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Common Learning

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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File URL: http://economics.sas.upenn.edu/system/files/working-papers/07-018.pdf
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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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Keywords: Common learning; common belief; private signals; private beliefs;

Other versions of this item:

  • Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2008. "Common Learning," Econometrica, Econometric Society, vol. 76(4), pages 909-933, 07.
Find related papers by JEL classification:
  • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
  • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

References listed on IDEAS
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  1. Martin W. Cripps & George J. Mailath & Larry Samuelson, 2006. "Disappearing Private Reputations in Long-Run Relationships," Levine's Bibliography 321307000000000152, UCLA Department of Economics.
  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. repec:ner:tilbur:urn:nbn:nl:ui:12-154416 is not listed on IDEAS
  4. Morris, S., 1999. "Approximate Common Knowledge Revisited," Papers 987r, Yale - Economic Growth Center.
  5. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
  6. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
  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. 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.
  9. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2007. "Learning and Disagreement in an Uncertain World," Carlo Alberto Notebooks 48, Collegio Carlo Alberto.
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Cited by:

  1. Martin Cripps & Jeffrey Ely & George Mailath & Larry Samuelson, 2013. "Common learning with intertemporal dependence," International Journal of Game Theory, Springer, vol. 42(1), pages 55-98, February.
  2. 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.
  3. Jakub Steiner & Colin Stewart, 2008. "Communication Can Destroy Common Learning," Working Papers tecipa-330, University of Toronto, Department of Economics.
  4. Steiner, Jakub & Stewart, Colin, 2011. "Communication, timing, and common learning," Journal of Economic Theory, Elsevier, vol. 146(1), pages 230-247, January.
  5. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc.
  6. Dasgupta, Amil & Steiner, Jakub & Stewart, Colin, 2012. "Dynamic coordination with individual learning," Games and Economic Behavior, Elsevier, vol. 74(1), pages 83-101.
  7. Fudenberg, Drew & Takahashi, Satoru, 2011. "Heterogeneous beliefs and local information in stochastic fictitious play," Games and Economic Behavior, Elsevier, vol. 71(1), pages 100-120, January.
  8. Daron Acemoglu & Asuman E. Ozdaglar, 2010. "Opinion Dynamics and Learning in Social Networks," Levine's Working Paper Archive 661465000000000222, David K. Levine.
  9. Wiseman, Thomas, 2009. "Reputation and exogenous private learning," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1352-1357, May.
  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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