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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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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2005063.

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Date of creation: 00 Sep 2005
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Handle: RePEc:cor:louvco:2005063

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Keywords: implementation; elementary mechanism; Walrasian equilibrium; Rational Expectations equilibrium;

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  1. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-68, October.
  2. Blume, Lawrence & Easley, David, 1990. "Implementation of Walrasian expectations equilibria," Journal of Economic Theory, Elsevier, vol. 51(1), pages 207-227, June.
  3. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-819, November.
  4. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  5. Hurwicz, L, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 217-25, April.
  6. Serrano, R. & Yosha, O., 1995. "Decentralized Information and the Walrasian Outcome : A Pairwise Meetings Market with Private Values," Papers 26-95, Tel Aviv.
  7. Bhaskar Dutta & Arunava Sen & Rajiv Vohra, 1994. "Nash implementation through elementary mechanisms in economic environments," Review of Economic Design, Springer, vol. 1(1), pages 173-203, December.
  8. F. Forges & E. Minelli, 1996. "Self-fulfilling mechanisms and rational expectations," THEMA Working Papers 96-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  9. Wettstein, David, 1990. "Continuous implementation of constrained rational expectations equilibria," Journal of Economic Theory, Elsevier, vol. 52(1), pages 208-222, October.
  10. Gale, Douglas, 1987. "Limit theorems for markets with sequential bargaining," Journal of Economic Theory, Elsevier, vol. 43(1), pages 20-54, October.
  11. Piero Gottardi & Roberto Serrano, 2004. "Market Power and Information Revelation in Dynamic Trading," CESifo Working Paper Series 1300, CESifo Group Munich.
  12. Wolinsky, Asher, 1987. "Information Revelation in a Market with Pairwise Meetings," The Warwick Economics Research Paper Series (TWERPS) 284, University of Warwick, Department of Economics.
  13. 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.
  14. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 193-208, April.
  15. Roy Radner, 1997. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Levine's Working Paper Archive 1594, David K. Levine.
  16. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  17. 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, vol. 16(2), pages 105-137, April.
  18. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-93, November.
  19. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  20. Laffont, Jean-Jacques M, 1985. "On the Welfare Analysis of Rational Expectations Equilibria with Asymmetric Information," Econometrica, Econometric Society, vol. 53(1), pages 1-29, January.
  21. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
  22. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-78, May.
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