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Claim games for estate division problems

Author

Listed:
  • Vermeulen A.J.
  • Schröder M.J.W.
  • Peters H.J.M.

    (GSBE)

Abstract

This paper considers the estate division problem from a non-cooperative perspective. The integer claim game initiated by ONeill 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

  • Vermeulen A.J. & Schröder M.J.W. & Peters H.J.M., 2013. "Claim games for estate division problems," Research Memorandum 055, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2013055
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    File URL: https://cris.maastrichtuniversity.nl/portal/files/1734689/content
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. 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.
    5. 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.
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    Cited by:

    1. 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.
    2. 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.

    More about this item

    Keywords

    Noncooperative Games; Conflict; Conflict Resolution; Alliances;

    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

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