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Reduced-form implementation

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Author Info
Eiichi Miyagawa () (Columbia University - Department of Economics)

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Abstract

This paper studies resource-allocation mechanisms by using a reduced-form notion of mechanism. We formulate a mechanism by specifying the state space of the mechanism, the set of outcomes that agents can induce in a given state, and the set of admissible outcomes in each state. This notion of mechanism includes the Walrasian mechanism and majority voting as well as all game forms. With this notion, monotonicity is not only necessary but sufficient for a social choice correspondence to be implementable. Our main result is that in the context of exchange economies, if a mechanism implements a sub-correspondence of the Pareto correspondence and satisfies localness (one's "budget set" in a given state is independent of other agents' endowments), then the mechanism necessarily implements a sub-correspondence of the core correspondence. If the mechanism also satisfies anonymity, then it actually implements a sub-correspondence of the Walrasian equilibrium correspondence.

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File URL: http://www.econ.columbia.edu/RePEc/pdf/DP0203-09.pdf
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Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0203-09.

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Length: 39 pages
Date of creation: 2002
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Handle: RePEc:clu:wpaper:0203-09

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  2. Nir Dagan, 1994. "Recontracting and Competition," Economics Working Papers 152, Department of Economics and Business, Universitat Pompeu Fabra, revised Jan 1996. [Downloadable!]
    Other versions:
  3. Wilson, Robert, 1971. "Stable coalition proposals in majority-rule voting," Journal of Economic Theory, Elsevier, vol. 3(3), pages 254-271, September. [Downloadable!] (restricted)
  4. Rosenthal, Robert W., 1972. "Cooperative games in effectiveness form," Journal of Economic Theory, Elsevier, vol. 5(1), pages 88-101, August. [Downloadable!] (restricted)
  5. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June. [Downloadable!] (restricted)
  6. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Blackwell Publishing, vol. 59(4), pages 757-75, October. [Downloadable!] (restricted)
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  7. Muench, Thomas J., 1972. "The core and the Lindahl equilibrium of an economy with a public good: an example," Journal of Economic Theory, Elsevier, vol. 4(2), pages 241-255, April. [Downloadable!] (restricted)
  8. Schmeidler, David & Vind, Karl, 1972. "Fair Net Trades," Econometrica, Econometric Society, vol. 40(4), pages 637-42, July. [Downloadable!] (restricted)
  9. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-93, November. [Downloadable!] (restricted)
  10. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September. [Downloadable!] (restricted)
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  12. Serrano, Roberto & Volij, Oscar, 2000. "Walrasian Allocations without Price-Taking Behavior," Journal of Economic Theory, Elsevier, vol. 95(1), pages 79-106, November. [Downloadable!] (restricted)
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  13. 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. [Downloadable!] (restricted)
  14. Hurwicz, Leonid, 1979. "On allocations attainable through Nash equilibria," Journal of Economic Theory, Elsevier, vol. 21(1), pages 140-165, August. [Downloadable!] (restricted)
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  16. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Blackwell Publishing, vol. 66(1), pages 23-38, January. [Downloadable!] (restricted)
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  17. Thomson, William, 1988. "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, Elsevier, vol. 46(2), pages 237-254, December. [Downloadable!] (restricted)
  18. Roberts, John, 1976. "The incentives for correct revelation of preferences and the number of consumers," Journal of Public Economics, Elsevier, vol. 6(4), pages 359-374, November. [Downloadable!] (restricted)
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  20. Hurwicz, L, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Blackwell Publishing, vol. 46(2), pages 217-25, April. [Downloadable!] (restricted)
  21. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics. [Downloadable!]
  22. Saijo, Tatsuyoshi, 1988. "Strategy Space Reduction in Maskin's Theorem: Sufficient Conditions for Nash Implementation," Econometrica, Econometric Society, vol. 56(3), pages 693-700, May. [Downloadable!] (restricted)
  23. Nagahisa, Ryo-ichi, 1991. "A local independence condition for characterization of Walrasian allocations rule," Journal of Economic Theory, Elsevier, vol. 54(1), pages 106-123, June. [Downloadable!] (restricted)
  24. Saijo, Tatsuyoshi & Tatamitani, Yoshikatsu & Yamato, Takehiko, 1996. "Toward Natural Implementation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 949-80, November.
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  25. Sang-Chul Suh, 1996. "An algorithm for checking strong Nash implementability," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 109-122. [Downloadable!] (restricted)
  26. Ostroy, Joseph M., 1980. "The no-surplus condition as a characterization of perfectly competitive equilibrium," Journal of Economic Theory, Elsevier, vol. 22(2), pages 183-207, April. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Ilya Segal, 2004. "The Communication Requirements of of Social Choice Rules and Supporting Budget Sets," Economics Working Papers 0039, Institute for Advanced Study, School of Social Science. [Downloadable!]
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