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Divide-and-Permute

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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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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  1. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January.
  2. Thomson, William, 1994. "Consistent extensions," Mathematical Social Sciences, Elsevier, vol. 28(1), pages 35-49, August.
  3. Crawford, Vincent P, 1977. "A Game of Fair Division," Review of Economic Studies, Wiley Blackwell, vol. 44(2), pages 235-47, June.
  4. 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.
  5. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  6. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  7. 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.
  8. Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 193-208, April.
  10. James Schummer, 1996. "Strategy-proofness versus efficiency on restricted domains of exchange economies," Social Choice and Welfare, Springer, vol. 14(1), pages 47-56.
  11. 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.
  12. Kolpin, Van, 1991. "Equity and the core," Mathematical Social Sciences, Elsevier, vol. 22(2), pages 137-150, October.
  13. Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, vol. 52(5), pages 1167-77, September.
  14. Postlewaite, Andrew & Wettstein, David, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 603-11, October.
  15. Yamato Takehiko, 1993. "Double Implementation in Nash and Undominated Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 59(2), pages 311-323, April.
  16. Lin Zhou, 1990. "Inefficiency of Strategy-Proof Allocation Mechanisms in Pure Exchange Economies," Cowles Foundation Discussion Papers 954, Cowles Foundation for Research in Economics, Yale University.
  17. Crawford, Vincent P, 1979. "A Procedure for Generating Pareto-Efficient Egalitarian-Equivalent Allocations," Econometrica, Econometric Society, vol. 47(1), pages 49-60, January.
  18. Jackson, Matthew O, 1992. "Implementation in Undominated.Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 59(4), pages 757-75, October.
  19. 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.
  20. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
  21. 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.
  22. repec:cup:cbooks:9780521556446 is not listed on IDEAS
  23. Thomson, William, 1982. "An informationally efficient equity criterion," Journal of Public Economics, Elsevier, vol. 18(2), pages 243-263, July.
  24. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February.
  25. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
  26. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer, vol. 4(1), pages 13-33.
  27. 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.
  28. Reichelstein, Stefan & Reiter, Stanley, 1988. "Game Forms with Minimal Message Spaces," Econometrica, Econometric Society, vol. 56(3), pages 661-92, May.
  29. Tian, Guoqiang, 1989. "Implementation of the Lindahl Correspondence by a Single-Valued, Feasible, and Continuous Mechanism," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 613-21, October.
  30. 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.
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