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Common knowledge and consensus with noisy communication

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  • Koessler, Frederic

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 42 (2001)
Issue (Month): 2 (September)
Pages: 139-159

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Handle: RePEc:eee:matsoc:v:42:y:2001:i:2:p:139-159

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Web page: http://www.elsevier.com/locate/inca/505565

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  1. Cave, Jonathan A. K., 1983. "Learning to agree," Economics Letters, Elsevier, vol. 12(2), pages 147-152.
  2. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
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  4. 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).
  5. Nishihara, Ko, 1991. "A note on the equivalence of the two definitions of common knowledge," Mathematical Social Sciences, Elsevier, vol. 21(2), pages 177-178, April.
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  8. Dulleck, Uwe, 1997. "A note on the E-mail game: Bounded rationality and induction," SFB 373 Discussion Papers 1997,47, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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  10. Geanakoplos, John, 1994. "Common knowledge," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 40, pages 1437-1496 Elsevier.
  11. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
  12. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006, December.
  13. Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, vol. 70(1), pages 273-277, July.
  14. Parikh, Rohit & Krasucki, Paul, 1990. "Communication, consensus, and knowledge," Journal of Economic Theory, Elsevier, vol. 52(1), pages 178-189, October.
  15. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  16. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
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Cited by:
  1. Jakub Steiner & Colin Stewart, 2010. "Communication, Timing, and Common Learning," Working Papers tecipa-389, University of Toronto, Department of Economics.
  2. Jakub Steiner & Colin Stewart, 2008. "Communication Can Destroy Common Learning," Working Papers tecipa-330, University of Toronto, Department of Economics.
  3. Penelope Hernandez & Amparo Urbano Salvador & Jose E. Vila, 2010. "Pragmatic Languages with Universal Grammars," Discussion Papers in Economic Behaviour 0110, University of Valencia, ERI-CES.
  4. Tsakas, Elias & Voorneveld, Mark, 2011. "On consensus through communication without a commonly known protocol," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 733-739.
  5. Penélope Hernández & Bernhard von Stengel, 2012. "Nash Codes for Noisy Channels," Discussion Papers in Economic Behaviour 0912, University of Valencia, ERI-CES.
  6. Tsakas, Elias & Voorneveld, Mark, 2007. "Efficient communication, common knowledge, and consensus," Working Papers in Economics 255, University of Gothenburg, Department of Economics.
  7. Tsakas Elias & Voorneveld Mark, 2010. "On consensus through communication without a commonly known protocol," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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