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Maximal manipulation of envy-free solutions in economies with indivisible goods and money

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  • Fujinaka, Yuji
  • Wakayama, Takuma

Abstract

We consider the problem of the fair allocation of indivisible goods and money with non-quasi-linear preferences. The purpose of the present study is to examine strategic manipulation under envy-free solutions. We show that under a certain domain-richness condition, each individual obtains the welfare level of his “optimal” envy-free allocation by maximally manipulating the solutions. This maximal manipulation theorem is helpful in analyzing the set of Nash equilibrium allocations in the direct revelation games associated with a given envy-free solution: if an envy-free solution satisfies a mild condition, the set of Nash equilibrium allocations in its associated direct revelation game coincides with that of envy-free allocations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jetheo:v:158:y:2015:i:pa:p:165-185
    DOI: 10.1016/j.jet.2015.03.014
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    Cited by:

    1. Rodrigo A. Velez, 2017. "Equitable rent division," Working Papers 20170818-001, Texas A&M University, Department of Economics.
    2. Decerf, Benoit & Van der Linden, Martin, 2021. "Manipulability in school choice," Journal of Economic Theory, Elsevier, vol. 197(C).
    3. 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.
    4. DECERF, Benoit & VAN DER LINDEN, Martin, 2016. "A criterion to compare mechanisms when solutions are not unique, with applications to constrained school choice," LIDAM Discussion Papers CORE 2016033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. David Pérez-Castrillo & Marilda Sotomayor, 2017. "On the manipulability of competitive equilibrium rules in many-to-many buyer–seller markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1137-1161, November.
    6. Velez, Rodrigo A., 2023. "Equitable rent division on a soft budget," Games and Economic Behavior, Elsevier, vol. 139(C), pages 1-14.
    7. Tommy Andersson & Lars Ehlers, 2022. "An algorithm for identifying least manipulable envy‐free and budget‐balanced allocations in economies with indivisibilities," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 50-60, March.
    8. Nicolò, Antonio & Velez, Rodrigo A., 2017. "Divide and compromise," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 100-110.
    9. Kristof Bosmans & Z. Emel Öztürk, 2018. "An axiomatic approach to the measurement of envy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 247-264, February.
    10. Rodrigo A. Velez, 2019. "Expressive mechanisms for equitable rent division on a budget," Papers 1902.02935, arXiv.org, revised Apr 2020.
    11. 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.

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    More about this item

    Keywords

    Envy-freeness; Indivisible good; Manipulation; Nash implementation;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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