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Divide-and-Permute

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Abstract

We construct "simple" games implementing in Nash equilibria several solutions to the problem of fair division. These solutions are the no-envy solution, which selects the allocations such that no agent would prefer someone else's bundle to his own, and several variants of this solution. Components of strategies can be interpreted as allocations, consumption bundles, permutations, points in simplices of dimensionalities equal to the number of goods or to the number of agents, and integers. We also propose a simple game implementing the Pareto solution and games implementing the intersections of the Pareto solution with each of these solutions.

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File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_510.pdf
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Bibliographic Info

Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 510.

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Length: 20 pages
Date of creation: Nov 2004
Date of revision:
Handle: RePEc:roc:rocher:510

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Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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Keywords: Nash implementation. No-envy. Divide-and-permute.;

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References

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  1. Thomson, William, 1994. "Consistent extensions," Mathematical Social Sciences, Elsevier, vol. 28(1), pages 35-49, August.
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  18. 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.
  19. Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  20. Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, vol. 52(5), pages 1167-77, September.
  21. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
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  23. 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.
  24. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  25. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
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Citations

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Cited by:
  1. Nicolò, Antonio & Yu, Yan, 2008. "Strategic divide and choose," Games and Economic Behavior, Elsevier, vol. 64(1), pages 268-289, September.
  2. Marco LiCalzi & Antonio Nicolò, 2009. "Efficient egalitarian equivalent allocations over a single good," Economic Theory, Springer, vol. 40(1), pages 27-45, July.
  3. Luis C. Corchon, 2007. "The theory of implementation : what did we learn?," Economics Working Papers we081207, Universidad Carlos III, Departamento de Economía.
  4. BOCHET, Olivier, 2005. "Implementation of the Walrasian correspondence: the boundary problem," CORE Discussion Papers 2005060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. R?bert F. Veszteg, 2004. "Fairness under Uncertainty with Indivisibilities," UFAE and IAE Working Papers 613.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  6. Amorós, Pablo, 2009. "Eliciting socially optimal rankings from unfair jurors," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1211-1226, May.
  7. Takashi Hayashi & Toyotaka Sakai, 2009. "Nash implementation of competitive equilibria in the job-matching market," International Journal of Game Theory, Springer, vol. 38(4), pages 453-467, November.

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