Common knowledge and consensus with noisy communication
AbstractParikh 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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Bibliographic InfoPaper provided by Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg in its series Working Papers of BETA with number 2000-05.
Date of creation: 2000
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Noisy communication protocols; common knowledge; consensus; Nash equilibrium; conjectures;
Other versions of this item:
- Koessler, Frederic, 2001. "Common knowledge and consensus with noisy communication," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 139-159, September.
- Frederic Koessler, 2000. "Common Knowledge and Consensus with Noisy Communication," Econometric Society World Congress 2000 Contributed Papers 0887, Econometric Society.
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
This paper has been announced in the following NEP Reports:
- NEP-ALL-2000-04-04 (All new papers)
- NEP-CDM-2000-04-11 (Collective Decision-Making)
- NEP-MIC-2000-04-04 (Microeconomics)
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