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Self-Fulfilling Mechanisms and Rational Expectations

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  • FORGES, Françoise

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • MINELLI , Enrico

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

Abstract

In a Bayesian game G, the players first receive private information on the state of nature and then simultaneously choose an action. We assume that the vector of actions a generates a signal g(a). A mechanism for G is a mapping [ mu ] from the set of states of nature S to the product sert of players’ actions A. [ mu ] is self-fulfilling if, given the information revealed by [ mu ] (namely, g([ mu ] )(s)) if the state of nature is s), no player can gain in unilaterally deviating from the action prescribed by the mechanism. Let SF(G) denote the set of payoffs achievable through an incentive compatible self-fulfilling mechanism. Examples show that SF(G) may not intersect the set N(G) of Nash equilibrium payoffs of G. Obviously, SF(G) and N(G) coincide if G is a game of complete information. Let E be an exchange economy with differential information. We associate a ( Bayesian) market game GE with E. In GE, the signal generated by the players’ actions is a vector of prices. We prove that the allocations achieved through a self-fulfilling mechanism in GE coincide with the rational expectations equilibrium allocations in E. In order to understand how self-fulfillingness can be achieved in a dynamic framework, we analyze the relationship between SF(G) and the Nash equilibria of the infinitely repeated game G [ infinity] generated by G. We show in particular that SF(G) can be interpreted as a set of inert solutions of G [ infinity].

Suggested Citation

  • FORGES, Françoise & MINELLI , Enrico, 1994. "Self-Fulfilling Mechanisms and Rational Expectations," CORE Discussion Papers 1994044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1994044
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    References listed on IDEAS

    as
    1. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
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    6. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
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    Citations

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    Cited by:

    1. Codognato, Giulio & Ghosal, Sayantan, 2003. "Self-fulfilling mechanisms and rational expectations in large markets," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 421-431, July.
    2. Heifetz, Aviad & Minelli, Enrico, 2002. "Informational smallness in rational expectations equilibria," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 197-218, September.
    3. Forges, Francoise & Minelli, Enrico, 1998. "Self-Fulfilling Mechanisms in Bayesian Games," Games and Economic Behavior, Elsevier, vol. 25(2), pages 292-310, November.
    4. Yusuke Kamishiro & Roberto Serrano, 2011. "Equilibrium Blocking in Large Quasilinear Economies," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 552-567, August.
    5. Bochet, Olivier, 2007. "Switching from complete to incomplete information," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 735-748, August.
    6. E. Minelli & H. Polemarchakis, 2003. "Information at equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 573-584, March.
    7. Lorenzo Rocco, 2001. "Nonatomic Games with Limited Anonymity," Working Papers 39, University of Milano-Bicocca, Department of Economics, revised Nov 2001.
    8. Forges, Francoise & Minelli, Enrico, 1997. "A Property of Nash Equilibria in Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 18(2), pages 159-175, February.
    9. Peck, James, 2014. "A battle of informed traders and the market game foundations for rational expectations equilibrium," Games and Economic Behavior, Elsevier, vol. 88(C), pages 153-173.
    10. Hu, Tai-Wei & Wallace, Neil, 2016. "Information aggregation in a large multi-stage market game," Journal of Economic Theory, Elsevier, vol. 161(C), pages 103-144.
    11. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.

    More about this item

    Keywords

    communication equilibrium; Nash equilibrium; rational expectations equilibrium;

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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