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The probability of nontrivial common knowledge

Author

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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.

Suggested Citation

  • Andrea Collevecchio & Marco LiCalzi, 2011. "The probability of nontrivial common knowledge," Working Papers 6, Venice School of Management - Department of Management, Università Ca' Foscari Venezia, revised Mar 2012.
    • Handle: RePEc:vnm:wpdman:6
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    References listed on IDEAS

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    1. Rinott, Yosef & Scarsini, Marco, 2000. "On the Number of Pure Strategy Nash Equilibria in Random Games," Games and Economic Behavior, Elsevier, vol. 33(2), pages 274-293, November.
    2. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    3. Hellman, Ziv & Samet, Dov, 2012. "How common are common priors?," Games and Economic Behavior, Elsevier, vol. 74(2), pages 517-525.
    4. Geanakoplos, John, 1994. "Common knowledge," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 40, pages 1437-1496, Elsevier.
    5. Marco LiCalzi & Oktay Surucu, 2012. "The Power of Diversity over Large Solution Spaces," Management Science, INFORMS, vol. 58(7), pages 1408-1421, July.
    6. Dimitri, Nicola, 1993. "Learning partitions," Economics Letters, Elsevier, vol. 42(2-3), pages 195-199.
    7. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
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    Cited by:

    1. Marco LiCalzi & Oktay Surucu, 2012. "The Power of Diversity over Large Solution Spaces," Management Science, INFORMS, vol. 58(7), pages 1408-1421, July.
    2. Marco LiCalzi & Lucia Milone, 2012. "Talent management in triadic organizational architectures," Lecture Notes in Economics and Mathematical Systems, in: Andrea Teglio & Simone Alfarano & Eva Camacho-Cuena & Miguel Ginés-Vilar (ed.), Managing Market Complexity, edition 127, chapter 0, pages 169-181, Springer.

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    More about this item

    Keywords

    Common knowledge; Epistemic game theory; Random partitions;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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