The probability of nontrivial common knowledge

Andrea Collevecchio and Marco LiCalzi

Games and Economic Behavior, 2012, vol. 76, issue 2, 556-570

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.

Keywords: Epistemic game theory; Random partitions; Meet of partitions (search for similar items in EconPapers)
JEL-codes: C72 D83 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:76:y:2012:i:2:p:556-570

DOI: 10.1016/j.geb.2012.07.014

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