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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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Bibliographic Info

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. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  3. Minelli, Enrico & Forges, Françoise, 1997. "Self-Fulfilling Mechanisms and Rational Expectations," Economics Papers from University Paris Dauphine 123456789/12327, Paris Dauphine University.
  4. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-819, November.
  5. Douglas Gale, 2010. "Limit theorems for markets with sequential bargaining," Levine's Working Paper Archive 621, David K. Levine.
  6. 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.
  7. 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.
  8. 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.
  9. Roberto Serrano, 2000. "Decentralized Information and the Walrasian Outcome:A Pairwise Meetings Market with Private Values," Working Papers 2000-13, Brown University, Department of Economics.
  10. Roy Radner, 1997. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Levine's Working Paper Archive 1594, David K. Levine.
  11. 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.
  12. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 193-208, April.
  13. Piero Gottardi & Roberto Serrano, 2004. "Market Power and Information Revelation in Dynamic Trading," CESifo Working Paper Series 1300, CESifo Group Munich.
  14. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  15. 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.
  16. 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.
  17. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  18. Blume, Lawrence & Easley, David, 1990. "Implementation of Walrasian expectations equilibria," Journal of Economic Theory, Elsevier, vol. 51(1), pages 207-227, June.
  19. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-78, May.
  20. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
  21. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-93, November.
  22. Wettstein, David, 1990. "Continuous implementation of constrained rational expectations equilibria," Journal of Economic Theory, Elsevier, vol. 52(1), pages 208-222, October.
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