The probability of nontrivial common knowledge
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.
|Date of creation:||Jul 2011|
|Date of revision:||Mar 2012|
|Contact details of provider:|| Postal: |
Phone: +39 0412348721
Fax: +39 0412348701
Web page: http://www.unive.it/dip.management
More information through EDIRC
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.:
- Ziv Hellman & Dov Samet, 2010.
"How Common Are Common Priors?,"
Discussion Paper Series
dp532, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- 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 & Oktay Surucu, 2011.
"The power of diversity over large solution spaces,"
206, Department of Applied Mathematics, Università Ca' Foscari Venezia, revised Sep 2011.
- 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.
- John Geanakoplos, 1992. "Common Knowledge," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 53-82, Fall.
- Dimitri, Nicola, 1993. "Learning partitions," Economics Letters, Elsevier, vol. 42(2-3), pages 195-199.
When requesting a correction, please mention this item's handle: RePEc:vnm:wpdman:6. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marco LiCalzi)
If references are entirely missing, you can add them using this form.