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A random arrival rule for NTU-bankruptcy problems

Author

Listed:
  • Gong, Doudou

    (RS: GSBE other - not theme-related research, Quantitative Economics)

  • Dietzenbacher, Bas

    (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory)

  • Peters, Hans

    (RS: FSE DKE Mathematics Centre Maastricht, QE Math. Economics & Game Theory, RS: GSBE other - not theme-related research)

Abstract

This paper introduces and studies a random arrival rule for bankruptcy problems with nontransferable utility. This bankruptcy rule generalizes the random arrival rule for bankruptcy problems with transferable utility which assigns the unique efficient allocation proportional to the sum of marginal vectors. We provide two axiomatic characterizations based on symmetry and monotonicity, respectively.

Suggested Citation

  • Gong, Doudou & Dietzenbacher, Bas & Peters, Hans, 2022. "A random arrival rule for NTU-bankruptcy problems," Research Memorandum 006, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2022006
    DOI: 10.26481/umagsb.2022006
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    References listed on IDEAS

    as
    1. Carlos González-Alcón & Peter Borm & Ruud Hendrickx, 2007. "A composite run-to-the-bank rule for multi-issue allocation situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 339-352, April.
    2. Yan-an Hwang & Tsung-fu Wang, 2009. "Population monotonicity, consistency and the random arrival rule," Economics Bulletin, AccessEcon, vol. 29(4), pages 2816-2821.
    3. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
    4. Guni Orshan & Federico Valenciano & José M. Zarzuelo, 2003. "The Bilateral Consistent Prekernel, the Core, and NTU Bankruptcy Problems," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 268-282, May.
    5. Bas Dietzenbacher & Peter Borm & Arantza Estévez-Fernández, 2020. "NTU-bankruptcy problems: consistency and the relative adjustment principle," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 101-122, June.
    6. Bezalel Peleg & Stef Tijs & Peter Borm & Gert-Jan Otten, 1998. "The MC-value for monotonic NTU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 37-47.
    7. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    8. Albizuri, M.J. & Leroux, J. & Zarzuelo, J.M., 2010. "Updating claims in bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 144-148, September.
    9. Thomson,William, 2019. "How to Divide When There Isn't Enough," Cambridge Books, Cambridge University Press, number 9781107194625.
    10. Albizuri, M.J. & Dietzenbacher, B.J. & Zarzuelo, J.M., 2020. "Bargaining with independence of higher or irrelevant claims," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 11-17.
    11. Lombardi, Michele & Yoshihara, Naoki, 2010. "Alternative characterizations of the proportional solution for nonconvex bargaining problems with claims," Economics Letters, Elsevier, vol. 108(2), pages 229-232, August.
    12. Morgenstern, Ilan & Domínguez, Diego, 2019. "A characterization of the random arrival rule for bankruptcy problems," Economics Letters, Elsevier, vol. 174(C), pages 214-217.
    13. Thomson,William, 2019. "How to Divide When There Isn't Enough," Cambridge Books, Cambridge University Press, number 9781316646441.
    14. Saavedra-Nieves, Alejandro & Saavedra-Nieves, Paula, 2020. "On systems of quotas from bankruptcy perspective: the sampling estimation of the random arrival rule," European Journal of Operational Research, Elsevier, vol. 285(2), pages 655-669.
    15. Youngsub Chun & Junghoon Lee, 2007. "On the convergence of the random arrival rule in large claims problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 259-273, October.
    16. 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.
    17. 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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    More about this item

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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