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Interactive and common knowledge in the state-space model

  • Moscati Ivan

    ()

This paper deals with the prevailing formal model for knowledge in contemporary economics, namely the state-space model introduced by Robert Aumann in 1976. In particular, the paper addresses the following question arising in this formalism: in order to state that an event is interactively or commonly known among a group of agents, do we need to assume that each of them knows how the information is imparted to the others? Aumann answered in the negative, but his arguments apply only to canonical, i.e., completely specified state spaces, while in most applications the state space is not canonical. This paper addresses the same question along original lines, demonstrating that the answer is negative for both canonical and not-canonical state spaces. Further, it shows that this result ensues from two counterintuitive properties held by knowledge in the state-space model, namely Substitutivity and Monotonicity.

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File URL: http://www.cesmep.unito.it/WP/2009/3_WP_Cesmep.pdf
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Paper provided by University of Turin in its series CESMEP Working Papers with number 200903.

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Length: 23 pages
Date of creation: Mar 2009
Date of revision:
Handle: RePEc:uto:cesmep:200903
Contact details of provider: Web page: http://www.unito.it/
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  12. Aumann, Robert J. & Heifetz, Aviad, 2001. "Incomplete Information," Working Papers 1124, California Institute of Technology, Division of the Humanities and Social Sciences.
  13. John Geanakoplos & (**), Moshe Y. Vardi & Joseph Y. Halpern & Ronald Fagin, 1999. "The hierarchical approach to modeling knowledge and common knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 331-365.
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