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We consider the problem of fairly allocating a bundle of infinitely divisible commodities among a group of agents with "classical" preferences. We propose to measure an agent's "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, Decision and Organization, U. Minnesota Press), we identify the equilibrium allocations of the manipulation game associated with this solution when all commodities are normal: (i) for each preference profile, each equal-division constrained Walrasian allocation is an equilibrium allocation; (ii) conversely, each equilibrium allocation is equal-division constrained Walrasian. (iii) Furthermore, we show that if normality of goods is dropped, then equilibrium allocations may not be efficient.

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File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_552.pdf
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Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 552.

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Length: 30 pages
Date of creation: Aug 2009
Date of revision:
Handle: RePEc:roc:rocher:552
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University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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  8. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  9. 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.
  10. 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.
  11. Thomson, William, 1988. "The Manipulability of the Shapley-Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 101-27.
  12. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
  13. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  14. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
  15. 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.
  16. José Alcalde, 1995. "Implementation of Stable Solutions to Marriage Problems," Working Papers. Serie AD 1995-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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  18. Serizawa, Shigehiro, 2002. "Inefficiency of Strategy-Proof Rules for Pure Exchange Economies," Journal of Economic Theory, Elsevier, vol. 106(2), pages 219-241, October.
  19. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer;Society for Economic Design, vol. 4(1), pages 13-33.
  20. 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.
  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. William Thomson, 1984. "The Manipulability of Resource Allocation Mechanisms," Review of Economic Studies, Oxford University Press, vol. 51(3), pages 447-460.
  23. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
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  25. Crawford, Vincent P., 1980. "Maximin behavior and efficient allocation," Economics Letters, Elsevier, vol. 6(3), pages 211-215.
  26. 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.
  27. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
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