IDEAS home Printed from https://ideas.repec.org/p/cca/wpaper/58.html

Disputed Lands

Author

Listed:
  • Marco Dall'Aglio
  • Fabio Maccheroni

Abstract

In this paper we consider the classical problem of dividing a land among many agents so that everybody is satisfied with the parcel she receives. In the literature, it is usually assumed that all the agents are endowed with cardinally comparable, additive, and monotone utility functions. In many economic and political situations violations of these assumptions may arise. We show how a family of cardinally comparable utility functions can be obtained starting directly from the agents’ preferences, and how a fair division of the land is feasible, without additivity or monotonicity requirements. Moreover, if the land to be divided can be modelled as a finite dimensional simplex, it is possible to obtain envy-free (and a fortiori fair) divisions of it into subsimplexes. The main tool is an extension of a representation theorem of Gilboa and Schmeidler (1989).

Suggested Citation

  • Marco Dall'Aglio & Fabio Maccheroni, 2007. "Disputed Lands," Carlo Alberto Notebooks 58, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:58
    as

    Download full text from publisher

    File URL: https://www.carloalberto.org/wp-content/uploads/2018/11/no.58.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Berliant, Marcus & Thomson, William & Dunz, Karl, 1992. "On the fair division of a heterogeneous commodity," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 201-216.
    2. Ichiishi, Tatsuro & Idzik, Adam, 1999. "Equitable allocation of divisible goods," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 389-400, December.
    3. Itzhak Gilboa, 2004. "Uncertainty in Economic Theory," Post-Print hal-00756317, HAL.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    5. Fabio Maccheroni & Fabio Maccheroni & Massimo Marinacci & Massimo Marinacci, 2003. "How to cut a pizza fairly: Fair division with decreasing marginal evaluations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 457-465, June.
    6. Berliant, Marcus & Dunz, Karl, 2004. "A foundation of location theory: existence of equilibrium, the welfare theorems, and core," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 593-618, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. is not listed on IDEAS
    2. Farhad Hüsseinov & Nobusumi Sagara, 2013. "Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 923-940, October.
    3. Erel Segal-Halevi & Shmuel Nitzan, 2014. "Cake Cutting – Fair and Square," Working Papers 2014-01, Bar-Ilan University, Department of Economics.
    4. Segal-Halevi, Erel & Nitzan, Shmuel & Hassidim, Avinatan & Aumann, Yonatan, 2017. "Fair and square: Cake-cutting in two dimensions," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 1-28.

    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. Segal-Halevi, Erel & Nitzan, Shmuel & Hassidim, Avinatan & Aumann, Yonatan, 2017. "Fair and square: Cake-cutting in two dimensions," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 1-28.
    2. Erel Segal-Halevi & Shmuel Nitzan & Avinatan Hassidim & Yonatan Aumann, 2020. "Envy-Free Division of Land," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 896-922, August.
    3. Marco LiCalzi & Antonio Nicolò, 2009. "Efficient egalitarian equivalent allocations over a single good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 27-45, July.
    4. 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.
    5. Erel Segal-Halevi & Shmuel Nitzan, 2019. "Fair cake-cutting among families," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 709-740, December.
    6. Dall'Aglio, M. & Brânzei, R. & Tijs, S.H., 2008. "Cooperation in Dividing the Cake," Discussion Paper 2008-101, Tilburg University, Center for Economic Research.
    7. Amarante, M & Ghossoub, M & Phelps, E, 2013. "Innovation, Entrepreneurship and Knightian Uncertainty," Working Papers 12241, Imperial College, London, Imperial College Business School.
    8. Rebille, Yann, 2007. "Patience in some non-additive models," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 749-763, August.
    9. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Coping with imprecise information: a decision theoretic approach," Cahiers de la Maison des Sciences Economiques v04056, Université Panthéon-Sorbonne (Paris 1), revised May 2004.
    10. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
    11. ,, 2013. "Endogenous indeterminacy and volatility of asset prices under ambiguity," Theoretical Economics, Econometric Society, vol. 8(3), September.
    12. Fabio Maccheroni & Fabio Maccheroni & Massimo Marinacci & Massimo Marinacci, 2003. "How to cut a pizza fairly: Fair division with decreasing marginal evaluations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 457-465, June.
    13. Lang, Matthias & Wambach, Achim, 2013. "The fog of fraud – Mitigating fraud by strategic ambiguity," Games and Economic Behavior, Elsevier, vol. 81(C), pages 255-275.
    14. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    15. Fontini, Fulvio & Umgiesser, Georg & Vergano, Lucia, 2010. "The role of ambiguity in the evaluation of the net benefits of the MOSE system in the Venice lagoon," Ecological Economics, Elsevier, vol. 69(10), pages 1964-1972, August.
    16. Giuseppe Attanasi & Aldo Montesano, 2012. "The price for information about probabilities and its relation with risk and ambiguity," Theory and Decision, Springer, vol. 73(1), pages 125-160, July.
    17. Bade, Sophie, 2011. "Ambiguous act equilibria," Games and Economic Behavior, Elsevier, vol. 71(2), pages 246-260, March.
    18. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "Decision principles derived from risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 294-302, December.
    19. Olivier L’Haridon & Lætitia Placido, 2010. "Betting on Machina’s reflection example: an experiment on ambiguity," Theory and Decision, Springer, vol. 69(3), pages 375-393, September.
    20. Azrieli, Yaron & Teper, Roee, 2011. "Uncertainty aversion and equilibrium existence in games with incomplete information," Games and Economic Behavior, Elsevier, vol. 73(2), pages 310-317.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

    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:cca:wpaper:58. 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: Giovanni Bert (email available below). General contact details of provider: https://edirc.repec.org/data/fccaait.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.