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A strategic approach to multiple estate division problems

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  • Pálvölgyi, Dénes
  • Peters, Hans
  • Vermeulen, Dries

Abstract

The classical bankruptcy problem is extended by assuming that there are multiple estates. In the finite estate case, the agents have homogeneous preferences per estate, which may differ across estates. In the more general infinite estate problem, players have arbitrary preferences over an interval of real numbers each of which is regarded as an estate. A strategic estate game is formulated in which each agent distributes his legal entitlement over the estates, resulting in individual claims per estate: each estate is then divided according to some allocation rule. The paper focuses on existence and on computational aspects of Nash equilibria in finite and infinite estate games, with some focus on the proportional allocation rule. For this rule, it also studies Pareto optimality and envy-freeness of equilibrium allocations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:gamebe:v:88:y:2014:i:c:p:135-152
    DOI: 10.1016/j.geb.2014.09.005
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    References listed on IDEAS

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    1. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
    2. Peters, Hans & Schröder, Marc & Vermeulen, Dries, 2019. "Claim games for estate division problems," Games and Economic Behavior, Elsevier, vol. 116(C), pages 105-115.
    3. Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 441-460, March.
    4. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    5. Cramton, Peter & Gibbons, Robert & Klemperer, Paul, 1987. "Dissolving a Partnership Efficiently," Econometrica, Econometric Society, vol. 55(3), pages 615-632, May.
    6. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    7. Chambers, Christopher P., 2005. "Allocation rules for land division," Journal of Economic Theory, Elsevier, vol. 121(2), pages 236-258, April.
    8. 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.
    9. 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.
    10. 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.
    11. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
    12. Berliant, Marcus, 1985. "An equilibrium existence result for an economy with land," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 53-56, February.
    13. Ramesh Johari & John N. Tsitsiklis, 2004. "Efficiency Loss in a Network Resource Allocation Game," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 407-435, August.
    14. Adib Bagh & Alejandro Jofre, 2006. "Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment," Econometrica, Econometric Society, vol. 74(6), pages 1715-1721, November.
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    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. Qianqian Kong & Hans Peters, 2023. "Sequential claim games," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 955-975, September.
    3. Mirjam Groote Schaarsberg & Hans Reijnierse & Peter Borm, 2018. "On solving mutual liability problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(3), pages 383-409, June.

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    More about this item

    Keywords

    Bankruptcy problem; Multiple estate division; Non-cooperative estate division game;
    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

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