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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)

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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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Publisher 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
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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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Find related papers by JEL classification:
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

References listed on IDEAS
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.:

  1. Stephen Morris, 1999. "Approximate common knowledge revisited," International Journal of Game Theory, Springer, vol. 28(3), pages 385-408. [Downloadable!] (restricted)
    Other versions:
  2. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  3. 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. [Downloadable!] (restricted)
  4. Martin Cripps & George J. Mailath & Larry Samuelson, 2004. "Disappearing Private Reputations in Long-Run Relationships," Levine's Bibliography 122247000000000086, UCLA Department of Economics. [Downloadable!]
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  5. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July. [Downloadable!] (restricted)
  6. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September. [Downloadable!] (restricted)
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  7. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June. [Downloadable!] (restricted)
  8. Thomas Wiseman, 2005. "A Partial Folk Theorem for Games with Unknown Payoff Distributions," Econometrica, Econometric Society, vol. 73(2), pages 629-645, 03. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Amil Dasgupta & Jakub Steiner & Colin Stewart, 2007. "Efficient Dynamic Coordination with Individual Learning," Working Papers tecipa-301, University of Toronto, Department of Economics. [Downloadable!]
    Other versions:
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