Information Independence and Common Knowledge

Olivier Gossner, Ehud Kalai and Robert Weber

No 1476, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

Abstract: In Bayesian environments with private information, as described by the types of Harsanyi, how can types of agents be (statistically) disassociated from each other and how are such disassociations reflected in the agents’ knowledge structure? Conditions studied are (i) subjective independence (the opponents’ types are independent conditional on one’s own) and (ii) type disassociation under common knowledge (the agents’ types are independent, conditional on some common-knowledge variable). Subjective independence is motivated by its implications in Bayesian games and in studies of equilibrium concepts. We find that a variable that disassociates types is more informative than any common-knowledge variable. With three or more agents, conditions (i) and (ii) are equivalent. They also imply that any variable which is common knowledge to two agents is common knowledge to all, and imply the existence of a unique common-knowledge variable that disassociates types, which is the one defined by Aumann.

Keywords: Bayesian games; independent types; common knowledge. (search for similar items in EconPapers)
JEL-codes: C70 D80 D82 (search for similar items in EconPapers)
Date: 2009-07
New Economics Papers: this item is included in nep-cba, nep-cta, nep-gth and nep-knm
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Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Information Independence and Common Knowledge (2009)
Working Paper: Information Independence and Common Knowledge (2009)
Working Paper: Information Independence and Common Knowledge (2009)
Working Paper: Information Independence and Common Knowledge (2007)
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