Game-theoretic axioms for local rationality and bounded knowledge

Journal of Logic, Language and Information 4 (2):145-167 (1995)
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Abstract

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory

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Author Profiles

G. Aldo Antonelli
University of California, Davis
Cristina Bicchieri
University of Pennsylvania

References found in this work

Convention: A Philosophical Study.David Kellogg Lewis - 1969 - Cambridge, MA, USA: Wiley-Blackwell.
Modeling Rational Players: Part I.Ken Binmore - 1987 - Economics and Philosophy 3 (2):179-214.
The backward induction paradox.Philip Pettit & Robert Sugden - 1989 - Journal of Philosophy 86 (4):169-182.
Rationality and Coordination.Cristina Bicchieri - 1996 - British Journal for the Philosophy of Science 47 (4):627-629.
The Backward Induction Paradox.Philip Pettit & Robert Sugden - 1989 - Journal of Philosophy 86 (4):169-182.

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