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Common Learning

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Author Info

  • Martin W. Cripps

    ()
    (Department of Economics, University College London)

  • Jeffrey C. Ely

    ()
    (Department of Economics, Northwestern University)

  • George J. Mailath

    ()
    (Department of Economics, University of Pennsylvania)

  • Larry Samuelson

    ()
    (Social Science Computing Cooperative, University of Wisconsin Madison)

Abstract

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that that when each agent's signal space is finite, the agents will commonly learn its value, i.e., that the true value of the parameter will become approximate common-knowledge. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.

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Bibliographic Info

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 07-018.

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Length: 33 pages
Date of creation: 20 Jun 2007
Date of revision:
Handle: RePEc:pen:papers:07-018

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Related research

Keywords: Common learning; common belief; private signals; private beliefs;

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References

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  1. Stephen Morris, . "Approximate Common Knowledge Revisited," Penn CARESS Working Papers 6be11f49fbded40b2a623aebf, Penn Economics Department.
  2. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
  3. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
  4. 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.
  5. Martin Cripps & George J. Mailath & Larry Samuelson, 2004. "Disappearing Private Reputations in Long-Run Relationships," Levine's Bibliography 122247000000000086, UCLA Department of Economics.
  6. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2007. "Learning and Disagreement in an Uncertain World," Carlo Alberto Notebooks 48, Collegio Carlo Alberto.
  7. Thomas Wiseman, 2005. "A Partial Folk Theorem for Games with Unknown Payoff Distributions," Econometrica, Econometric Society, vol. 73(2), pages 629-645, 03.
  8. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
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Citations

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Cited by:
  1. Amil Dasgupta & Jakub Steiner & Colin Stewart, 2007. "Efficient dynamic coordination with individual learning," LSE Research Online Documents on Economics 24498, London School of Economics and Political Science, LSE Library.
  2. Drew Fudenberg & Satoru Takahashi, 2008. "Heterogeneous Beliefs and Local Information in Stochastic Fictitious Play," Levine's Working Paper Archive 122247000000001695, David K. Levine.
  3. 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.
  4. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2007. "Learning and Disagreement in an Uncertain World," Carlo Alberto Notebooks 48, Collegio Carlo Alberto.
  5. Dasgupta, Amil & Steiner, Jakub & Stewart, Colin, 2012. "Dynamic coordination with individual learning," Games and Economic Behavior, Elsevier, vol. 74(1), pages 83-101.
  6. Wiseman, Thomas, 2009. "Reputation and exogenous private learning," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1352-1357, May.
  7. Jakub Steiner & Colin Stewart, 2010. "Communication, Timing, and Common Learning," Working Papers tecipa-389, University of Toronto, Department of Economics.
  8. Daron Acemoglu & Asuman E. Ozdaglar, 2010. "Opinion Dynamics and Learning in Social Networks," Levine's Working Paper Archive 661465000000000222, David K. Levine.
  9. Jakub Steiner & Colin Stewart, 2008. "Communication Can Destroy Common Learning," ESE Discussion Papers 184, Edinburgh School of Economics, University of Edinburgh.
  10. Chong Huang, 2011. "Coordination and Social Learning," PIER Working Paper Archive 11-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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