Knowing and Supposing in Games with Perfect Information

Abstract
The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a sufficient for them to play the backward induction solution in centipede games. To obtain this result, we do not need to assume that rationality is commonly known (as is done in [Aumann (1995)]) or commonly hypothesized by the players (as done in [Samet (1996)]). The proposed model is compared with the account of hypothetical knowledge presented by Samet in [Samet (1996)] and with other possible strategies for extending information structures with conditional propositions
Keywords Game Theory  Hypothetical Knowledge  Conditionals  Common Knowledge
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Cristina Bicchieri (1988). Backward Induction Without Common Knowledge. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:329 - 343.
Giacomo Bonanno (1992). Players' Information in Extensive Games. Mathematical Social Sciences 24 (1):35-48.
Philip J. Reny (1988). Common Knowledge and Games with Perfect Information. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:363 - 369.
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