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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Games and Economic Behavior.
Volume (Year): 75 (2012)
Issue (Month): 2 ()
Contact details of provider:
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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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).
- 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.
- 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.
- 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.
- 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.
- 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.
- Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992.
Cambridge University Press, number 9780521437882, October.
- 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.
- Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
- Maskin, Eric & Sjostrom, Tomas, 2002.
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
- Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
- Matthew O. Jackson, 2001.
"A crash course in implementation theory,"
Social Choice and Welfare,
Springer, vol. 18(4), pages 655-708.
- William Thomson, 1999.
"Monotonic extensions on economic domains,"
Review of Economic Design,
Springer, vol. 4(1), pages 13-33.
- 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.
- 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.
- Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
- William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
- Barbera, Salvador & Jackson, Matthew O, 1995.
Econometric Society, vol. 63(1), pages 51-87, January.
- Thomson, William, 1984. "The Manipulability of Resource Allocation Mechanisms," Review of Economic Studies, Wiley Blackwell, vol. 51(3), pages 447-60, July.
- Postlewaite, Andrew, 1979. "Manipulation via Endowments," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 255-62, April.
- 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.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
- Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
- Thomson, William, 1988. "The Manipulability of the Shapley-Value," International Journal of Game Theory, Springer, vol. 17(2), pages 101-27.
- 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., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.