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No-Envy and Egalitarian-Equivalence under Multi-Object-Demand for Heterogeneous Objects

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  • Duygu Yengin

    (School of Economics, University of Adelaide)

Abstract

We study the problem of allocating heterogeneous indivisible tasks in a multi-object-demand model (i.e., each agent can be assigned multiple objects) where monetary transfers are allowed. Agents. costs for performing tasks are their private information and depend on what other tasks they are obtained with. First, we show that when costs are unrestricted or superadditive, then there is no envy-free and egalitarian-equivalent mechanism that assigns the tasks efficiently. Then, we characterize the class of envy-free and egalitarian-equivalent Groves mechanisms when costs are subadditive. Finally, within this class, we identify the Pareto-dominant subclass under a bounded-deficit condition. We show that the mechanisms in this subclass are Pareto-undominated by any other Groves mechanism or neutral Weighted-Groves mechanism satisfying the same bounded-deficit condition.

Suggested Citation

  • Duygu Yengin, 2015. "No-Envy and Egalitarian-Equivalence under Multi-Object-Demand for Heterogeneous Objects," School of Economics and Public Policy Working Papers 2015-10, University of Adelaide, School of Economics and Public Policy.
    • Handle: RePEc:adl:wpaper:2015-10
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    File URL: https://economics.adelaide.edu.au/research/papers/doc/wp2015-10.pdf
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    Cited by:

    1. Grossman, Zachary & Pincus, Jonathan & Shapiro, Perry & Yengin, Duygu, 2019. "Second-best mechanisms for land assembly and hold-out problems," Journal of Public Economics, Elsevier, vol. 175(C), pages 1-16.
    2. Chun, Youngsub & Yengin, Duygu, 2017. "Welfare lower bounds and strategy-proofness in the queueing problem," Games and Economic Behavior, Elsevier, vol. 102(C), pages 462-476.
    3. Mackenzie, Andrew & Trudeau, Christian, 2023. "On Groves mechanisms for costly inclusion," Theoretical Economics, Econometric Society, vol. 18(3), July.
    4. Hagen, Martin, 2023. "Collusion-proof mechanisms for multi-unit procurement," Games and Economic Behavior, Elsevier, vol. 138(C), pages 281-298.
    5. Duygu Yengin, 2017. "No-envy and egalitarian-equivalence under multi-object-demand for heterogeneous objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 81-108, January.
    6. Hiroki Shinozaki, 2022. "Egalitarian-Equivalence and Strategy-Proofness in the Object Allocation Problem with Non-Quasi-Linear Preferences," Games, MDPI, vol. 13(6), pages 1-24, November.
    7. Mackenzie, Andrew & Trudeau, Christian, 2018. "Club good mechanisms: from free-riders to citizen-shareholders, from impossibility to characterization," Research Memorandum 012, Maastricht University, Graduate School of Business and Economics (GSBE).
    8. Susumu Cato, 2020. "Compatibility of egalitarian equivalence and envy-freeness in a continuum-agent economy," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 97-103, April.
    9. Yengin, Duygu & Chun, Youngsub, 2020. "No-envy, solidarity, and strategy-proofness in the queueing problem," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 87-97.

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    More about this item

    Keywords

    egalitarianism; egalitarian-equivalence; no-envy; strategy-proofness; population monotonicity; fair division; the Groves mechanisms; the Weighted-Groves mechanisms; allocation of indivisible goods and money; multi-object-demand; discrete public goods.;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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