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Divide-and-Permute

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Author Info
William Thomson () (University of Rochester)

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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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Publisher 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

Contact details of provider:
Postal: UNIVERSITY OF ROCHESTER, CENTER FOR ECONOMIC RESEARCH, DEPARTMENT OF ECONOMICS, HARKNESS 231 ROCHESTER NEW YORK 14627 U.S.A.

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Related research
Keywords: Nash implementation. No-envy. Divide-and-permute.

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This paper has been announced in the following NEP Reports: References listed on IDEAS
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. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Blackwell Publishing, vol. 56(4), pages 603-11, October. [Downloadable!] (restricted)
  2. Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, vol. 52(5), pages 1167-77, September. [Downloadable!] (restricted)
  3. Kolpin, Van, 1991. "Equity and the core," Mathematical Social Sciences, Elsevier, vol. 22(2), pages 137-150, October. [Downloadable!] (restricted)
  4. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January. [Downloadable!] (restricted)
  5. Lin Zhou, 1990. "Inefficiency of Strategy-Proof Allocation Mechanisms in Pure Exchange Economies," Cowles Foundation Discussion Papers 954, Cowles Foundation, Yale University. [Downloadable!]
  6. Tian, Guoqiang, 1989. "Implementation of the Lindahl Correspondence by a Single-Valued, Feasible, and Continuous Mechanism," Review of Economic Studies, Blackwell Publishing, vol. 56(4), pages 613-21, October. [Downloadable!] (restricted)
  7. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May. [Downloadable!] (restricted)
  8. Pazner, Elisha A & Schmeidler, David, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, MIT Press, vol. 92(4), pages 671-87, November. [Downloadable!] (restricted)
    Other versions:
  9. 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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  10. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January. [Downloadable!] (restricted)
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    • Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  11. Reichelstein, Stefan & Reiter, Stanley, 1988. "Game Forms with Minimal Message Spaces," Econometrica, Econometric Society, vol. 56(3), pages 661-92, May. [Downloadable!] (restricted)
  12. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Blackwell Publishing, vol. 54(2), pages 193-208, April. [Downloadable!] (restricted)
  13. Berliant, Marcus & Thomson, William & Dunz, Karl, 1992. "On the fair division of a heterogeneous commodity," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 201-216. [Downloadable!] (restricted)
  14. Crawford, Vincent P, 1977. "A Game of Fair Division," Review of Economic Studies, Blackwell Publishing, vol. 44(2), pages 235-47, June. [Downloadable!] (restricted)
  15. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February. [Downloadable!] (restricted)
  16. 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. [Downloadable!] (restricted)
Full references

Cited by:
(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. Marco LiCalzi & Antonio Nicolò, 2005. "Efficient Egalitarian Equivalent Allocations over a Single Good," Microeconomics 0510014, EconWPA. [Downloadable!]
    Other versions:
  2. Antonio Nicolo' & Yan Yu, 2006. "Strategic Divide and Choose," "Marco Fanno" Working Papers 0022, Dipartimento di Scienze Economiche "Marco Fanno". [Downloadable!]
  3. Luis C. Corchon, 2007. "The theory of implementation : what did we learn?," Economics Working Papers we081207, Universidad Carlos III, Departamento de Economía. [Downloadable!]
  4. Veiga Helena & Vorsatz Marc, 2006. "Price Manipulation in an Experimental Asset Market," Research Memoranda 024, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  5. Pablo Amorós, 2006. "Eliciting Socially Optimal Rankings from Unfair Jurors," Economic Working Papers at Centro de Estudios Andaluces E2006/10, Centro de Estudios Andaluces. [Downloadable!]
  6. Eiichi Miyagawa, 2002. "Subgame-perfect implementation of bargaining solutions," Discussion Papers 0102-16, Columbia University, Department of Economics. [Downloadable!]
    Other versions:
  7. 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). [Downloadable!]
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