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Common Knowledge and Games with Perfect Information

Published online by Cambridge University Press:  28 February 2022

Philip J. Reny
Philip J. Reny*
Affiliation:
The University of Western Ontario
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Extract

It is by now rather well understood that the notion of common knowledge (first introduced by Lewis (1969) and later formalized by Aumann (1976)) plays a central role in the theory of games. (An event E is common knowledge between two individuals, if each knows E, each knows the other knows E, etc…). Indeed, most justifications of Nash's (1951) equilibrium concept usually include (perhaps only implicitly) the assumption that it is common knowledge among the players that both the Nash equilibrium in question will be played by all and that all players are expected utility maximizers. (We shall henceforth call expected utility maximizers, “rational”.) We hope to illustrate in an informal manner that there is in fact a large class of extensive form games, in which each of which it is not possible for rationality to be common knowledge throughout the game.

Type
Part XI. Decision and Game Theory
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1988 , Issue 2: Volume Two: Symposia and Invited Papers 1988 , 1988 , pp. 363 - 369
Copyright
Copyright © 1989 by the Philosophy of Science Association

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