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The relation between implementability and the core

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

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Abstract

This paper proves a simple and general theorem on resource-allocation mechanisms that achieve Pareto efficiency. We say that a mechanism (game form) is normal if at any action profile, an agent who obtains his endowments neither pays nor receives a positive amount. In the context of auctions, this simply means that losers receive no bill. We prove that for any normal mechanism, if its Nash equilibrium allocations are Pareto efficient for all preference profiles, then the equilibrium allocations are necessarily in the core. The result holds for a large class of allocation problems in which monetary transfers are feasible and the consumption space is discrete except for the space of transfers. Examples include auctions with any number of objects, economies with indivisible public goods, marriage problems, and coalition formation.

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File URL: http://www.econ.columbia.edu/RePEc/pdf/DP0102-64.pdf
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Paper provided by Columbia University, Department of Economics in its series Discussion Papers with number 0102-64.

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Length: 37 pages
Date of creation: 2002
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Handle: RePEc:clu:wpaper:0102-64

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  1. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer, vol. 18(1), pages 135-153. [Downloadable!] (restricted)
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  2. 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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  3. 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)
  4. Hurwicz, Leonid, 1979. "On allocations attainable through Nash equilibria," Journal of Economic Theory, Elsevier, vol. 21(1), pages 140-165, August. [Downloadable!] (restricted)
  5. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February. [Downloadable!] (restricted)
  6. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, vol. 18(4), pages 655-708. [Downloadable!] (restricted)
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  7. 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)
  8. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February. [Downloadable!] (restricted)
  9. Alvin E. Roth & Uriel G. Rothblum, 1999. "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, Econometric Society, vol. 67(1), pages 21-44, January.
  10. 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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