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  • Thomson, William

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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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 52 (2005)
Issue (Month): 1 (July)
Pages: 186-200

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Handle: RePEc:eee:gamebe:v:52:y:2005:i:1:p:186-200
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  1. Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers 5-01-1, Pennsylvania State University, Department of Economics.
  2. Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. James Schummer, 1996. "Strategy-proofness versus efficiency on restricted domains of exchange economies," Social Choice and Welfare, Springer, vol. 14(1), pages 47-56.
  4. 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.
  5. Walker, Mark, 1981. "A Simple Incentive Compatible Scheme for Attaining Lindahl Allocations," Econometrica, Econometric Society, vol. 49(1), pages 65-71, January.
  6. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Oxford University Press, vol. 59(4), pages 757-775.
  7. Guoqiang Tian, 1989. "Implementation of the Lindahl Correspondence by a Single-Valued, Feasible, and Continuous Mechanism," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 613-621.
  8. Kolpin, Van, 1991. "Equity and the core," Mathematical Social Sciences, Elsevier, vol. 22(2), pages 137-150, October.
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  10. Crawford, Vincent P, 1979. "A Procedure for Generating Pareto-Efficient Egalitarian-Equivalent Allocations," Econometrica, Econometric Society, vol. 47(1), pages 49-60, January.
  11. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
  12. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446.
  13. Vincent P. Crawford, 1977. "A Game of Fair Division," Review of Economic Studies, Oxford University Press, vol. 44(2), pages 235-247.
  14. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer, vol. 4(1), pages 13-33.
  15. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February.
  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.
  17. Saijo, T. & Tatamitani, Y. & Yamato, T., 1994. "Toward Natural Implementation," ISER Discussion Paper 0340, Institute of Social and Economic Research, Osaka University.
    • 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.
  18. Andrew Postlewaite & David Wettstein, 1989. "Feasible and Continuous Implementation," Review of Economic Studies, Oxford University Press, vol. 56(4), pages 603-611.
  19. Yamato Takehiko, 1993. "Double Implementation in Nash and Undominated Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 59(2), pages 311-323, April.
  20. Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, vol. 52(5), pages 1167-77, September.
  21. Thomson, William, 1982. "An informationally efficient equity criterion," Journal of Public Economics, Elsevier, vol. 18(2), pages 243-263, July.
  22. Thomas R. Palfrey & Sanjay Srivastava, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Oxford University Press, vol. 54(2), pages 193-208.
  23. 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.
  24. L. Hurwicz, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 217-225.
  25. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
  26. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  27. 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.
  28. Thomson, W., 1992. "Consistent Extensions," RCER Working Papers 329, University of Rochester - Center for Economic Research (RCER).
  29. Elisha A. Pazner & David Schmeidler, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, Oxford University Press, vol. 92(4), pages 671-687.
  30. 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.
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