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Guaranteed shares of benefits and costs

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  • Anna Bogomolnaia
  • Herv'e Moulin

Abstract

In a general fair division model with transferable utilities we discuss endogenous lower and upper guarantees on individual shares of benefits or costs. Like the more familiar exogenous bounds on individual shares described by an outside option or a stand alone utility, these guarantees depend on my type but not on others' types, only on their number and the range of types. Keeping the range from worst share to best share as narrow as permitted by the physical constraints of the model still leaves a large menu of tight guarantee functions. We describe in detail these design options in several iconic problems where each tight pair of guarantees has a clear normative meaning: the allocation of indivisible goods or costly chores, cost sharing of a public facility and the exploitation of a commons with substitute or complementary inputs. The corresponding benefit or cost functions are all sub- or super-modular, and for this class we characterise the set of minimal upper and maximal lower guarantees in all two agent problems.

Suggested Citation

  • Anna Bogomolnaia & Herv'e Moulin, 2024. "Guaranteed shares of benefits and costs," Papers 2406.14198, arXiv.org.
  • Handle: RePEc:arx:papers:2406.14198
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    References listed on IDEAS

    as
    1. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 117(1), pages 7-36.
    2. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2017. "Competitive Division of a Mixed Manna," Econometrica, Econometric Society, vol. 85(6), pages 1847-1871, November.
    3. Bogomolnaia, Anna & Holzman, Ron & Moulin, Hervé, 2023. "On guarantees, vetoes and random dictators," Theoretical Economics, Econometric Society, vol. 18(1), January.
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