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  • Velez, Rodrigo A.
  • Thomson, William

Abstract

We consider the problem of fairly allocating a bundle of infinitely divisible goods among a group of agents with “classical” preferences. We propose to measure an agentʼs “sacrifice” at an allocation by the size of the set of feasible bundles that the agent prefers to her consumption. As a solution, we select the allocations at which sacrifices are equal across agents and this common sacrifice is minimal. We then turn to the manipulability of this solution. In the tradition of Hurwicz (1972), we identify, under some mild assumptions on preferences, the equilibrium allocations of the manipulation game associated with this solution when all commodities are normal: for each preference profile, each equal-division constrained Walrasian allocation is an equilibrium allocation; conversely, each equilibrium allocation is equal-division constrained Walrasian. Furthermore, we show that if normality of goods is dropped, then equilibrium allocations may not be equal-division constrained Walrasian.

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Bibliographic Info

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

Volume (Year): 75 (2012)
Issue (Month): 2 ()
Pages: 948-963

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Handle: RePEc:eee:gamebe:v:75:y:2012:i:2:p:948-963

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Equal-sacrifice solution; Manipulation game; Equal-division Walrasian solution;

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  1. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  2. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
  3. Helmuts Azacis, 2004. "Double Implementation in a Market for Indivisible Goods with a Price Constraint," UFAE and IAE Working Papers 623.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. Thomson, William, 1988. "The Manipulability of the Shapley-Value," International Journal of Game Theory, Springer, vol. 17(2), pages 101-27.
  5. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
  6. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
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  8. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
  9. William Thomson, 2010. "Implementation of solutions to the problem of fair division when preferences are single-peaked," Review of Economic Design, Springer, vol. 14(1), pages 1-15, March.
  10. KIBRIS, Özgür, . "Misrepresentation of utilities in bargaining: pure exchange and public good economies," CORE Discussion Papers RP -1546, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  12. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, April.
  13. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer, vol. 4(1), pages 13-33.
  14. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
  15. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
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  18. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
  19. Murat R. Sertel & M. Remzi Sanver, 2004. "Strong equilibrium outcomes of voting games ¶are the generalized Condorcet winners," Social Choice and Welfare, Springer, vol. 22(2), pages 331-347, 04.
  20. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
  21. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
  22. Thomson, William, 1984. "The Manipulability of Resource Allocation Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 51(3), pages 447-60, July.
  23. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, vol. 18(4), pages 655-708.
  24. Hurwicz, Leonid, 1979. "On allocations attainable through Nash equilibria," Journal of Economic Theory, Elsevier, vol. 21(1), pages 140-165, August.
  25. Serizawa, Shigehiro, 2002. "Inefficiency of Strategy-Proof Rules for Pure Exchange Economies," Journal of Economic Theory, Elsevier, vol. 106(2), pages 219-241, October.
  26. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-54, July.
  27. 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.
  28. Carmen Beviá, 2010. "Manipulation games in economies with indivisible goods," International Journal of Game Theory, Springer, vol. 39(1), pages 209-222, March.
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