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Common Learning with Intertemporal Dependence

Author

Listed:
  • 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

    (Department of Economics, Yale University)

Abstract

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. Will the agents commonly learn the value of the parameter, i.e., will the true value of the parameter become approximate common-knowledge? If the signals are independent and identically distributed across time (but not necessarily across agents), the answer is yes (Cripps, Ely, Mailath, and Samuelson, 2008). This paper explores the implications of allowing the signals to be dependent over time. We present a counterexample showing that even extremely simple time dependence can preclude common learning, and present sufficient conditions for common learning.

Suggested Citation

  • 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.
    • Handle: RePEc:pen:papers:11-012
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    References listed on IDEAS

    as
    1. Stephen Morris, 1999. "Approximate common knowledge revisited," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 385-408.
    2. Steiner, Jakub & Stewart, Colin, 2011. "Communication, timing, and common learning," Journal of Economic Theory, Elsevier, vol. 146(1), pages 230-247, January.
    3. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    4. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    5. Martin W. Cripps & Jeffrey C. Ely & George J. Mailath & Larry Samuelson, 2008. "Common Learning," Econometrica, Econometric Society, vol. 76(4), pages 909-933, July.
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    Cited by:

    1. 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.
    2. Morris, Stephen, 2014. "Coordination, timing and common knowledge," Research in Economics, Elsevier, vol. 68(4), pages 306-314.
    3. Takuo Sugaya & Yuichi Yamamoto, 2019. "Common Learning and Cooperation in Repeated Games," PIER Working Paper Archive 19-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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    More about this item

    Keywords

    Common learning; common belief; private signals; private beliefs;
    All these keywords.

    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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