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The Manipulability of Fair Solutions in Assignment of an Indivisible Object with Monetary Transfers

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  • YUJI FUJINAKA
  • TOYOTAKA SAKAI

Abstract

Public decision making often involves the problem of fairly assigning one indivisible object to agents with monetary transfers. An example is the choice of the location of a garbage incineration facility where the accepting district should receive fair compensations from other districts. In this problem, we show that for broad classes of solutions satisfying a welfare lower bound and an efficiency‐oriented condition, the set of equilibrium allocations in the manipulation game associated with a given solution coincides with the set of all envy‐free allocations. This generalizes Tadenuma and Thomson's equivalence result for a class of envy‐free solutions. Our result covers the Shapley value, which is not covered by Tadenuma and Thomson's result.

Suggested Citation

  • Yuji Fujinaka & Toyotaka Sakai, 2007. "The Manipulability of Fair Solutions in Assignment of an Indivisible Object with Monetary Transfers," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(6), pages 993-1011, December.
    • Handle: RePEc:bla:jpbect:v:9:y:2007:i:6:p:993-1011
    DOI: 10.1111/j.1467-9779.2007.00341.x
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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.
    2. Conan Mukherjee, 2014. "Fair and group strategy-proof good allocation with money," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 289-311, February.
    3. 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.
    4. Yuji Fujinaka, 2008. "A Bayesian Incentive Compatible Mechanism for Fair Division," ISER Discussion Paper 0721, Institute of Social and Economic Research, Osaka University.
    5. Toyotaka Sakai, 2012. "Fair waste pricing: an axiomatic analysis to the NIMBY problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 499-521, June.
    6. 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.
    7. Kazuhiko Hashimoto, 2018. "Strategy-proofness and identical preferences lower bound in allocation problem of indivisible objects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 1045-1078, June.
    8. Toyotaka Sakai, 2008. "Second price auctions on general preference domains: two characterizations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(2), pages 347-356, November.
    9. Di Feng & Jacob Coreno, 2024. "Justified Fairness in House Allocation Problems: two Characterizations of Strategy-proof Mechanisms," Papers 2407.14101, arXiv.org.
    10. Toyotaka Sakai, 2013. "An equity characterization of second price auctions when preferences may not be quasilinear," Review of Economic Design, Springer;Society for Economic Design, vol. 17(1), pages 17-26, March.
    11. Hirofumi Yamamura & Ryo Kawasaki, 2013. "Generalized average rules as stable Nash mechanisms to implement generalized median rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 815-832, March.

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