Knowing and Supposing in Games of Perfect Information
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 cond...
| Veröffentlicht in: | Studia Logica: An International Journal for Symbolic Logic. - Springer, 1953. - 86(2007), 3, Seite 353-373 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2007
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| Zugriff auf das übergeordnete Werk: | Studia Logica: An International Journal for Symbolic Logic |
| Schlagworte: | Game Theory Hypothetical Knowledge Conditionals Common Knowledge Mathematics Philosophy Behavioral sciences |
| Zusammenfassung: | 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. |
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| ISSN: | 15728730 |