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Least Manipulable Envy-free Rules in Economies with Indivisibilities

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  • Andersson, Tommy

    ()
    (Department of Economics, Lund University)

  • Ehlers, Lars

    ()
    (Université de Montréal)

  • Svensson, Lars-Gunnar

    ()
    (Department of Economics, Lund University)

Abstract

We consider envy-free and budget-balanced allocation rules for problems where a number of indivisible objects and a fixed amount of money is allocated among a group of agents. In "small" economies, we identify under classical preferences each agent's maximal gain from manipulation. Using this result we find the envy-free and budget-balanced allocation rules which are least manipulable for each preference profile in terms of any agent's maximal gain. If preferences are quasi-linear, then we can find an envy-free and budget-balanced allocation rule such that for any problem, the maximal utility gain from manipulation is equalized among all agents.

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Bibliographic Info

Paper provided by Lund University, Department of Economics in its series Working Papers with number 2012:8.

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Length: 16 pages
Date of creation: 25 Apr 2012
Date of revision: 30 Sep 2013
Publication status: Published as Andersson, Tommy, Lars Ehlers and Lars-Gunnar Svensson, 'Least Manipulable Envy-free Rules in Economies with Indivisibilities' in Mathematical Social Sciences, 2014, pages 43-49.
Handle: RePEc:hhs:lunewp:2012_008

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Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund,Sweden
Phone: +46 +46 222 0000
Fax: +46 +46 2224613
Web page: http://www.nek.lu.se/en
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Keywords: (Least) Manipulability; Envy-freeness; Budget-Balance; Indivisibilities.;

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References

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  1. Flip Klijn, 2000. "An algorithm for envy-free allocations in an economy with indivisible objects and money," Social Choice and Welfare, Springer, vol. 17(2), pages 201-215.
  2. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer, vol. 21(2), pages 241-261, 03.
  3. Svensson, Lars-Gunnar, 2006. "Coalition Strategy-Proofness and Fairness," Working Papers 2006:10, Lund University, Department of Economics.
  4. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
  5. Paula Jaramillo & Çagatay Kayi & Flip Klijn, 2012. "Asymmetrically Fair Rules for an Indivisible Good Problem with a Budget Constraint," Working Papers 610, Barcelona Graduate School of Economics.
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  8. Maus, Stefan & Peters, Hans & Storcken, Ton, 2007. "Anonymous voting and minimal manipulability," Journal of Economic Theory, Elsevier, vol. 135(1), pages 533-544, July.
  9. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-39, July.
  10. Ning Sun & Zaifu Yang, 2003. "A General Strategy Proof Fair Allocation Mechanism," Working Papers 346, Bielefeld University, Center for Mathematical Economics.
  11. Parag A. Pathak & Tayfun Sönmez, 2013. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation," American Economic Review, American Economic Association, vol. 103(1), pages 80-106, February.
  12. Stefan Maus & Hans Peters & Ton Storcken, 2007. "Minimal manipulability: anonymity and unanimity," Social Choice and Welfare, Springer, vol. 29(2), pages 247-269, September.
  13. ANDERSSON, Tommy & EHLERS, Lars & SVENSSON, Lars-Gunnar, 2010. "Budget-Balance, Fairness and Minimal Manipulability," Cahiers de recherche 18-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  14. 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.
  15. Claus-Jochen Haake & Matthias G. Raith & Francis Su, 2000. "Bidding for Envy-Freeness: A Procedural Approach to n-Player Fair Division Problems," Claremont Colleges Working Papers 2000-47, Claremont Colleges.
  16. Sun, Ning & Yang, Zaifu, 2003. "A general strategy proof fair allocation mechanism," Economics Letters, Elsevier, vol. 81(1), pages 73-79, October.
  17. Roberts, Donald John & Postlewaite, Andrew, 1976. "The Incentives for Price-Taking Behavior in Large Exchange Economies," Econometrica, Econometric Society, vol. 44(1), pages 115-27, January.
  18. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  19. Andersson, Tommy & Svensson, Lars-Gunnar, 2008. "Non-manipulable assignment of individuals to positions revisited," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 350-354, November.
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