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Common Learning

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Author Info

  • Martin W. Cripps

    (University College and Washington University, St. Louis)

  • Jeffrey C. Ely

    (Northwestern University)

  • George J. Mailath

    (Cowles Foundation, Yale University)

  • Larry Samuelson

    (University of Wisconsin)

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://cowles.econ.yale.edu/P/cd/d15b/d1575-r.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1575R.

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Length: 33 pages
Date of creation: Aug 2006
Date of revision: Jun 2007
Publication status: Published in Econometrics (2008), 76(4): 909-933
Handle: RePEc:cwl:cwldpp:1575r

Note: CFP 1257.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Common learning; Common belief; Private signals; Private beliefs;

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References

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  1. Cripps, Martin W. & Mailath, George J. & Samuelson, Larry, 2007. "Disappearing private reputations in long-run relationships," Journal of Economic Theory, Elsevier, vol. 134(1), pages 287-316, May.
  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. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2007. "Learning and Disagreement in an Uncertain World," Carlo Alberto Notebooks 48, Collegio Carlo Alberto.
  4. Thomas Wiseman, 2005. "A Partial Folk Theorem for Games with Unknown Payoff Distributions," Econometrica, Econometric Society, vol. 73(2), pages 629-645, 03.
  5. Morris, S., 1999. "Approximate Common Knowledge Revisited," Papers 987r, Yale - Economic Growth Center.
  6. 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.
  7. Carlsson, H. & Damme, E.E.C. van, 1990. "Global games and equilibrium selection," Discussion Paper 1990-52, Tilburg University, Center for Economic Research.
  8. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
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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," Working Papers tecipa-301, University of Toronto, Department of Economics.
  2. Jakub Steiner & Colin Stewart, 2010. "Communication, Timing, and Common Learning," Discussion Papers 1484, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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 & Asuman E. Ozdaglar, 2010. "Opinion Dynamics and Learning in Social Networks," Levine's Working Paper Archive 661465000000000222, David K. Levine.
  5. Wiseman, Thomas, 2009. "Reputation and exogenous private learning," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1352-1357, May.
  6. 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.
  7. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc.
  8. Dasgupta, Amil & Steiner, Jakub & Stewart, Colin, 2012. "Dynamic coordination with individual learning," Games and Economic Behavior, Elsevier, vol. 74(1), pages 83-101.
  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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