# The probability of nontrivial common knowledge

*Andrea Collevecchio* and
*Marco LiCalzi* ()

No 6, Working Papers from 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.

**Keywords:** Common knowledge; Epistemic game theory; Random partitions (search for similar items in EconPapers)

**JEL-codes:** C72 D83 (search for similar items in EconPapers)

**New Economics Papers:** this item is included in nep-gth, nep-knm and nep-mic

**Date:** 2011-07, Revised 2012-03

**References:** View references in EconPapers View complete reference list from CitEc

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http://virgo.unive.it/wpideas/storage/2011wp6.pdf Revised version, 2012 (application/pdf)

**Related works:**

Journal Article: The probability of nontrivial common knowledge (2012)

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**Persistent link:** http://EconPapers.repec.org/RePEc:vnm:wpdman:6

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