Information independence and common knowledge

Olivier Gossner*, Ehud Kalai, Robert Weber

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1317-1328
Number of pages12
JournalEconometrica
Volume77
Issue number4
DOIs
StatePublished - Jul 2009

Keywords

  • Bayesian games
  • Common knowledge
  • Independent types

ASJC Scopus subject areas

  • Economics and Econometrics

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