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

We provide an epistemic analysis of arbitrary strategic games based on possibility correspondences. Such an analysis calls for the use of transfinite iterations of the corresponding operators. In the case of common beliefs and common knowledge our approach is based on Tarski’s Fixpoint Theorem and applies to ‘monotonic’ properties. In the case of an analysis based on the notion of a public announcement our approach applies to ‘global properties’. Both classes of properties include the notions of rationalizability and the iterated elimination of strictly dominated strategies. We also provide an axiomatic presentation of the main results concerning common beliefs and monotonic properties.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Krzysztof R. Apt, Jonathan A. Zvesper
• Keywords: Arbitrary Strategic Games, Common Beliefs, CORR 2007, Education, Tarski’s Fixpoint Theorem