Incomplete information

Robert J. Aumann, Aviad Heifetz

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In interactive contexts such as games and economies, it is important to take account not only of what the players believe about substantive matters (such as payoffs), but also of what they believe about the beliefs of other players. Two different but equivalent ways of dealing with this matter, the semantic and the syntactic, are set forth. Canonical and universal semantic systems are then defined and constructed, and the concepts of common knowledge and common priors formulated and characterized. The last two sections discuss relations with Bayesian games of incomplete information and their applications, and with interactive epistemology - the theory of multi-agent knowledge and belief as formulated in mathematical logic.

Original languageEnglish
Title of host publicationHandbook of Game Theory with Economic Applications
EditorsRobert Aumann, Sergiu Hart
Number of pages22
StatePublished - 2002
Externally publishedYes

Publication series

NameHandbook of Game Theory with Economic Applications
ISSN (Print)1574-0005

Bibliographical note

Funding Information:
*Important input from Sergiu Hart, Martin Meier, and Dubi Samet is gratefully acknowledged. *Research partially supported under NSF grant SES-9730205.


  • common priors
  • incomplete or differential information
  • interactive epistemology
  • semantic belief systems
  • syntactic belief systems


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