IDEAS home Printed from https://ideas.repec.org/a/bla/jpbect/v23y2021i2p376-401.html
   My bibliography  Save this article

Individually rational rules for the division problem when the number of units to be allotted is endogenous

Author

Listed:
  • Gustavo Bergantiños
  • Jordi Massó
  • Alejandro Neme

Abstract

We study individually rational rules to be used to allot, among a group of agents, a perfectly divisible good that is freely available only in whole units. A rule is individually rational if, at each preference profile, each agent finds that her allotment is at least as good as any whole unit of the good. We study and characterize two individually rational and efficient families of rules, whenever agents' preferences are symmetric single‐peaked on the set of possible allotments. Rules in the two families are in addition envy‐free, but they differ on whether envy‐freeness is considered on losses or on awards. Our main result states that (a) the family of constrained equal losses rules coincides with the class of all individually rational and efficient rules that satisfy justified envy‐freeness on losses and (b) the family of constrained equal awards rules coincides with the class of all individually rational and efficient rules that satisfy envy‐freeness on awards.

Suggested Citation

  • Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2021. "Individually rational rules for the division problem when the number of units to be allotted is endogenous," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 376-401, April.
    • Handle: RePEc:bla:jpbect:v:23:y:2021:i:2:p:376-401
    DOI: 10.1111/jpet.12492
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jpet.12492
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jpet.12492?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
    2. Adachi, Tsuyoshi, 2010. "The uniform rule with several commodities: A generalization of Sprumont's characterization," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 952-964, November.
    3. Bergantiños, Gustavo & Massó, Jordi & Neme, Alejandro, 2015. "The division problem under constraints," Games and Economic Behavior, Elsevier, vol. 89(C), pages 56-77.
    4. Shuhei Morimoto & Shigehiro Serizawa & Stephen Ching, 2013. "A characterization of the uniform rule with several commodities and agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 871-911, March.
    5. Ching, Stephen, 1992. "A simple characterization of the uniform rule," Economics Letters, Elsevier, vol. 40(1), pages 57-60, September.
    6. Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 229-246, March.
    7. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
    8. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with voluntary participation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 371-406, March.
    9. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    10. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with maximal capacity constraints," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 29-57, March.
    11. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
    12. Hidekazu Anno & Hiroo Sasaki, 2013. "Second-best efficiency of allocation rules: strategy-proofness and single-peaked preferences with multiple commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 693-716, November.
    13. Manjunath, Vikram, 2012. "When too little is as good as nothing at all: Rationing a disposable good among satiable people with acceptance thresholds," Games and Economic Behavior, Elsevier, vol. 74(2), pages 576-587.
    14. Sonmez, Tayfun, 1994. "Consistency, monotonicity, and the uniform rule," Economics Letters, Elsevier, vol. 46(3), pages 229-235, November.
    15. William Thomson, 1997. "The replacement principle in economies with indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 57-66.
    16. Kim, Sunyoung & Bergantiños, Gustavo & Chun, Youngsub, 2015. "The separability principle in single-peaked economies with participation constraints," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 69-75.
    17. Erlanson, Albin & Flores-Szwagrzak, Karol, 2015. "Strategy-proof assignment of multiple resources," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 137-162.
    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. Kim, Sunyoung & Bergantiños, Gustavo & Chun, Youngsub, 2015. "The separability principle in single-peaked economies with participation constraints," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 69-75.
    2. Bergantiños, Gustavo & Massó, Jordi & Neme, Alejandro, 2015. "The division problem under constraints," Games and Economic Behavior, Elsevier, vol. 89(C), pages 56-77.
    3. Gustavo Bergantiños & Jordi Massó & Inés Moreno de Barreda & Alejandro Neme, 2015. "Stable partitions in many division problems: the proportional and the sequential dictator solutions," Theory and Decision, Springer, vol. 79(2), pages 227-250, September.
    4. Erlanson, Albin & Flores-Szwagrzak, Karol, 2015. "Strategy-proof assignment of multiple resources," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 137-162.
    5. Ruben Juarez & Jung S. You, 2019. "Optimality of the uniform rule under single-peaked preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 27-36, May.
    6. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with maximal capacity constraints," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 29-57, March.
    7. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with voluntary participation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 371-406, March.
    8. Bochet, Olivier & Tumennasan, Norovsambuu, 2020. "Dominance of truthtelling and the lattice structure of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 185(C).
    9. Abizada, Azar & Chen, Siwei, 2014. "A characterization of the uniform rule based on new robustness properties," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 80-85.
    10. Takuma Wakayama, 2017. "Bribe-proofness for single-peaked preferences: characterizations and maximality-of-domains results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 357-385, August.
    11. Schummer, James & Thomson, William, 1997. "Two derivations of the uniform rule and an application to bankruptcy," Economics Letters, Elsevier, vol. 55(3), pages 333-337, September.
    12. Kazuhiko Hashimoto & Takuma Wakayama, 2021. "Fair reallocation in economies with single-peaked preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 773-785, September.
    13. Shuhei Morimoto & Shigehiro Serizawa & Stephen Ching, 2013. "A characterization of the uniform rule with several commodities and agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 871-911, March.
    14. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
    15. Rebelo, S., 1997. "On the Determinant of Economic Growth," RCER Working Papers 443, University of Rochester - Center for Economic Research (RCER).
    16. Manjunath, Vikram, 2012. "When too little is as good as nothing at all: Rationing a disposable good among satiable people with acceptance thresholds," Games and Economic Behavior, Elsevier, vol. 74(2), pages 576-587.
    17. Erlanson, Albin & Szwagrzak, Karol, 2013. "Strategy-Proof Package Assignment," Working Papers 2013:43, Lund University, Department of Economics.
    18. Pablo Amorós, 2002. "Single-peaked preferences with several commodities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(1), pages 57-67.
    19. Karol Flores-Szwagrzak, 2016. "The replacement principle in networked economies with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 763-789, December.
    20. Masso, Jordi & Neme, Alejandro, 2001. "Maximal Domain of Preferences in the Division Problem," Games and Economic Behavior, Elsevier, vol. 37(2), pages 367-387, November.

    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    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:bla:jpbect:v:23:y:2021:i:2:p:376-401. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/apettea.html .

    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.