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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. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  2. Thomson, William, 1984. "The Manipulability of Resource Allocation Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 51(3), pages 447-60, July.
  3. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
  4. 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.
  5. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
  6. Thomson, W., 1996. "Monotonic Extension on Economic Domains," RCER Working Papers 431, University of Rochester - Center for Economic Research (RCER).
  7. Salvador Barbera & Matthew O. Jackson, 1993. "Strategy-Proof Exchange," Discussion Papers 1021, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. MANIQUET, François, . "Implementation of allocation rules under perfect information," CORE Discussion Papers RP -1734, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, vol. 18(4), pages 655-708.
  10. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  11. 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.
  12. Carmen Beviá, 2010. "Manipulation games in economies with indivisible goods," International Journal of Game Theory, Springer, vol. 39(1), pages 209-222, March.
  13. 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.
  14. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, September.
  15. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
  16. Hurwicz, Leonid, 1979. "On allocations attainable through Nash equilibria," Journal of Economic Theory, Elsevier, vol. 21(1), pages 140-165, August.
  17. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
  18. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
  19. Murat R. Sertel & Remzi Sanver, 2001. "Strong Equilibrium Outcomes of Voting Games are the Generalized Condorcet Winners," Departmental Working Papers 0107, Bilkent University, Department of Economics.
  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. Serizawa, Shigehiro, 2002. "Inefficiency of Strategy-Proof Rules for Pure Exchange Economies," Journal of Economic Theory, Elsevier, vol. 106(2), pages 219-241, October.
  22. Postlewaite, Andrew, 1979. "Manipulation via Endowments," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 255-62, April.
  23. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  24. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
  25. Crawford, Vincent P., 1980. "Maximin behavior and efficient allocation," Economics Letters, Elsevier, vol. 6(3), pages 211-215.
  26. 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.
  27. Thomson, William, 1988. "The Manipulability of the Shapley-Value," International Journal of Game Theory, Springer, vol. 17(2), pages 101-27.
  28. 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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