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Common knowledge and consensus with noisy communication

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  • Frédéric Koessler

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

Paper provided by Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg in its series Working Papers of BETA with number 2000-05.

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Date of creation: 2000
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Handle: RePEc:ulp:sbbeta:2000-05

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Keywords: Noisy communication protocols; common knowledge; consensus; Nash equilibrium; conjectures;

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  1. repec:wop:humbsf:1997-47 is not listed on IDEAS
  2. Cave, Jonathan A. K., 1983. "Learning to agree," Economics Letters, Elsevier, vol. 12(2), pages 147-152.
  3. 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.
  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. Krasucki, Paul, 1996. "Protocols Forcing Consensus," Journal of Economic Theory, Elsevier, vol. 70(1), pages 266-272, July.
  6. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
  7. 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.
  8. Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, vol. 70(1), pages 273-277, July.
  9. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  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. 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.
  12. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
  13. 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.
  14. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  15. 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.
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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. Tsakas, Elias & Voorneveld, Mark, 2007. "Efficient communication, common knowledge, and consensus," Working Papers in Economics 255, University of Gothenburg, Department of Economics.
  3. Jakub Steiner & Colin Stewart, 2008. "Communication Can Destroy Common Learning," ESE Discussion Papers 184, Edinburgh School of Economics, University of Edinburgh.
  4. Hernández, Penélope & Urbano, Amparo & Vila, José E., 2012. "Pragmatic languages with universal grammars," Games and Economic Behavior, Elsevier, vol. 76(2), pages 738-752.
  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, 2011. "On consensus through communication without a commonly known protocol," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 733-739.
  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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