Common Beliefs and Public Announcements in Strategic Games with Arbitrary Strategy Sets

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dc.creatorApt, Krzysztof R.
dc.creatorZvesper, Jonathan A.
dc.date2007-10-18
dc.date2008-11-07
dc.date.accessioned2026-07-07T10:16:02Z
dc.date.available2026-07-07T10:16:02Z
dc.descriptionWe provide an epistemic analysis of arbitrary strategic games based on possibility correspondences. We first establish a generic result that links true common beliefs (and, respectively, common knowledge) of players' rationality defined by means of `monotonic' properties, with the iterated elimination of strategies that do not satisfy these properties. It allows us to deduce the customary results concerned with true common beliefs of rationality and iterated elimination of strictly dominated strategies as simple corollaries. This approach relies on Tarski's Fixpoint Theorem. We also provide an axiomatic presentation of this generic result. This allows us to clarify the proof-theoretic principles assumed in players' reasoning. Finally, we provide an alternative characterization of the iterated elimination of strategies based on the concept of a public announcement. It applies to `global properties'. Both classes of properties include the notions of rationalizability and the iterated elimination of strictly dominated strategies.
dc.description36 pages. Revised version
dc.identifierhttps://arxiv.org/abs/0710.3536
dc.identifierhttp://arxiv.org/abs/0710.3536
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173371
dc.subjectComputer Science and Game Theory
dc.titleCommon Beliefs and Public Announcements in Strategic Games with Arbitrary Strategy Sets
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