Studia Logica 57 (2-3):325 - 354 (1996)
AbstractThis paper provides a logic framework for investigations of game theoretical problems. We adopt an infinitary extension of classical predicate logic as the base logic of the framework. The reason for an infinitary extension is to express the common knowledge concept explicitly. Depending upon the choice of axioms on the knowledge operators, there is a hierarchy of logics. The limit case is an infinitary predicate extension of modal propositional logic KD4, and is of special interest in applications. In Part I, we develop the basic framework, and show some applications: an epistemic axiomatization of Nash equilibrium and formal undecidability on the playability of a game. To show the formal undecidability, we use a term existence theorem, which will be proved in Part II.
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Citations of this work
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References found in this work
Knowledge and Belief: An Introduction to the Logic of the Two Notions.Jaakko Hintikka - 1962 - Ithaca: Cornell University Press.
Theory of Games and Economic Behavior.John Von Neumann & Oskar Morgenstern - 1944 - Princeton, NJ, USA: Princeton University Press.
Knowledge and Belief: An Introduction to the Logic of the Two Notions.Jaakko Hintikka - 1962 - Studia Logica 16:119-122.
Theory of Games and Economic Behavior.John von Neumann & Oskar Morgenstern - 1944 - Science and Society 9 (4):366-369.