IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2406.14198.html
   My bibliography  Save this paper

Guaranteed shares of benefits and costs

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2406.14198
    File Function: Latest version
    Download Restriction: no
    ---><---

    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.
    4. Friedman, Eric & Moulin, Herve, 1999. "Three Methods to Share Joint Costs or Surplus," Journal of Economic Theory, Elsevier, vol. 87(2), pages 275-312, August.
    5. Faulhaber, Gerald R, 1975. "Cross-Subsidization: Pricing in Public Enterprises," American Economic Review, American Economic Association, vol. 65(5), pages 966-977, December.
    6. Varian, Hal R., 1976. "Two problems in the theory of fairness," Journal of Public Economics, Elsevier, vol. 5(3-4), pages 249-260.
    7. Fleurbaey, Marc & Maniquet, Francois, 1996. "Cooperative Production: A Comparison of Welfare Bounds," Games and Economic Behavior, Elsevier, vol. 17(2), pages 200-208, December.
    8. Hervé Moulin, 2019. "Fair Division in the Internet Age," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 407-441, August.
    9. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    10. repec:bla:scandj:v:94:y:1992:i:1:p:37-51 is not listed on IDEAS
    11. Moulin, Herve, 1992. "Welfare bounds in the cooperative production problem," Games and Economic Behavior, Elsevier, vol. 4(3), pages 373-401, July.
    12. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    13. Demko, Stephen & Hill, Theodore P., 1988. "Equitable distribution of indivisible objects," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 145-158, October.
    14. Tadenuma, Koichi & Thomson, William, 1993. "The fair allocation of an indivisible good when monetary compensations are possible," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 117-132, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    2. 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.
    3. Anna Bogomolnaia & Herve Moulin, 2022. "Fair Division with Money and Prices," Papers 2202.08117, arXiv.org.
    4. Moulin, Herve & Shenker, Scott, 1999. "Distributive and Additive Costsharing of an Homogeneous Good," Games and Economic Behavior, Elsevier, vol. 27(2), pages 299-330, May.
    5. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 117(1), pages 7-36.
    6. Watts, Alison, 1999. "Cooperative production: a comparison of lower and upper bounds," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 317-331, November.
    7. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
    8. Miralles, Antonio & Pycia, Marek, 2021. "Foundations of pseudomarkets: Walrasian equilibria for discrete resources," Journal of Economic Theory, Elsevier, vol. 196(C).
    9. Bogomolnaia, Anna & Holzman, Ron & Moulin, Hervé, 2023. "On guarantees, vetoes and random dictators," Theoretical Economics, Econometric Society, vol. 18(1), January.
    10. Pierre Dehez, 2013. "Cooperative provision of indivisible public goods," Theory and Decision, Springer, vol. 74(1), pages 13-29, January.
    11. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    12. Shende, Priyanka & Purohit, Manish, 2023. "Strategy-proof and envy-free mechanisms for house allocation," Journal of Economic Theory, Elsevier, vol. 213(C).
    13. Fedor Sandomirskiy & Philip Ushchev, 2024. "The geometry of consumer preference aggregation," Papers 2405.06108, arXiv.org.
    14. Soroush Ebadian & Dominik Peters & Nisarg Shah, 2022. "How to Fairly Allocate Easy and Difficult Chores," Post-Print hal-03834514, HAL.
    15. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Tvede, Mich & Østerdal, Lars Peter, 2017. "Sharing the proceeds from a hierarchical venture," Games and Economic Behavior, Elsevier, vol. 102(C), pages 98-110.
    16. Anna bogomolnaia Ron Holzman Herve Moulin, 2021. "Wost Case in Voting and Bargaining," Papers 2104.02316, arXiv.org.
    17. Eric Bahel & Christian Trudeau, 2018. "Consistency requirements and pattern methods in cost sharing problems with technological cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 737-765, September.
    18. 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.
    19. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    20. Jens Hougaard & Hervé Moulin & Lars Østerdal, 2010. "Decentralized pricing in minimum cost spanning trees," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(2), pages 293-306, August.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2406.14198. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.