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Efficient communication, common knowledge, and consensus

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Author Info

  • Tsakas, Elias

    ()
    (Department of Economics, School of Business, Economics and Law, Göteborg University)

  • Voorneveld, Mark

    ()
    (Tilburg University, Department of Econometrics and Operations Research, The Netherlands)

Abstract

We study a model of pairwise communication in a finite population of Bayesian agents. We show that, in contrast with claims to the contrary in the existing literature, communication under a fair protocol may not lead to common knowledge of signals. We prove that commonly known signals are achieved if the individuals convey, in addition to their own message, the information about every individual’s most recent signal they are aware of. If the signal is a posterior probability about some event, common knowledge implies consensus.

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File URL: http://hdl.handle.net/2077/4576
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Bibliographic Info

Paper provided by University of Gothenburg, Department of Economics in its series Working Papers in Economics with number 255.

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Length: 15 pages
Date of creation: 18 Jun 2007
Date of revision:
Handle: RePEc:hhs:gunwpe:0255

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Postal: Department of Economics, School of Business, Economics and Law, University of Gothenburg, Box 640, SE 405 30 GÖTEBORG, Sweden
Phone: 031-773 10 00
Web page: http://www.handels.gu.se/econ/
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Keywords: Private information; communication; common knowledge; consensus;

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  1. Samet, Dov, 2010. "Agreeing to disagree: The non-probabilistic case," Games and Economic Behavior, Elsevier, vol. 69(1), pages 169-174, May.
  2. Koessler, Frederic, 2001. "Common knowledge and consensus with noisy communication," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 139-159, September.
  3. Brandenburger, Adam & Dekel, Eddie, 1987. "Common knowledge with probability 1," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 237-245, June.
  4. Robert J. Aumann & Sergiu Hart & Motty Perry, 2005. "Conditioning and the Sure-Thing Principle," Levine's Bibliography 784828000000000193, UCLA Department of Economics.
  5. Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, vol. 70(1), pages 273-277, July.
  6. Krasucki, Paul, 1996. "Protocols Forcing Consensus," Journal of Economic Theory, Elsevier, vol. 70(1), pages 266-272, July.
  7. Nielsen, Lars Tyge, 1984. "Common knowledge, communication, and convergence of beliefs," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 1-14, August.
  8. Parikh, Rohit & Krasucki, Paul, 1990. "Communication, consensus, and knowledge," Journal of Economic Theory, Elsevier, vol. 52(1), pages 178-189, October.
  9. Bacharach, Michael, 1985. "Some extensions of a claim of Aumann in an axiomatic model of knowledge," Journal of Economic Theory, Elsevier, vol. 37(1), pages 167-190, October.
  10. Milgrom, Paul, 1981. "An Axiomatic Characterization of Common Knowledge," Econometrica, Econometric Society, vol. 49(1), pages 219-22, January.
  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. Shin Hyun Song, 1993. "Logical Structure of Common Knowledge," Journal of Economic Theory, Elsevier, vol. 60(1), pages 1-13, June.
  13. McKelvey, Richard D & Page, Talbot, 1986. "Common Knowledge, Consensus, and Aggregate Information," Econometrica, Econometric Society, vol. 54(1), pages 109-27, January.
  14. D. Samet, 1987. "Ignoring Ignorance and Agreeing to Disagree," Discussion Papers 749, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Rubinstein, Ariel & Wolinsky, Asher, 1990. "On the logic of "agreeing to disagree" type results," Journal of Economic Theory, Elsevier, vol. 51(1), pages 184-193, June.
  16. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
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