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Summary: Studia Logica (2007) 86: 353373
DOI: 10.1007/s11225-007-9065-6 © Springer 2007
Horacio Arl´o-Costa
Cristina Bicchieri
Knowing and Supposing in
Games of Perfect
Information
Abstract. The paper provides a framework for representing belief-contravening hy-
potheses 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.1
Keywords: Game Theory, Hypothetical Knowledge, Conditionals, Common Knowledge.
1. Introduction: Extending Information Structures
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