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Projection Equilibrium: Definition and Applications to Social Investment and Persuasion


  • Kristóf Madarász


People exaggerate the extent to which their private information is shared with others. This paper introduces this phenomenon portably into Bayesian games where people wrongly think that if they can condition their strategy on an event others can do as well. I apply the model to a variety of settings. In the context of social investment people misattribute the uncertainty they face about others preferences to others having antagonistic motives. Even if all parties prefer mutual investment, none invests, yet all come to believe that others prefer not to invest. In the context of communication with costly state veri…cation, the model predicts credulity: persuasion by advisors, who are known to have an incentive to exaggerate the quality of an asset, will nevertheless induce uniformly exaggerated average posteriors for receivers. When endogenizing the con‡ict of interest between senders and receivers, I show that such credulous belief-bubbles rise discontinuously as the size of the market or the complexity of the asset increases. Further implications to auctions, common value trade and zero-sum games are explored.

Suggested Citation

  • Kristóf Madarász, 2015. "Projection Equilibrium: Definition and Applications to Social Investment and Persuasion," STICERD - Theoretical Economics Paper Series /2015/566, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  • Handle: RePEc:cep:stitep:/2015/566

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    References listed on IDEAS

    1. Jehiel, Philippe & Koessler, Frédéric, 2008. "Revisiting games of incomplete information with analogy-based expectations," Games and Economic Behavior, Elsevier, vol. 62(2), pages 533-557, March.
    2. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    3. Williamson, Oliver E, 1979. "Transaction-Cost Economics: The Governance of Contractural Relations," Journal of Law and Economics, University of Chicago Press, vol. 22(2), pages 233-261, October.
    4. Malmendier, Ulrike & Shanthikumar, Devin, 2007. "Are small investors naive about incentives?," Journal of Financial Economics, Elsevier, vol. 85(2), pages 457-489, August.
    5. Erik Eyster & Matthew Rabin, 2005. "Cursed Equilibrium," Econometrica, Econometric Society, vol. 73(5), pages 1623-1672, September.
    6. Grossman, Sanford J & Hart, Oliver D, 1986. "The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 691-719, August.
    7. Bruno Biais & Martin Weber, 2009. "Hindsight Bias, Risk Perception, and Investment Performance," Management Science, INFORMS, vol. 55(6), pages 1018-1029, June.
    8. 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.
    9. Kristóf Madarász, 2012. "Information Projection: Model and Applications," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 961-985.
    10. Daron Acemoglu & Simon Johnson & James A. Robinson, 2001. "The Colonial Origins of Comparative Development: An Empirical Investigation," American Economic Review, American Economic Association, vol. 91(5), pages 1369-1401, December.
    11. Yann Algan & Pierre Cahuc, 2010. "Inherited Trust and Growth," American Economic Review, American Economic Association, vol. 100(5), pages 2060-2092, December.
    12. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    13. Riley, John G, 1989. "Expected Revenue from Open and Sealed Bid Auctions," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 41-50, Summer.
    14. George A. Akerlof, 1970. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, Oxford University Press, vol. 84(3), pages 488-500.
    15. Ignacio Esponda, 2008. "Behavioral Equilibrium in Economies with Adverse Selection," American Economic Review, American Economic Association, vol. 98(4), pages 1269-1291, September.
    16. Madarasz, Kristof, 2008. "Information projection: model and applications," MPRA Paper 38612, University Library of Munich, Germany, revised 2011.
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    More about this item


    Projection; Social Investment; Pluralistic Ignorance; Persuasion Belief-Bubbles.;

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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