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Dividing bads under additive utilities

Author

Listed:
  • Anna Bogomolnaia

    (University of Glasgow
    Higher School of Economics)

  • Hervé Moulin

    (University of Glasgow
    Higher School of Economics)

  • Fedor Sandomirskiy

    (Higher School of Economics
    St. Petersburg Institute for Economics and Mathematics)

  • Elena Yanovskaia

    (Higher School of Economics)

Abstract

We compare the Egalitarian rule (aka Egalitarian Equivalent) and the Competitive rule (aka Comeptitive Equilibrium with Equal Incomes) to divide bads (chores). They are both welfarist: the competitive disutility profile(s) are the critical points of their Nash product on the set of efficient feasible profiles. The C rule is Envy Free, Maskin Monotonic, and has better incentives properties than the E rule. But, unlike the E rule, it can be wildly multivalued, admits no selection continuous in the utility and endowment parameters, and is harder to compute. Thus in the division of bads, unlike that of goods, no rule normatively dominates the other.

Suggested Citation

  • Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy & Elena Yanovskaia, 2019. "Dividing bads under additive utilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 395-417, March.
    • Handle: RePEc:spr:sochwe:v:52:y:2019:i:3:d:10.1007_s00355-018-1157-x
    DOI: 10.1007/s00355-018-1157-x
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    Cited by:

    1. Mariotti, Marco & Wen, Quan, 2021. "A noncooperative foundation of the competitive divisions for bads," Journal of Economic Theory, Elsevier, vol. 194(C).
    2. Moshe Babaioff & Noam Nisan & Inbal Talgam-Cohen, 2021. "Competitive Equilibrium with Indivisible Goods and Generic Budgets," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 382-403, February.
    3. Kim, Duk Gyoo & Lim, Wooyoung, 2024. "Multilateral bargaining over the division of losses," Games and Economic Behavior, Elsevier, vol. 146(C), pages 59-76.
    4. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy, 2022. "On the Fair Division of a Random Object," Management Science, INFORMS, vol. 68(2), pages 1174-1194, February.
    5. Miralles, Antonio & Pycia, Marek, 2021. "Foundations of pseudomarkets: Walrasian equilibria for discrete resources," Journal of Economic Theory, Elsevier, vol. 196(C).
    6. Dall’Aglio, Marco, 2023. "Fair division of goods in the shadow of market values," European Journal of Operational Research, Elsevier, vol. 307(2), pages 785-801.
    7. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    8. Krist'of B'erczi & Erika R. B'erczi-Kov'acs & Endre Boros & Fekadu Tolessa Gedefa & Naoyuki Kamiyama & Telikepalli Kavitha & Yusuke Kobayashi & Kazuhisa Makino, 2020. "Envy-free Relaxations for Goods, Chores, and Mixed Items," Papers 2006.04428, arXiv.org.
    9. Anna Bogomolnaia & Hervé Moulin, 2023. "Guarantees in Fair Division: General or Monotone Preferences," Mathematics of Operations Research, INFORMS, vol. 48(1), pages 160-176, February.
    10. Fedor Sandomirskiy & Erel Segal-Halevi, 2019. "Efficient Fair Division with Minimal Sharing," Papers 1908.01669, arXiv.org, revised Apr 2022.

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