IDEAS home Printed from https://ideas.repec.org/p/hbs/wpaper/09-069.html
   My bibliography  Save this paper

A Noncooperative Support for Equal Division in Estate Division Problems

Author

Listed:
  • Itai Ashlagi

    (Harvard Business School, Negotiation, Organizations & Markets Unit)

  • Emin Karagozoglu

    (Department of Economics, Maastricht University)

  • Bettina Klaus

    (Harvard Business School, Negotiation, Organizations & Markets Unit)

Abstract

We consider estate division problems, a generalization of bankruptcy problems. We show that in a direct revelation claim game, if the underlying division rule satisfies efficiency, equal treatment of equals, and weak order preservation, then all (pure strategy) Nash equilibria induce equal division. Next, we consider division rules satisfying efficiency, equal treatment of equals, and claims monotonicity. For claim games with at most three agents, again all Nash equilibria induce equal division. Surprisingly, this result does not extend to claim games with more than three agents. However, if nonbossiness is added, then equal division is restored.

Suggested Citation

  • Itai Ashlagi & Emin Karagozoglu & Bettina Klaus, 2008. "A Noncooperative Support for Equal Division in Estate Division Problems," Harvard Business School Working Papers 09-069, Harvard Business School.
    • Handle: RePEc:hbs:wpaper:09-069
    as

    Download full text from publisher

    File URL: http://www.hbs.edu/research/pdf/09-069.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. 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.
    3. Ashlagi, Itai & Karagözoğlu, Emin & Klaus, Bettina, 2012. "A non-cooperative support for equal division in estate division problems," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 228-233.
    4. William Thomson, 2010. "Implementation of solutions to the problem of fair division when preferences are single-peaked," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 1-15, March.
    5. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    6. Simon Gächter & Arno Riedl, 2005. "Moral Property Rights in Bargaining with Infeasible Claims," Management Science, INFORMS, vol. 51(2), pages 249-263, February.
    7. Chun, Youngsub, 1989. "A noncooperative justification for egalitarian surplus sharing," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 245-261, June.
    8. Allan M. Feldman & Jeonghyun Kim, 2005. "The Hand Rule and United States v. Carroll Towing Co. Reconsidered," American Law and Economics Review, Oxford University Press, vol. 7(2), pages 523-543.
    9. Simon G�chter & Arno Riedl, "undated". "Moral Property Rights in Bargaining," IEW - Working Papers 113, Institute for Empirical Research in Economics - University of Zurich.
    10. Manuel Pulido & Joaquín Sánchez-Soriano & Natividad Llorca, 2002. "Game Theory Techniques for University Management: An Extended Bankruptcy Model," Annals of Operations Research, Springer, vol. 109(1), pages 129-142, January.
    11. Mark A. Satterthwaite & Hugo Sonnenschein, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(4), pages 587-597.
    12. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, 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. Emin Karagözoğlu, 2014. "A noncooperative approach to bankruptcy problems with an endogenous estate," Annals of Operations Research, Springer, vol. 217(1), pages 299-318, June.
    2. Mariotti, Marco & Wen, Quan, 2021. "A noncooperative foundation of the competitive divisions for bads," Journal of Economic Theory, Elsevier, vol. 194(C).
    3. Soo-Haeng Cho & Christopher S. Tang, 2014. "Technical Note---Capacity Allocation Under Retail Competition: Uniform and Competitive Allocations," Operations Research, INFORMS, vol. 62(1), pages 72-80, February.
    4. Esat Cetemen & Emin Karagözoğlu, 2014. "Implementing equal division with an ultimatum threat," Theory and Decision, Springer, vol. 77(2), pages 223-236, August.
    5. Anita Gantner & Kristian Horn & Rudolf Kerschbamer, 2013. "Fair Division in Unanimity Bargaining with Subjective Claims," Working Papers 2013-31, Faculty of Economics and Statistics, Universität Innsbruck.
    6. Emin Karagözoğlu & Shiran Rachmilevitch, 2018. "Implementing egalitarianism in a class of Nash demand games," Theory and Decision, Springer, vol. 85(3), pages 495-508, October.
    7. Emin Karagözoğlu & Kerim Keskin & Çağrı Sağlam, 2023. "(In)efficiency and equitability of equilibrium outcomes in a family of bargaining games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 175-193, March.
    8. Greil, Stefan & Schwarz, Christian & Stein, Stefan, "undated". "Perceived Fairness in the Taxation of a Digital Business Model [Fairness und die Besteuerung digitaler Geschäftsmodelle]," Duesseldorf Working Papers in Applied Management and Economics 47, Duesseldorf University of Applied Sciences.
    9. Urs Fischbacher & Nadja Kairies-Schwarz & Ulrike Stefani, 2017. "Non-additivity and the Salience of Marginal Productivities: Experimental Evidence on Distributive Fairness," Economica, London School of Economics and Political Science, vol. 84(336), pages 587-610, October.
    10. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    11. Doudou Gong & Genjiu Xu & Xuanzhu Jin & Loyimee Gogoi, 2022. "A sequential partition method for non-cooperative games of bankruptcy problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 359-379, July.
    12. Karagözoğlu, Emin & Keskin, Kerim & Sağlam, Çağrı, 2013. "A minimally altruistic refinement of Nash equilibrium," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 422-430.
    13. Ashlagi, Itai & Karagözoğlu, Emin & Klaus, Bettina, 2012. "A non-cooperative support for equal division in estate division problems," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 228-233.
    14. Shiran Rachmilevitch, 2020. "Rewarding moderate behavior in a dynamic Nash Demand Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 639-650, June.

    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. Emin Karagözoğlu, 2014. "A noncooperative approach to bankruptcy problems with an endogenous estate," Annals of Operations Research, Springer, vol. 217(1), pages 299-318, June.
    2. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    3. Büyükboyacı, Mürüvvet & Gürdal, Mehmet Y. & Kıbrıs, Arzu & Kıbrıs, Özgür, 2019. "An experimental study of the investment implications of bankruptcy laws," Journal of Economic Behavior & Organization, Elsevier, vol. 158(C), pages 607-629.
    4. Carmen Herrero & Juan Moreno-Ternero & Giovanni Ponti, 2010. "On the adjudication of conflicting claims: an experimental study," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(1), pages 145-179, January.
    5. Cano Berlanga, Sebastian & Giménez Gómez, José M. (José Manuel) & Vilella Bach, Misericòrdia, 2015. "Enjoying cooperative games: The R package GameTheory," Working Papers 2072/247653, Universitat Rovira i Virgili, Department of Economics.
    6. Jens Leth Hougaard & Juan D. Moreno-Ternero & Lars Peter Østerdal, 2010. "Baseline Rationing," Discussion Papers 10-16, University of Copenhagen. Department of Economics.
    7. Juan D. Moreno-Ternero & Min-Hung Tsay & Chun-Hsien Yeh, 2020. "A strategic justification of the Talmud rule based on lower and upper bounds," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1045-1057, December.
    8. Emin Karagözoğlu & Kerim Keskin, 2015. "A Tale of Two Bargaining Solutions," Games, MDPI, vol. 6(2), pages 1-14, June.
    9. Gantner, Anita & Kerschbamer, Rudolf, 2016. "Fairness and efficiency in a subjective claims problem," Journal of Economic Behavior & Organization, Elsevier, vol. 131(PA), pages 21-36.
    10. José-Manuel Giménez-Gómez & M. Marco-Gil, 2014. "A new approach for bounding awards in bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 447-469, August.
    11. Anita Gantner & Kristian Horn & Rudolf Kerschbamer, 2013. "Fair Division in Unanimity Bargaining with Subjective Claims," Working Papers 2013-31, Faculty of Economics and Statistics, Universität Innsbruck.
    12. Andrea Gallice, 2019. "Bankruptcy problems with reference-dependent preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 311-336, March.
    13. Jens Hougaard & Juan Moreno-Ternero & Lars Østerdal, 2013. "Rationing in the presence of baselines," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1047-1066, April.
    14. Schouten, Jop, 2022. "Cooperation, allocation and strategy in interactive decision-making," Other publications TiSEM d5d41448-8033-4f6b-8ec0-c, Tilburg University, School of Economics and Management.
    15. Simon Gächter & Arno Riedl, 2006. "Dividing Justly in Bargaining Problems with Claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 571-594, December.
    16. Emin Karagözoğlu & Kerim Keskin & Çağrı Sağlam, 2023. "(In)efficiency and equitability of equilibrium outcomes in a family of bargaining games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 175-193, March.
    17. Ansink, Erik, 2011. "The Arctic scramble: Introducing claims in a contest model," European Journal of Political Economy, Elsevier, vol. 27(4), pages 693-707.
    18. Erlanson, Albin & Szwagrzak, Karol, 2013. "Strategy-Proof Package Assignment," Working Papers 2013:43, Lund University, Department of Economics.
    19. Peter Knudsen & Lars Østerdal, 2012. "Merging and splitting in cooperative games: some (im)possibility results," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 763-774, November.
    20. 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.

    More about this item

    Keywords

    Bankruptcy/estate division problems; claims monotonicity; direct revelation claim game; equal division; equal treatment of equals; Nash equilibria; nonbossiness; (weak) order preservation.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    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:hbs:wpaper:09-069. 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: HBS (email available below). General contact details of provider: https://edirc.repec.org/data/harbsus.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.