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Efficient communication, common knowledge, and consensus

  • 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)

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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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
Contact details of provider: 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
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  1. Frederic Koessler, 2000. "Common Knowledge and Consensus with Noisy Communication," Econometric Society World Congress 2000 Contributed Papers 0887, Econometric Society.
  2. D. Samet, 1987. "Ignoring Ignorance and Agreeing to Disagree," Discussion Papers 749, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. John Geanakoplos & Heracles M. Polemarchakis, 1982. "We Can't Disagree Forever," Cowles Foundation Discussion Papers 639, Cowles Foundation for Research in Economics, Yale University.
  4. Shin Hyun Song, 1993. "Logical Structure of Common Knowledge," Journal of Economic Theory, Elsevier, vol. 60(1), pages 1-13, June.
  5. Paul Milgrom, 1979. "An Axiomatic Characterization of Common Knowledge," Discussion Papers 393R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. 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.
  7. Brandenburger, Adam & Dekel, Eddie, 1987. "Common knowledge with probability 1," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 237-245, June.
  8. Nielsen, Lars Tyge, 1984. "Common knowledge, communication, and convergence of beliefs," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 1-14, August.
  9. Samet, Dov, 2010. "Agreeing to disagree: The non-probabilistic case," Games and Economic Behavior, Elsevier, vol. 69(1), pages 169-174, May.
  10. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  11. Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, vol. 70(1), pages 273-277, July.
  12. Parikh, Rohit & Krasucki, Paul, 1990. "Communication, consensus, and knowledge," Journal of Economic Theory, Elsevier, vol. 52(1), pages 178-189, October.
  13. 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.
  14. Krasucki, Paul, 1996. "Protocols Forcing Consensus," Journal of Economic Theory, Elsevier, vol. 70(1), pages 266-272, July.
  15. Robert J. Aumann & Sergiu Hart & Motty Perry, 2005. "Conditioning and the Sure-Thing Principle," Levine's Bibliography 784828000000000193, UCLA Department of Economics.
  16. McKelvey, Richard D & Page, Talbot, 1986. "Common Knowledge, Consensus, and Aggregate Information," Econometrica, Econometric Society, vol. 54(1), pages 109-27, January.
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