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Common Learning

Author

Listed:
  • 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 when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. 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. Copyright Copyright 2008 by The Econometric Society.

Suggested Citation

  • Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2008. "Common Learning," Econometrica, Econometric Society, vol. 76(4), pages 909-933, July.
    • Handle: RePEc:ecm:emetrp:v:76:y:2008:i:4:p:909-933
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2008.00862.x
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    Cited by:

    1. 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.
    2. Chong Huang, 2011. "Coordination and Social Learning," PIER Working Paper Archive 11-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    3. Jakub Steiner & Colin Stewart, 2008. "Communication Can Destroy Common Learning," Edinburgh School of Economics Discussion Paper Series 184, 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;Game Theory Society, vol. 42(1), pages 55-98, February.
    5. Daron Acemoglu & Asuman Ozdaglar, 2011. "Opinion Dynamics and Learning in Social Networks," Dynamic Games and Applications, Springer, vol. 1(1), pages 3-49, March.
    6. Eeckhout, Jan & Weng, Xi, 2015. "Common value experimentation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 317-339.
    7. Amil Dasgupta & Jakub Steiner & Colin Stewart, 2007. "Efficient Dynamic Coordination with Individual Learning," Working Papers tecipa-301, University of Toronto, Department of Economics.
    8. Sharma, Priyanka, 2017. "Is more information always better? A case in credit markets," Journal of Economic Behavior & Organization, Elsevier, vol. 134(C), pages 269-283.
    9. Daron Acemoglu & Victor Chernozhukov & Muhamet Yildiz, 2006. "Learning and Disagreement in an Uncertain World," NBER Working Papers 12648, National Bureau of Economic Research, Inc.
    10. Chong Huang, 2018. "Coordination and social learning," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 155-177, January.
    11. Morris, Stephen, 2014. "Coordination, timing and common knowledge," Research in Economics, Elsevier, vol. 68(4), pages 306-314.
    12. Wiseman, Thomas, 2009. "Reputation and exogenous private learning," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1352-1357, May.
    13. Steiner, Jakub & Stewart, Colin, 2011. "Communication, timing, and common learning," Journal of Economic Theory, Elsevier, vol. 146(1), pages 230-247, January.
    14. Dasgupta, Amil & Steiner, Jakub & Stewart, Colin, 2012. "Dynamic coordination with individual learning," Games and Economic Behavior, Elsevier, vol. 74(1), pages 83-101.
    15. Arieli, Itai & Levy, Yehuda John, 2015. "Determinacy of games with Stochastic Eventual Perfect Monitoring," Games and Economic Behavior, Elsevier, vol. 91(C), pages 166-185.
    16. Antonio Jiménez-Martínez, 2015. "A model of belief influence in large social networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 21-59, May.

    More about this item

    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

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