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The probability of nontrivial common knowledge

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Author Info

  • Collevecchio, Andrea
  • LiCalzi, Marco

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 consistent with his cognitive capacity. Assuming that agentsʼ partitions are independently 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. Our proofs rely on a graph-theoretic characterization of common knowledge that has independent interest.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 76 (2012)
Issue (Month): 2 ()
Pages: 556-570

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Handle: RePEc:eee:gamebe:v:76:y:2012:i:2:p:556-570

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Epistemic game theory; Random partitions; Meet of partitions;

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References

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  1. 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.
  2. Marco LiCalzi & Oktay Surucu, 2012. "The Power of Diversity over Large Solution Spaces," Management Science, INFORMS, vol. 58(7), pages 1408-1421, July.
  3. Ziv Hellman & Dov Samet, 2010. "How Common Are Common Priors?," Discussion Paper Series dp532, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  4. John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
  5. Dimitri, Nicola, 1993. "Learning partitions," Economics Letters, 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, 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 4, Department of Management, Università Ca' Foscari Venezia.

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