IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v75y2012i2p948-963.html
   My bibliography  Save this article

Let them cheat!

Author

Listed:
  • 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.

Suggested Citation

  • Velez, Rodrigo A. & Thomson, William, 2012. "Let them cheat!," Games and Economic Behavior, Elsevier, vol. 75(2), pages 948-963.
    • Handle: RePEc:eee:gamebe:v:75:y:2012:i:2:p:948-963
    DOI: 10.1016/j.geb.2012.01.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825612000048
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2012.01.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Azacis, Helmuts, 2008. "Double implementation in a market for indivisible goods with a price constraint," Games and Economic Behavior, Elsevier, vol. 62(1), pages 140-154, January.
    2. Andrew Postlewaite, 1979. "Manipulation via Endowments," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 255-262.
    3. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
    4. 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.
    5. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, September.
    6. Sobel, Joel, 2001. "Manipulation of Preferences and Relative Utilitarianism," Games and Economic Behavior, Elsevier, vol. 37(1), pages 196-215, October.
    7. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer;Society for Economic Design, vol. 4(1), pages 13-33.
    8. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
    9. 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.
    10. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
    11. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    12. William Thomson, 1984. "The Manipulability of Resource Allocation Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(3), pages 447-460.
    13. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-954, July.
    14. Hurwicz, Leonid, 1979. "On allocations attainable through Nash equilibria," Journal of Economic Theory, Elsevier, vol. 21(1), pages 140-165, August.
    15. Crawford, Vincent P., 1980. "Maximin behavior and efficient allocation," Economics Letters, Elsevier, vol. 6(3), pages 211-215.
    16. Thomson, W., 1990. "Monotonic And Consistent Solutions To The Problem Of Fair Allocation When Preferences Are Single-Peaked," RCER Working Papers 231, University of Rochester - Center for Economic Research (RCER).
    17. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    18. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    19. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    20. Sobel, Joel, 1981. "Distortion of Utilities and the Bargaining Problem," Econometrica, Econometric Society, vol. 49(3), pages 597-619, May.
    21. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
    22. Murat R. Sertel & M. Remzi Sanver, 2004. "Strong equilibrium outcomes of voting games ¶are the generalized Condorcet winners," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 331-347, April.
    23. Tadenuma Koichi & Thomson William, 1995. "Games of Fair Division," Games and Economic Behavior, Elsevier, vol. 9(2), pages 191-204, May.
    24. Thomson, William, 1988. "The Manipulability of the Shapley-Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 101-127.
    25. 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.
    26. 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.
    27. 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.
    28. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
    29. Serizawa, Shigehiro, 2002. "Inefficiency of Strategy-Proof Rules for Pure Exchange Economies," Journal of Economic Theory, Elsevier, vol. 106(2), pages 219-241, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rodrigo A. Velez, 2017. "Equitable rent division," Working Papers 20170818-001, Texas A&M University, Department of Economics.
    2. Fujinaka, Yuji & Wakayama, Takuma, 2015. "Maximal manipulation of envy-free solutions in economies with indivisible goods and money," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 165-185.
    3. Churkin, Andrey & Bialek, Janusz & Pozo, David & Sauma, Enzo & Korgin, Nikolay, 2021. "Review of Cooperative Game Theory applications in power system expansion planning," Renewable and Sustainable Energy Reviews, Elsevier, vol. 145(C).
    4. Biung†Ghi Ju & Juan D. Moreno†Ternero, 2017. "Fair Allocation Of Disputed Properties," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(4), pages 1279-1301, November.
    5. Velez, Rodrigo A., 2015. "Sincere and sophisticated players in an equal-income market," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1114-1129.
    6. Rodrigo A. Velez, 2019. "Expressive mechanisms for equitable rent division on a budget," Papers 1902.02935, arXiv.org, revised Apr 2020.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
    2. Fujinaka, Yuji & Wakayama, Takuma, 2015. "Maximal manipulation of envy-free solutions in economies with indivisible goods and money," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 165-185.
    3. Velez, Rodrigo A., 2015. "Sincere and sophisticated players in an equal-income market," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1114-1129.
    4. Ju, Biung-Ghi, 2005. "Strategy-proof risk sharing," Games and Economic Behavior, Elsevier, vol. 50(2), pages 225-254, February.
    5. Rodrigo A. Velez, 2017. "Equitable rent division," Working Papers 20170818-001, Texas A&M University, Department of Economics.
    6. 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.
    7. repec:cte:werepe:we081207 is not listed on IDEAS
    8. Yamamura, Hirofumi, 2016. "Coalitional stability in the location problem with single-dipped preferences: An application of the minimax theorem," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 48-57.
    9. Thomson, William, 2005. "Divide-and-permute," Games and Economic Behavior, Elsevier, vol. 52(1), pages 186-200, July.
    10. Gomez, Juan Camilo, 2006. "Achieving efficiency with manipulative bargainers," Games and Economic Behavior, Elsevier, vol. 57(2), pages 254-263, November.
    11. Sakai, Toyotaka, 2007. "Fairness and implementability in allocation of indivisible objects with monetary compensations," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 549-563, June.
    12. BOSSERT, Walter & WEYMARK, J.A., 2006. "Social Choice: Recent Developments," Cahiers de recherche 01-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    13. Takashi Hayashi & Toyotaka Sakai, 2009. "Nash implementation of competitive equilibria in the job-matching market," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 453-467, November.
    14. Claus-Jochen Haake & Bettina Klaus, 2009. "Monotonicity and Nash implementation in matching markets with contracts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 393-410, December.
    15. Rodrigo A. Velez, 2017. "Sharing an increase of the rent fairly," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 59-80, January.
    16. Shuhei Morimoto & Shigehiro Serizawa & Stephen Ching, 2013. "A characterization of the uniform rule with several commodities and agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 871-911, March.
    17. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," 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 2, chapter 21, pages 393-506, Elsevier.
    18. Yuji Fujinaka & Toyotaka Sakai, 2009. "The positive consequence of strategic manipulation in indivisible good allocation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 325-348, November.
    19. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
    20. 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.
    21. Claus-Jochen Haake & Bettina Klaus, 2010. "Stability and Nash implementation in matching markets with couples," Theory and Decision, Springer, vol. 69(4), pages 537-554, October.

    More about this item

    Keywords

    Equal-sacrifice solution; Manipulation game; Equal-division Walrasian solution;
    All these keywords.

    JEL classification:

    • 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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:75:y:2012:i:2:p:948-963. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.