The probability of nontrivial common knowledge☆
Highlights
► We study the probability that two or more agents attain nontrivial common knowledge. ► Each agent has a random knowledge partition consistent with his cognitive capacity. ► When the size of the state space grows, nontrivial common knowledge undergoes a phase transition. ► Our proofs rely on a novel graph-theoretic characterization of common knowledge.
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We acknowledge insightful comments from the referees, and useful feedback from audiences at Paris-Sorbonne, UECE Lisbon 2011, and Amases 2011. We thank Lucia Milone for graciously sharing one of her amazingly fast computer codes.
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