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Common Knowledge and Consensus with Noisy Communication

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  • Frederic Koessler

    (Universite Louis Pasteur)

Abstract

Parikh and Krasucki (1990, JET 52) have suggested in an informal manner that a consensus does not require common knowledge. Weyers (1992, CORE DP 9228) has proved that their model does not permit such a conclusion, and that a more general one has to be constructed. Heifetz (1996, JET 70) has given an example with three agents, inspired by computer science works, which illustrates the intuition of the first authors, 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 for any non public and noisy communication, no event can become common knowledge if it was not at the beginning, but that under some assumptions a consensus and arbitrary high levels of interactive knowledge are achievable. A minimal example is given, with two agents and two states. Nevertheless, for public and noisy communication, some results on common knowledge are obtained, depending on the richness of available language. 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 Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0887.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0887

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  1. Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262562006, December.
  2. Stephen Morris & Hyun Song Shin, . "Approximate Common Knowledge and Co-ordination: Recent Lessons from Game Theory," CARESS Working Papres, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences 97-8, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  3. Parikh, Rohit & Krasucki, Paul, 1990. "Communication, consensus, and knowledge," Journal of Economic Theory, Elsevier, Elsevier, vol. 52(1), pages 178-189, October.
  4. Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, Elsevier, vol. 70(1), pages 273-277, July.
  5. Geanakoplos, John, 1994. "Common knowledge," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 40, pages 1437-1496 Elsevier.
  6. 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.
  7. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
  8. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1161-80, September.
  9. Krasucki, Paul, 1996. "Protocols Forcing Consensus," Journal of Economic Theory, Elsevier, Elsevier, vol. 70(1), pages 266-272, July.
  10. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, American Economic Association, vol. 79(3), pages 385-91, June.
  11. Nishihara, Ko, 1991. "A note on the equivalence of the two definitions of common knowledge," Mathematical Social Sciences, Elsevier, Elsevier, vol. 21(2), pages 177-178, April.
  12. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, Elsevier, vol. 28(1), pages 192-200, October.
  13. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 639, Cowles Foundation for Research in Economics, Yale University.
  14. Cave, Jonathan A. K., 1983. "Learning to agree," Economics Letters, Elsevier, Elsevier, vol. 12(2), pages 147-152.
  15. repec:wop:humbsf:1997-47 is not listed on IDEAS
  16. WEYERS , Sonia, 1992. "Three results on communication, information and common knowledge," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1992028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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Cited by:
  1. Hernández, Penélope & Urbano, Amparo & Vila, José E., 2012. "Pragmatic languages with universal grammars," Games and Economic Behavior, Elsevier, Elsevier, vol. 76(2), pages 738-752.
  2. Steiner, Jakub & Stewart, Colin, 2011. "Communication, timing, and common learning," Journal of Economic Theory, Elsevier, Elsevier, vol. 146(1), pages 230-247, January.
  3. 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.
  4. Jakub Steiner & Colin Stewart, 2008. "Communication Can Destroy Common Learning," Working Papers tecipa-330, University of Toronto, Department of Economics.
  5. 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).
  6. Tsakas, Elias & Voorneveld, Mark, 2007. "Efficient communication, common knowledge, and consensus," Working Papers in Economics, University of Gothenburg, Department of Economics 255, University of Gothenburg, Department of Economics.
  7. Penélope Hernández & Bernhard von Stengel, 2012. "Nash Codes for Noisy Channels," Discussion Papers in Economic Behaviour, University of Valencia, ERI-CES 0912, University of Valencia, ERI-CES.

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