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Common Learning

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Author Info

  • Martin W. Cripps
  • Jeffrey C. Ely
  • George J. Mailath
  • Larry Samuelson

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.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 321307000000000355.

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Date of creation: 02 Sep 2006
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Handle: RePEc:cla:levrem:321307000000000355

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References

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  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.
  2. 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.
  3. Cripps,M.W. & Mailath,G.J. & Samuelson,L., 2004. "Disappearing private reputations in long-run relationships," Working papers 5, Wisconsin Madison - Social Systems.
  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. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
  6. Stephen Morris, 1999. "Approximate common knowledge revisited," International Journal of Game Theory, Springer, vol. 28(3), pages 385-408.
  7. Samet, Dov, 1998. "Iterated Expectations and Common Priors," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 131-141, July.
  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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Cited by:
  1. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2007. "Learning and Disagreement in an Uncertain World," Carlo Alberto Notebooks 48, Collegio Carlo Alberto.
  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. Amil Dasgupta & Jakub Steiner & Colin Stewart, 2007. "Efficient Dynamic Coordination with Individual Learning," ESE Discussion Papers 175, Edinburgh School of Economics, University of Edinburgh.
  4. 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.
  5. Jakub Steiner & Colin Stewart, 2008. "Communication Can Destroy Common Learning," Working Papers tecipa-330, University of Toronto, Department of Economics.
  6. Wiseman, Thomas, 2009. "Reputation and exogenous private learning," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1352-1357, May.
  7. Chong Huang, 2011. "Coordination and Social Learning," PIER Working Paper Archive 11-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  8. Drew Fudenberg & Satoru Takahashi, 2008. "Heterogeneous Beliefs and Local Information in Stochastic Fictitious Play," Levine's Working Paper Archive 122247000000001695, David K. Levine.
  9. Daron Acemoglu & Asuman E. Ozdaglar, 2010. "Opinion Dynamics and Learning in Social Networks," Levine's Working Paper Archive 661465000000000222, David K. Levine.
  10. Dasgupta, Amil & Steiner, Jakub & Stewart, Colin, 2012. "Dynamic coordination with individual learning," Games and Economic Behavior, Elsevier, vol. 74(1), pages 83-101.

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