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The concede-and-divide rule for liability problems

Author

Listed:
  • Chai, Ziyi
  • Gong, Doudou
  • Xu, Genjiu
  • Dietzenbacher, Bas

Abstract

Liability problems model the issue of allocating the asset value of an insolvent firm among the creditors and the firm itself. We introduce the concede-and-divide rule for liability problems with at most three agents, i.e. one firm and at most two creditors. Following a game-theoretic approach, we show that all solutions for liability games that satisfy symmetry and translation covariance induce the concede-and-divide rule, in particular the Shapley value and the nucleolus. Moreover, we provide axiomatic characterizations of the concede-and-divide rule using the minimal rights first property. We extend the analysis to liability problems with more agents but an almost solvent firm, i.e. reducing an arbitrary individual liability to zero would make the firm solvent.

Suggested Citation

  • Chai, Ziyi & Gong, Doudou & Xu, Genjiu & Dietzenbacher, Bas, 2025. "The concede-and-divide rule for liability problems," Economics Letters, Elsevier, vol. 256(C).
    • Handle: RePEc:eee:ecolet:v:256:y:2025:i:c:s0165176525004070
    DOI: 10.1016/j.econlet.2025.112570
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    References listed on IDEAS

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    1. Csóka, Péter & Illés, Ferenc & Solymosi, Tamás, 2022. "On the Shapley value of liability games," European Journal of Operational Research, Elsevier, vol. 300(1), pages 378-386.
    2. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 51-59, January.
    3. 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.
    4. 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).
    5. Robert J. Aumann, 2025. "Game-Theoretic Analysis of a Bankruptcy Problem from the Talmud," World Scientific Book Chapters, in: SELECTED CONTRIBUTIONS TO GAME THEORY, chapter 9, pages 219-242, World Scientific Publishing Co. Pte. Ltd..
    6. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    7. B. Dietzenbacher & A. Estévez-Fernández & P. Borm & R. Hendrickx, 2021. "Proportionality, equality, and duality in bankruptcy problems with nontransferable utility," Annals of Operations Research, Springer, vol. 301(1), pages 65-80, June.
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    JEL classification:

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

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