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- W2086825407 abstract "We continue the work of Aumann (Ann. Statist. 4 (1976), 1236–1239), Geanakoplos and Polemarchakis, (J. Econ. Theory 28 (1982), 192–200), Cave (Econ. Lett. 12 (1983), 147–152), and Bacharach (J. Econ. Theory 37 (1985), 167–190) on common knowledge and consesus, extending the results of Geanakoplos and Polemarchakis, Cave, and Bacharach to the case where the number n of communicants is greater than two, but communication is in pairs. When n > 2, then communication is pairs does not lead to common knowledge for the group. We show that, nevertheless, conditional probabilities will converge in any fair protocol for communication, i.e., when none of the participants is blocked from communication. We show that the Cave-Bacharach generalisation of the results of Geanakoplos and Polemarchakis and of Aumann does not hold for pairwise communication when n > 2, and hence any proof for this case must use methods different from theirs. In particular, our proof uses a convexity condition that is obeyed by conditional probabilities, but is not implied by Cave's union consistency principle." @default.
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- W2086825407 date "1990-10-01" @default.
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- W2086825407 title "Communication, consensus, and knowledge" @default.
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- W2086825407 doi "https://doi.org/10.1016/0022-0531(90)90073-s" @default.
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