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Switching from complete to incomplete information

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  • Bochet, Olivier

Abstract

We construct an elementary mechanism (Dutta, Sen and Vohra (1995)) that Nash implements the Constrained Walrasian correspondence. We extend it to incomplete and non-exclusive information economies by enlarging the message space of agents. We characterize the set of Bayesian equilibrium outcomes of the mechanism, and thus characterize an extension of the Constrained Walrasian correspondence when one switches from complete to incomplete information. First, measurability restrictions on allocations do not emerge from the strategic behavior of agents: there exist simple economies for which the set of Constrained Rational Expectations equilibrium allocations is not contained in the set of equilibrium outcomes of the mechanism. Next, by imposing measurability restrictions on allocations, the mechanism globally implements the Constrained Rational Expectations Equilibrium correspondence. This result shows game-theoretic connections between these two market equilibrium concepts. However, it is obtained at the price of strong restrictions on the behavior of agents.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 43 (2007)
Issue (Month): 6 (August)
Pages: 735-748

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Handle: RePEc:eee:mateco:v:43:y:2007:i:6:p:735-748

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Web page: http://www.elsevier.com/locate/jmateco

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  1. F. Forges & E. Minelli, 1996. "Self-fulfilling mechanisms and rational expectations," THEMA Working Papers, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise 96-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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  5. Serrano, R. & Yosha, O., 1995. "Decentralized Information and the Walrasian Outcome : A Pairwise Meetings Market with Private Values," Papers, Tel Aviv 26-95, Tel Aviv.
  6. Wettstein, David, 1990. "Continuous implementation of constrained rational expectations equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 52(1), pages 208-222, October.
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  8. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, Econometric Society, vol. 57(1), pages 115-34, January.
  9. Bhaskar Dutta & Arunava Sen & Rajiv Vohra, 1994. "Nash implementation through elementary mechanisms in economic environments," Review of Economic Design, Springer, Springer, vol. 1(1), pages 173-203, December.
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  11. Wolinsky, Asher, 1987. "Information Revelation in a Market with Pairwise Meetings," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 284, University of Warwick, Department of Economics.
  12. Roy Radner, 1997. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Levine's Working Paper Archive 1594, David K. Levine.
  13. Douglas Gale, 2010. "Limit theorems for markets with sequential bargaining," Levine's Working Paper Archive 621, David K. Levine.
  14. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  15. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 85(5), pages 937-68, October.
  16. Dubey, Pradeep & Geanakoplos, John & Shubik, Martin, 1987. "The revelation of information in strategic market games : A critique of rational expectations equilibrium," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 16(2), pages 105-137, April.
  17. Laffont, Jean-Jacques M, 1985. "On the Welfare Analysis of Rational Expectations Equilibria with Asymmetric Information," Econometrica, Econometric Society, Econometric Society, vol. 53(1), pages 1-29, January.
  18. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 461-77, March.
  19. Codognato, Giulio & Ghosal, Sayantan, 2003. "Self-fulfilling mechanisms and rational expectations in large markets," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 39(5-6), pages 421-431, July.
  20. Blume, Lawrence & Easley, David, 1990. "Implementation of Walrasian expectations equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 51(1), pages 207-227, June.
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  22. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 54(2), pages 193-208, April.
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