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Communication, Timing, and Common Learning

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  • Jakub Steiner
  • Colin Stewart

Abstract

We study the effect of stochastically delayed communication on common knowledge acquisition (common learning). If messages do not report dispatch times, communication prevents common learning under general conditions even if common knowledge is acquired without communication. If messages report dispatch times, communication can destroy common learning under more restrictive conditions. The failure of common learning in the two cases is based on divgerent infection arguments. Communication can destroy common learning even if it ends in finite time, or if agents communicate all of their information. We also identify conditions under which common learning is preserved in the presence of communication.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1484.

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Date of creation: 18 Jan 2010
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Handle: RePEc:nwu:cmsems:1484

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Keywords: communication; common learning; approximate common knowledge;

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  1. Koessler, Frederic, 2001. "Common knowledge and consensus with noisy communication," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 139-159, September.
  2. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  3. Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2006. "Common Learning," Cowles Foundation Discussion Papers 1575R, Cowles Foundation for Research in Economics, Yale University, revised Jun 2007.
    • Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2008. "Common Learning," Econometrica, Econometric Society, vol. 76(4), pages 909-933, 07.
  4. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
  5. Heifetz, Aviad, 1996. "Comment on Consensus without Common Knowledge," Journal of Economic Theory, Elsevier, vol. 70(1), pages 273-277, 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. Morris Stephen E, 2002. "Faulty Communication: Some Variations on the Electronic Mail Game," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-26, January.
  8. Parikh, Rohit & Krasucki, Paul, 1990. "Communication, consensus, and knowledge," Journal of Economic Theory, Elsevier, vol. 52(1), pages 178-189, October.
  9. Binmore, Ken & Samuelson, Larry, 2001. "Coordinated Action in the Electronic Mail Game," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 6-30, April.
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Cited by:
  1. Rodrigues-Neto, José Alvaro, 2012. "The cycles approach," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 207-211.
  2. Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2011. "Common Learning with Intertemporal Dependence," PIER Working Paper Archive 11-012, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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