The probability of nontrivial common knowledge
AbstractWe 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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Bibliographic InfoPaper provided by Department of Management, Università Ca' Foscari Venezia in its series Working Papers with number 6.
Length: 22 pages
Date of creation: Jul 2011
Date of revision: Mar 2012
Common knowledge; Epistemic game theory; Random partitions;
Other versions of this item:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-09 (All new papers)
- NEP-GTH-2011-08-09 (Game Theory)
- NEP-KNM-2011-08-09 (Knowledge Management & Knowledge Economy)
- NEP-MIC-2011-08-09 (Microeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- Marco LiCalzi & Oktay Surucu, 2011.
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206, Department of Applied Mathematics, Università Ca' Foscari Venezia, revised Sep 2011.
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"How Common Are Common Priors?,"
Discussion Paper Series
dp532, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Dimitri, Nicola, 1993. "Learning partitions," Economics Letters, Elsevier, vol. 42(2-3), pages 195-199.
- 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.
- 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.
- 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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