TY - JOUR

T1 - Common knowledge with probability 1

AU - Brandenburger, Adam

AU - Dekel, Eddie

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1987

Y1 - 1987

N2 - Two people, 1 and 2, are said to have common knowledge of an event if both know it, 1 knows that 2 knows it, 2 knows that 1 knows it, 1 knows that 2 knows that 1 knows it, and so on. This paper provides a Bayesian definition of common knowledge, that is, a definition in terms of beliefs (probability measures). The main result is an equivalence between this definition and a definition in terms of the σ-fields representing 1 and 2's information. To obtain this result the conditional probabilities must be proper and the σ-fields posterior completed.

AB - Two people, 1 and 2, are said to have common knowledge of an event if both know it, 1 knows that 2 knows it, 2 knows that 1 knows it, 1 knows that 2 knows that 1 knows it, and so on. This paper provides a Bayesian definition of common knowledge, that is, a definition in terms of beliefs (probability measures). The main result is an equivalence between this definition and a definition in terms of the σ-fields representing 1 and 2's information. To obtain this result the conditional probabilities must be proper and the σ-fields posterior completed.

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U2 - 10.1016/0304-4068(87)90010-3

DO - 10.1016/0304-4068(87)90010-3

M3 - Article

AN - SCOPUS:38149145661

VL - 16

SP - 237

EP - 245

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 3

ER -