Common knowledge and consensus with noisy communication
Parikh and Krasucki (1990) suggested in an informal manner that a consensus does not require common knowledge. Weyers (1992) proved that their model does not permit such a conclusion and that a more general one has to be constructed. Heifetz (1996) gave an example with three agents inspired by computer science which illustrates the intuition of Parikh and Krasucki (1990), i.e., where a consensus is obtained without common knowledge of it. We propose a general setting of noisy communication to confirm this result. We show that common knowledge cannot emerge with any non-public and noisy communication protocol. But, with ``fair\'\' protocols and a sufficiently rich language, a consensus and arbitrary high levels of interactive knowledge are achievable. A minimal example with two agents and two states is given. Nevertheless, for public and noisy communication, some results on common knowledge and consensus are obtained. We apply our results to describe some conditions that ensure or prevent epistemic conditions for Nash equilibrium. In general, non-public and noisy communication is not sufficient for the conjectures to form, during time, a Nash equilibrium, even if the game and mutual rationality are mutually known. However, with only two agents or with a noisy and public communication protocol, sufficient conditions are given for the conjectures to form a Nash equilibrium in a finite number of communication periods.
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- WEYERS , Sonia, 1992. "Three results on communication, information and common knowledge," CORE Discussion Papers 1992028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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CARESS Working Papres
97-8, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Stephen Morris & Hyun Song Shin, . ""Approximate Common Knowledge and Co-ordination: Recent Lessons from Game Theory''," CARESS Working Papres 96-07, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Stephen Morris & Hyun Song Shin, . "Approximate Common Knowledge and Co-ordination: Recent Lessons from Game Theory," Penn CARESS Working Papers 72042421d029130510780dde2, Penn Economics Department.
- Krasucki, Paul, 1996. "Protocols Forcing Consensus," Journal of Economic Theory, Elsevier, vol. 70(1), pages 266-272, July.
- John Geanakoplos & Heracles M. Polemarchakis, 1982.
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639, Cowles Foundation for Research in Economics, Yale University.
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