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An explicit solution to a game-theoretic bankruptcy problem

Author

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  • Isaac Elishakoff

    (Florida Atlantic University)

  • Avraham N. Dancygier

    (Technion - Israel Institute of Technology)

Abstract

This paper complements the breakthrough study by Aumann and Maschler on resolution of the conundrum from the Tractate of Kethuboth. The conundrum deals with the bankruptcy problem of the resources' allocation to the creditors when claims exceed the estate. The Mishnah and Talmud deal with three cases. Two of which did not raise questions, but the third case has perplexed Talmudic commentators over centuries. Aumann and Maschler provided the game theoretic framework for resolution of the asset distribution along with providing a rule, which leads to the numbers listed in the Mishnah. The paper series of Aumann and Maschler show the validity of Rabbi Nathan's argument who provided the ruling about the distribution. This study summarizes findings of previous studies on this subject and based on Kaminski's hydraulic rationing methodology - presents a closed-form solution for the resolution of the Talmudic conundrum, which also applies to an arbitrary number of creditors.

Suggested Citation

  • Isaac Elishakoff & Avraham N. Dancygier, 2023. "An explicit solution to a game-theoretic bankruptcy problem," SN Business & Economics, Springer, vol. 3(9), pages 1-16, September.
    • Handle: RePEc:spr:snbeco:v:3:y:2023:i:9:d:10.1007_s43546-023-00534-0
    DOI: 10.1007/s43546-023-00534-0
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    References listed on IDEAS

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    1. Thomson,William, 2019. "How to Divide When There Isn't Enough," Cambridge Books, Cambridge University Press, number 9781107194625.
    2. Thomson,William, 2019. "How to Divide When There Isn't Enough," Cambridge Books, Cambridge University Press, number 9781316646441.
    3. Tamas Fleiner & Balazs Sziklai, 2011. "Notes on the Bankruptcy Problem: an Application of Hydraulic Rationing," CERS-IE WORKING PAPERS 1123, Institute of Economics, Centre for Economic and Regional Studies.
    4. Peyton Young, H., 2008. "Michael Maschler, game theory, and the Talmud," Games and Economic Behavior, Elsevier, vol. 64(2), pages 382-382, November.
    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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