IDEAS home Printed from https://ideas.repec.org/p/unm/umagsb/2013055.html
   My bibliography  Save this paper

Claim games for estate division problems

Author

Listed:
  • Peters, H.J.M.

    (Quantitative Economics)

  • Schröder, M.J.W.

    (Quantitative Economics)

  • Vermeulen, A.J.

    (Quantitative Economics)

Abstract

This paper considers the estate division problem from a non-cooperative perspective. The integer claim game initiated by O'Neill (1982) and extended by Atlamaz et al. (2011) is generalized by considering different sharing rules to divide every interval among the claimants. For problems with an estate larger than half of the total entitlements, we show that every sharing rule satisfying four fairly general axioms yields the same set of Nash equilibrium profiles and corresponding payoffs. Every rule that always results in such equilibrium payoff vector is characterized by the properties minimal rights first and lower bound of degree half. Well-known examples are the Talmud rule, the adjusted proportional rule and the random arrival rule. Then our focus turns to more specific claim games, i.e. games that use the constrained equal awards rule, the Talmud rule, or the constrained equal losses rule as a sharing rule. Also a variation on the claim game is considered by allowing for arbitrary instead of integer claims.

Suggested Citation

  • Peters, H.J.M. & Schröder, M.J.W. & Vermeulen, A.J., 2013. "Claim games for estate division problems," Research Memorandum 055, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2013055
    DOI: 10.26481/umagsb.2013055
    as

    Download full text from publisher

    File URL: https://cris.maastrichtuniversity.nl/ws/files/1734689/guid-a76ab1f0-7557-407b-bf01-12d8a4c787cf-ASSET1.0.pdf
    Download Restriction: no

    File URL: https://libkey.io/10.26481/umagsb.2013055?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. Juan Moreno-Ternero & Antonio Villar, 2006. "The TAL-Family of Rules for Bankruptcy Problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 231-249, October.
    2. 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.
    3. 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.
    4. Jennifer Merolla & Michael Munger & Michael Tofias, 2005. "In Play: A Commentary on Strategies in the 2004 U.S. Presidential Election," Public Choice, Springer, vol. 123(1), pages 19-37, April.
    5. Atlamaz, Murat & Berden, Caroline & Peters, Hans & Vermeulen, Dries, 2011. "Non-cooperative solutions for estate division problems," Games and Economic Behavior, Elsevier, vol. 73(1), pages 39-51, September.
    6. 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.
    7. Peters, Hans & Schröder, Marc & Vermeulen, Dries, 2019. "Claim games for estate division problems," Games and Economic Behavior, Elsevier, vol. 116(C), pages 105-115.
    8. 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.
    9. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
    10. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 667-692, December.
    11. Pálvölgyi, Dénes & Peters, Hans & Vermeulen, Dries, 2014. "A strategic approach to multiple estate division problems," Games and Economic Behavior, Elsevier, vol. 88(C), pages 135-152.
    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. Peters, Hans & Schröder, Marc & Vermeulen, Dries, 2019. "Claim games for estate division problems," Games and Economic Behavior, Elsevier, vol. 116(C), pages 105-115.
    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. Pálvölgyi, Dénes & Peters, Hans & Vermeulen, Dries, 2014. "A strategic approach to multiple estate division problems," Games and Economic Behavior, Elsevier, vol. 88(C), pages 135-152.
    4. 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.

    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. Harless, Patrick, 2017. "Wary of the worst: Maximizing award guarantees when new claimants may arrive," Games and Economic Behavior, Elsevier, vol. 105(C), pages 316-328.
    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. Long, Yan & Sethuraman, Jay & Xue, Jingyi, 2021. "Equal-quantile rules in resource allocation with uncertain needs," Journal of Economic Theory, Elsevier, vol. 197(C).
    4. Pálvölgyi, Dénes & Peters, Hans & Vermeulen, Dries, 2014. "A strategic approach to multiple estate division problems," Games and Economic Behavior, Elsevier, vol. 88(C), pages 135-152.
    5. Sanchez-Soriano, Joaquin, 2021. "Families of sequential priority rules and random arrival rules with withdrawal limits," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 136-148.
    6. Juan D. Moreno-Ternero, 2017. "A Talmudic Approach to Bankruptcy Problems," Working Papers 17.01, Universidad Pablo de Olavide, Department of Economics.
    7. René Brink & Juan D. Moreno-Ternero, 2017. "The reverse TAL-family of rules for bankruptcy problems," Annals of Operations Research, Springer, vol. 254(1), pages 449-465, July.
    8. Arin, J. & Benito-Ostolaza, J. & Inarra, E., 2017. "The reverse Talmud family of rules for bankruptcy Problems: A characterization," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 43-49.
    9. Ephraim Zehavi & Amir Leshem, 2018. "On the Allocation of Multiple Divisible Assets to Players with Different Utilities," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 253-274, June.
    10. Flores-Szwagrzak, Karol, 2015. "Priority classes and weighted constrained equal awards rules for the claims problem," Journal of Economic Theory, Elsevier, vol. 160(C), pages 36-55.
    11. Josep Maria Izquierdo Aznar & Pere Timoner Lledó, 2016. "Constrained multi-issue rationing problems," UB Economics Working Papers 2016/347, Universitat de Barcelona, Facultat d'Economia i Empresa, UB School of Economics.
    12. William Thomson, 2014. "Compromising between the proportional and constrained equal awards rules," RCER Working Papers 584, University of Rochester - Center for Economic Research (RCER).
    13. 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.
    14. Patrick Harless, 2017. "Endowment additivity and the weighted proportional rules for adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 755-781, March.
    15. Moreno-Ternero, Juan D. & Villar, Antonio, 2004. "The Talmud rule and the securement of agents' awards," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 245-257, March.
    16. Csóka, Péter & Jean-Jacques Herings, P., 2019. "Liability games," Games and Economic Behavior, Elsevier, vol. 116(C), pages 260-268.
    17. William Thomson, 2015. "For claims problems, compromising between the proportional and constrained equal awards rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 495-520, November.
    18. Moreno-Ternero, Juan D., 2011. "Voting over piece-wise linear tax methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 29-36, January.
    19. Trudeau, Christian, 2018. "From the bankruptcy problem and its Concede-and-Divide solution to the assignment problem and its Fair Division solution," Games and Economic Behavior, Elsevier, vol. 108(C), pages 225-238.
    20. Stovall, John E., 2014. "Collective rationality and monotone path division rules," Journal of Economic Theory, Elsevier, vol. 154(C), pages 1-24.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • 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:unm:umagsb:2013055. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/meteonl.html .

    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: Andrea Willems or Leonne Portz (email available below). General contact details of provider: https://edirc.repec.org/data/meteonl.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.