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The probability of nontrivial common knowledge

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  • Andrea Collevecchio

    ()
    (Department of Management, Università Ca' Foscari Venezia)

  • Marco LiCalzi

    ()
    (Department of Management, Università Ca' Foscari Venezia)

Abstract

We study the probability that two or more agents can attain common knowledge of nontrivial events when the size of the state space grows large. We adopt the standard epistemic model where the knowledge of an agent is represented by a partition of the state space. Each agent is endowed with a partition generated by a random scheme. Assuming that agents' partitions are independently and identically distributed, we prove that the asymptotic probability of nontrivial common knowledge undergoes a phase transition. Regardless of the number of agents, when their cognitive capacity is sufficiently large, the probability goes to one; and when it is small, it goes to zero.

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File URL: http://virgo.unive.it/wpideas/storage/2011wp6.pdf
File Function: Revised version, 2012
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Bibliographic Info

Paper provided by Department of Management, Università Ca' Foscari Venezia in its series Working Papers with number 6.

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Length: 22 pages
Date of creation: Jul 2011
Date of revision: Mar 2012
Handle: RePEc:vnm:wpdman:6

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Web page: http://www.unive.it/dip.management
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Keywords: Common knowledge; Epistemic game theory; Random partitions;

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  1. Geanakoplos, John, 1994. "Common knowledge," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 40, pages 1437-1496 Elsevier.
  2. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, American Economic Association, vol. 6(4), pages 53-82, Fall.
  3. Marco LiCalzi & Oktay Surucu, 2011. "The power of diversity over large solution spaces," Working Papers, Department of Management, Università Ca' Foscari Venezia 1, Department of Management, Università Ca' Foscari Venezia, revised Sep 2011.
  4. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, Elsevier, vol. 74(2), pages 517-525.
  5. Dimitri, Nicola, 1993. "Learning partitions," Economics Letters, Elsevier, Elsevier, vol. 42(2-3), pages 195-199.
  6. Rinott, Yosef & Scarsini, Marco, 2000. "On the Number of Pure Strategy Nash Equilibria in Random Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 33(2), pages 274-293, November.
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Cited by:
  1. Marco LiCalzi & Lucia Milone, 2012. "Talent management in triadic organizational architectures," Working Papers, Department of Management, Università Ca' Foscari Venezia 4, Department of Management, Università Ca' Foscari Venezia.

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