Let them cheat!
AbstractWe 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 InfoArticle provided by Elsevier in its journal Games and Economic Behavior.
Volume (Year): 75 (2012)
Issue (Month): 2 ()
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Web page: http://www.elsevier.com/locate/inca/622836
Equal-sacrifice solution; Manipulation game; Equal-division Walrasian solution;
Other versions of this item:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
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- 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.
- Maskin, Eric, 1999.
"Nash Equilibrium and Welfare Optimality,"
Review of Economic Studies,
Wiley Blackwell, vol. 66(1), pages 23-38, January.
- Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
- 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.
- Barbera, Salvador & Jackson, Matthew O, 1995.
Econometric Society, vol. 63(1), pages 51-87, January.
- 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.
- Postlewaite, Andrew, 1979. "Manipulation via Endowments," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 255-62, April.
- 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.
- 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).
- William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
- Maskin, Eric & Sjostrom, Tomas, 2001.
5-01-1, Pennsylvania State University, Department of Economics.
- Thomson, William, 1988. "The Manipulability of the Shapley-Value," International Journal of Game Theory, Springer, vol. 17(2), pages 101-27.
- William Thomson, 1999.
"Monotonic extensions on economic domains,"
Review of Economic Design,
Springer, vol. 4(1), pages 13-33.
- Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
- Jackson, Matthew O., 1999.
"A Crash Course in Implementation Theory,"
1076, California Institute of Technology, Division of the Humanities and Social Sciences.
- Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
- Serizawa, Shigehiro, 2002. "Inefficiency of Strategy-Proof Rules for Pure Exchange Economies," Journal of Economic Theory, Elsevier, vol. 106(2), pages 219-241, October.
- Roth, Alvin E. & Sotomayor, Marilda, 1992.
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
- 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).
- François Maniquet, 2003. "Implementation of allocation rules under perfect information," Social Choice and Welfare, Springer, vol. 21(2), pages 323-346, October.
- Hurwicz, Leonid, 1979. "On allocations attainable through Nash equilibria," Journal of Economic Theory, Elsevier, vol. 21(1), pages 140-165, August.
- Alcalde, Jose, 1996.
"Implementation of Stable Solutions to Marriage Problems,"
Journal of Economic Theory,
Elsevier, vol. 69(1), pages 240-254, April.
- José Alcalde, 1995. "Implementation of Stable Solutions to Marriage Problems," Working Papers. Serie AD 1995-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
- Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
- Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
- 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.
- 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.
- Thomson, William, 1984. "The Manipulability of Resource Allocation Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 51(3), pages 447-60, July.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
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