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  • Velez, Rodrigo A.
  • Thomson, William

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. William Thomson, 2010. "Implementation of solutions to the problem of fair division when preferences are single-peaked," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 1-15, March.
  2. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
  3. Carmen Beviá, 2010. "Manipulation games in economies with indivisible goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 209-222, March.
  4. Murat R. Sertel & Remzi Sanver, 2001. "Strong Equilibrium Outcomes of Voting Games are the Generalized Condorcet Winners," Working Papers 0107, Department of Economics, Bilkent University.
  5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, June.
  6. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  7. Kibris, Ozgur, 2002. "Misrepresentation of Utilities in Bargaining: Pure Exchange and Public Good Economies," Games and Economic Behavior, Elsevier, vol. 39(1), pages 91-110, April.
  8. William Thomson, 1984. "The Manipulability of Resource Allocation Mechanisms," Review of Economic Studies, Oxford University Press, vol. 51(3), pages 447-460.
  9. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
  10. Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
  12. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  13. 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.
  14. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
  15. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, June.
  16. Serizawa, Shigehiro, 2002. "Inefficiency of Strategy-Proof Rules for Pure Exchange Economies," Journal of Economic Theory, Elsevier, vol. 106(2), pages 219-241, October.
  17. François Maniquet, 2003. "Implementation of allocation rules under perfect information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 323-346, October.
  18. Azacis, Helmuts, 2005. "Double Implementation in a Market for Indivisible Goods with a Price Constraint," Cardiff Economics Working Papers E2005/10, Cardiff University, Cardiff Business School, Economics Section.
  19. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
  20. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
  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.
  22. Andrew Postlewaite, 1979. "Manipulation via Endowments," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 255-262.
  23. Hurwicz, Leonid, 1979. "On allocations attainable through Nash equilibria," Journal of Economic Theory, Elsevier, vol. 21(1), pages 140-165, August.
  24. Crawford, Vincent P., 1980. "Maximin behavior and efficient allocation," Economics Letters, Elsevier, vol. 6(3), pages 211-215.
  25. Thomson, W., 1996. "Monotonic Extension on Economic Domains," RCER Working Papers 431, University of Rochester - Center for Economic Research (RCER).
  26. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
  27. Thomson, William, 1988. "The Manipulability of the Shapley-Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 101-27.
  28. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
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