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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].

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1994044.

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Date of creation: 01 Sep 1994
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Handle: RePEc:cor:louvco:1994044

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Keywords: communication equilibrium; Nash equilibrium; rational expectations equilibrium;

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Cited by:
  1. Enrico Minelli & Herakles Polemarchakis, 2001. "Information at Equilibrium," Working Papers 2001-27, Brown University, Department of Economics.
  2. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
  3. Heifetz, A & Minelli, E, 1997. "Informational Smallness in Rational Expectations Equilibria," Papers 10-97, Tel Aviv.
  4. Forges,F. & Minelli,E., 1995. "Property of Nash Equilibria in Repeated Games with Incomplete Information," Papers 9518, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  5. Forges, F. & Minelli, E., 1996. "Self-Fulfilling Mechanisms in Bayesian Games," Papers 9624, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  6. 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.
  7. Yusuke Kamishiro & Roberto Serrano, 2009. "Equilibrium Blocking in Large Quasilinear Economies," Working Papers 2009-12, Brown University, Department of Economics.
  8. Bochet, Olivier, 2007. "Switching from complete to incomplete information," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 735-748, August.
  9. Lorenzo Rocco, 2001. "Nonatomic Games with Limited Anonymity," Working Papers 39, University of Milano-Bicocca, Department of Economics, revised Nov 2001.

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