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Compromise solutions based on bankruptcy

Author

Listed:
  • Quant, M.

    (Tilburg University, School of Economics and Management)

  • Borm, P.E.M.

    (Tilburg University, School of Economics and Management)

  • Hendrickx, R.L.P.

    (Tilburg University, School of Economics and Management)

  • Zwikker, P.

Abstract

In this paper we introduce a new family of compromise solutions for the class of compromise admissible games.These solutions extend bankruptcy rules.In particular, we show that the compromise extension of the run-to-the-bank rule coincides with the barycentre of the core cover and characterise this rule by consistency.We also provide a characterisation of the TAL-family of rules.
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Suggested Citation

  • Quant, M. & Borm, P.E.M. & Hendrickx, R.L.P. & Zwikker, P., 2006. "Compromise solutions based on bankruptcy," Other publications TiSEM 89479e71-abee-42d9-9bba-3, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:89479e71-abee-42d9-9bba-378b69628c6d
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    References listed on IDEAS

    as
    1. Maschler, M. & Potters, J.A.M. & Tijs, S.H., 1992. "The general nucleolus and the reduced game property," Other publications TiSEM ab187dab-1b5b-40c3-a673-8, Tilburg University, School of Economics and Management.
    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. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Quant, M. & Borm, P.E.M. & Reijnierse, J.H. & van Velzen, S., 2003. "Compromise Stable TU-Games," Other publications TiSEM 01a28f48-0b1b-43f9-8dac-3, Tilburg University, School of Economics and Management.
    5. Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Other publications TiSEM 488a314a-179c-4628-91e6-7, Tilburg University, School of Economics and Management.
    6. Marieke Quant & Peter Borm & Hans Reijnierse & Bas van Velzen, 2005. "The core cover in relation to the nucleolus and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 491-503, November.
    7. Tijs, S.H. & Lipperts, F.A.S., 1982. "The hypercube and the core cover of N-person cooperative games," Other publications TiSEM f86cf523-f36d-4652-b774-6, Tilburg University, School of Economics and Management.
    8. Maschler, M & Potters, J A M & Tijs, S H, 1992. "The General Nucleolus and the Reduced Game Property," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 85-106.
    9. 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.
    10. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
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    Citations

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    Cited by:

    1. Lohmann, E.R.M.A. & Borm, P.E.M. & Quant, M., 2007. "A Stroll with Alexia," Other publications TiSEM 8107c8d1-2b1e-4051-a140-6, Tilburg University, School of Economics and Management.
    2. Doudou Gong & Bas Dietzenbacher & Hans Peters, 2024. "Two-bound core games and the nucleolus," Annals of Operations Research, Springer, vol. 336(3), pages 1419-1433, May.
    3. A. Estévez-Fernández & M. Fiestras-Janeiro & M. Mosquera & E. Sánchez-Rodríguez, 2012. "A bankruptcy approach to the core cover," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 343-359, December.
    4. 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.
    5. Marieke Quant & Peter Borm & Hans Reijnierse & Bas van Velzen, 2005. "The core cover in relation to the nucleolus and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 491-503, November.
    6. 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.
    7. Lohmann, E.R.M.A., 2012. "Joint decision making and cooperative solutions," Other publications TiSEM 500d8ee1-4f93-4e78-940b-9, Tilburg University, School of Economics and Management.
    8. Tijs, Stef & Borm, Peter & Lohmann, Edwin & Quant, Marieke, 2011. "An average lexicographic value for cooperative games," European Journal of Operational Research, Elsevier, vol. 213(1), pages 210-220, August.

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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