, R.: 1987, ‘Correlated Equilibrium as an Expression of Bayesian Rationality’,Econometrica 55, 1–18.
 Ayer, A.J.: 1956,Problem of Knowledge, Macmillan, London.
 Bacharach, M.O.L.: 1987, ‘A Theory of Rational Decision in Games’,Erkenntnis 27, 17–55.
 Bacharach, M.O.L.: 1992, ‘Backward Induction and Beliefs about Oneself’,Synthese 91, 247–84.
 Bacharach, M.O.L.: in press, ‘When Do We Have Information Partitons?’, in Dempster, M.A.H., Bacharach, M.O.L., and Enos, J.L. (eds.),Mathematical Models in Economics, Oxford University Press, Oxford.
 Bacharach, M.O.L., Shin, H.S., and Williams, M.E.: 1992, ‘Sophisticated Bounded Agents Play the Repeated Dilemma’, Institute of Economics and Statistics, Oxford Discussion Paper No. 143, University of Oxford.
 Binmore, K.: 1987a, ‘Modelling Rational Players I’,Economics and Philosophy 3, 179–214.
 Binmore, K.: 1987b, ‘Modelling Rational Players II’,Economics and Philosophy 4, 9–55.
 Binmore, K. and Brandenburger, A.: 1990, ‘Common Knowledge and Game Theory’, in Binmore, K. (ed.),Essays on the Foundations of Game Theory, Basil Blackwell, Oxford.
 Canning, D.: 1988, ‘Rationality and Game Theory when Players Are Turing Machines’, I.C.E.R.D. Discussion Paper 88/183, London School of Economics.
 Chellas, B.F.: 1980,Modal Logic: An Introduction, Cambridge University Press, Cambridge.
 Evans, G. and McDowell, J.: 1976, Introduction to Evans, G. and McDowell, J. (eds.),Truth and Meaning, Clarendon Press, Oxford.
 Fagin, R. and Halpern, J.: 1988, ‘Belief, Awareness, and Limited Reasoning’,Artificial Intelligence 34, 39–76.
 Fagin, R, Halpern, J. Y., Moses, Y., and Vardi, M.Y.: 1993,Reasoning about Knowledge, M.I.T. Press, Cambridge, Mass.
 Farrell, J.: (in press), ‘Meaning and Credibility in CheapTalk Games’ in Dempster, M.A.H., Bacharach, M.O.L., and Enos, J.L. (eds.),Mathematical Models in Economics, Oxford University Press, Oxford.
 Gärdenfors, P.: 1988,Knowledge in Flux, M.I.T. Press, Cambridge, Mass.
 Geffner, E.: 1992,Default Reasoning: Causal and Conditional Theories, M.I.T. Press, Cambridge, Mass.
 Gillet, E. and Gochet, P.: 1992, ‘La Logique de la Connaissance: Le Problème de l'Omniscience Logique’,Dialectica 47, 143–171.
 Hintikka, J.: 1962,Knowledge and Belief: An Introduction to the Logic of the Two Notions, Cornell University Press, Ithaca, N.Y.
 Hintikka, J.: 1975, ‘Impossible Worlds Vindicated’,Journal of Philosophy 72, 475–484.
 Hughes, G.E. and Cresswell, M.J.: 1968,An Introduction to Modal Logic, Methuen, London.
 Kaneko, M. and Nagashima, T.: 1990, ‘Game Logic I: Players' Deductions and the Common Knowledge of Deductive Abilities’, Working Paper E90031, Virginia Polytechnic Institute and Tate University.
 Konolige, K.: 1988, ‘On the Relation between Default and Autoepistemic Logic’,Artificial Intelligence 35, 343–82.
 Lakemayer, G. and Levesque, H.J.: 1988, ‘A Tractable Knowledge Representation Service with Full Introspection’, in M. Vardi (ed.),proceedings of the 2nd Conference on TARK, Morgan Kaufman, San Mateo, Calif.
 Levesque, H.J.: 1984, ‘A Logic of Explicit and Implicit Belief’,Proceedings of the National Conference on AI, Austin, Texas.
 Lewis, D.K.: 1976, ‘Probabilities of Conditionals and Conditional Probabilities’,Philosophical Review 85, 297–315.
 Lismont, L. and Mongin, P.: 1994, ‘On the Logic of Common Belief and Common Knowledge’,Theory and Decision,37, 75–106 (this issue).
 Makinson, D.: in press, ‘General Patterns in Nonmonotonic Reasoning’, in D. Gabbay and C. Hogger (eds.),Handbook of Logic for Artificial Intelligence and Logic Programming, II: Monotonic and Uncertain Reasoning, Oxford University Press, Oxford.
 Modica, S. and Rustichini, A.: 1994, ‘Awareness and Partitional Information Structures’,Theory and Decision,37, 107–124 (this issue).
 Mongin, P.: in press, ‘Some Connections between Epistemic Logic and the Theory of Nonadditive Probability’; in P. Humphreys (ed.),Patrick Suppes, Scientific Philosopher, Kluwer, Dordrecht.
 Moore, R.C.: 1985, ‘Semantical Considerations of Nonmonotonic Logic’,Artificial Intelligence 25, 75–94.
 Pearce, D.: 1984, ‘Rationalizable Strategic Behavior and the Problem of Perfection’,Econometrica 52, 1029–50.
 Pettit, P. and Sugden, R.: 1989, ‘The Backwards Induction Paradox’,Journal of Philosophy 86, 169–82.
 Reiter, R.: 1980, ‘A Logic for Default Reasoning’,Artificial Intelligence 13, 81–132.
 Rantala, V.: 1982, ‘Impossible Worlds Semantics and Logical Omniscience’,Acta Philosophica Fennica 35, 106–15.
 Samuelson, L.: 1992, ‘Dominated Strategies and Common Knowledge’,Games and Economic Behavior 4, 284–313.
 Sorensen, R.A.: 1988,Blindspots, Clarendon Press, Oxford.
 Stalnaker, R.: 1994, ‘On the Evaluation of Solution Concepts’,Theory and Decision,37, 49–73 (this issue).
 Sugden, R.: 1993, ‘A Theory of Focal Points’, School of Economic and Social Studies, University of East Anglia.
 Tan, T. and Werlang, S.: 1988, ‘The Bayesian Foundations of Solution Concepts of Games’,J. Econ. Theory 45, 370–91.
 Von Neumann, J. and Morgenstern, O.: 1944,Theory of Games and Economic Behavior, Princeton University Press, Princeton, N.J.
 Williamson, T.: 1992, ‘Inexact Knowledge’,Mind 101, 217–42.
 Title
 The epistemic structure of a theory of a game
 Journal

Theory and Decision
Volume 37, Issue 1 , pp 748
 Cover Date
 19940701
 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