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Communication and Learning

  • Luca Anderlini
  • Dino Gerardi
  • Roger Lagunoff

We study strategic information transmission in an organization consisting of an infinite sequence of individual decision makers. Each decision maker chooses an action and receives an informative but imperfect signal of the once-and-for-all realization of an unobserved state. The state affects all individuals' preferences over present and future decisions. Decision makers do not directly observe the realized signals or actions of their predecessors. Instead, they must rely on cheap-talk messages in order to accumulate information about the state. Each decision maker is therefore both a receiver of information with respect to his decision, and a sender with respect to all future decisions. We show that if preferences are not perfectly aligned "full learning" equilibria - ones in which the individuals' posterior beliefs eventually place full weight on the true state - do not exist. This is so both in the case of private communication, in which each individual only hears the message of his immediate predecessor, and in the case of public communication, in which a decision maker hears the message of all his predecessors. Surprisingly, in the latter case full learning may be impossible even in the limit as all members of the organization become infinitely patient. We also consider the case where all individuals have access to a mediator who can work across time periods arbitrarily far apart. In this case full learning equilibria exist.

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Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 82.

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Length: 50 pages
Date of creation: 2008
Date of revision: 2010
Handle: RePEc:cca:wpaper:82
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  1. Mikhail Golosov & Vasiliki Skreta & Aleh Tsyvinski & Andrea Wilson, 2013. "Dynamic Strategic Information Transmission," Working Papers 13-03, New York University, Leonard N. Stern School of Business, Department of Economics.
  2. David Spector, 2000. "Rational Debate And One-Dimensional Conflict," The Quarterly Journal of Economics, MIT Press, vol. 115(1), pages 181-200, February.
  3. Roger Lagunoff, 2002. "Credible Communication in Dynastic Government," Game Theory and Information 0203003, EconWPA.
  4. Joseph Farrell & Matthew Rabin, 1996. "Cheap Talk," Journal of Economic Perspectives, American Economic Association, vol. 10(3), pages 103-118, Summer.
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  6. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2007. "Social Memory and Evidence from the Past," Cowles Foundation Discussion Papers 1601, Cowles Foundation for Research in Economics, Yale University.
  7. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-85, November.
  8. Luca Anderlini & Roger Lagunoff, 2000. "Communication in Dynastic Repeated Games: 'Whitewashes' and 'Coverups'," Working Papers gueconwpa~01-01-03, Georgetown University, Department of Economics, revised 01 Jul 2001.
  9. Hajime Kobayashi, 2007. "Folk Theorems For Infinitely Repeated Games Played By Organizations With Short-Lived Members," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(2), pages 517-549, 05.
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  13. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
  14. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  15. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-51, November.
  16. Vijay Krishna & John Morgan, 1999. "A Model of Expertise," Game Theory and Information 9902003, EconWPA.
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  17. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 797-817, August.
  18. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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