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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
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. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
  2. Crawford, Vincent P., 1980. "Maximin behavior and efficient allocation," Economics Letters, Elsevier, vol. 6(3), pages 211-215.
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  4. 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.
  5. 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).
  6. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
  7. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
  8. 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.
  9. Hurwicz, Leonid, 1979. "On allocations attainable through Nash equilibria," Journal of Economic Theory, Elsevier, vol. 21(1), pages 140-165, August.
  10. Thomson, William, 1988. "The Manipulability of the Shapley-Value," International Journal of Game Theory, Springer, vol. 17(2), pages 101-27.
  11. Postlewaite, Andrew, 1979. "Manipulation via Endowments," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 255-62, April.
  12. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
  13. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
  14. Thomson, W., 1996. "Monotonic Extension on Economic Domains," RCER Working Papers 431, University of Rochester - Center for Economic Research (RCER).
  15. 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.
  16. 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.
  17. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882.
  18. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
  19. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  20. José Alcalde, 1995. "Implementation of Stable Solutions to Marriage Problems," Working Papers. Serie AD 1995-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  21. Thomson, William, 1984. "The Manipulability of Resource Allocation Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 51(3), pages 447-60, July.
  22. Serizawa, Shigehiro, 2002. "Inefficiency of Strategy-Proof Rules for Pure Exchange Economies," Journal of Economic Theory, Elsevier, vol. 106(2), pages 219-241, October.
  23. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  24. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
  25. Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  26. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
  27. Carmen Beviá, 2010. "Manipulation games in economies with indivisible goods," International Journal of Game Theory, Springer, vol. 39(1), pages 209-222, March.
  28. François Maniquet, 2003. "Implementation of allocation rules under perfect information," Social Choice and Welfare, Springer, vol. 21(2), pages 323-346, October.
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