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The Tort Law and the Nucleolus for Generalized Joint Liability Problems

Author

Listed:
  • Takayuki Oishi
  • Gerard van der Laan

    (VU University Amsterdam)

  • René van den Brink

    (VU University Amsterdam)

Abstract

We analyze a legal compensation scheme axiomatically under the situation where causation of the cumulative injury appears in multiple sequences of wrongful acts caused by tortfeasors. This situation is a generalization of joint liability problems on tort law, and it is described by a rooted-tree graph. We show that there is a unique compensation scheme that satisfies three axioms, one about lower bounds of individual compensations, one about upper bounds of individual compensations, and one about case-system consistency. These axioms are derived from legal observations on tort law. The unique compensation scheme satisfying the three axioms yields the Nucleolus of an associated liability game.

Suggested Citation

  • Takayuki Oishi & Gerard van der Laan & René van den Brink, 2018. "The Tort Law and the Nucleolus for Generalized Joint Liability Problems," Discussion Papers 37, Meisei University, School of Economics.
  • Handle: RePEc:mei:wpaper:37
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    References listed on IDEAS

    as
    1. René Brink & P. Herings & Gerard Laan & A. Talman, 2015. "The Average Tree permission value for games with a permission tree," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 99-123, January.
    2. Alcalde-Unzu, Jorge & Gómez-Rúa, María & Molis, Elena, 2015. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," Games and Economic Behavior, Elsevier, vol. 90(C), pages 134-150.
    3. Oishi, Takayuki & Nakayama, Mikio & Hokari, Toru & Funaki, Yukihiko, 2016. "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 44-53.
    4. Ju, Biung-Ghi, 2013. "Coalitional manipulation on networks," Journal of Economic Theory, Elsevier, vol. 148(2), pages 627-662.
    5. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    6. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2011. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 2, number 2.
    7. Rodica Brânzei & Tamás Solymosi & Stef Tijs, 2005. "Strongly essential coalitions and the nucleolus of peer group games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 447-460, September.
    8. Samuel Ferey & Pierre Dehez, 2016. "Multiple Causation, Apportionment, and the Shapley Value," The Journal of Legal Studies, University of Chicago Press, vol. 45(1), pages 143-171.
    9. René Brink & Chris Dietz & Gerard Laan & Genjiu Xu, 2017. "Comparable characterizations of four solutions for permission tree games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(4), pages 903-923, April.
    10. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
    11. Dehez, Pierre & Ferey, Samuel, 2013. "How to share joint liability: A cooperative game approach," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 44-50.
    12. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
    13. Charnes, A. & Littlechild, S. C., 1975. "On the formation of unions in n-person games," Journal of Economic Theory, Elsevier, vol. 10(3), pages 386-402, June.
    14. 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.
    15. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    16. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    17. Takayuki Oishi & Mikio Nakayama, 2009. "Anti‐Dual Of Economic Coalitional Tu Games," The Japanese Economic Review, Japanese Economic Association, vol. 60(4), pages 560-566, December.
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    More about this item

    Keywords

    Tort law; Rooted-tree graph; Axiomatization; Nucleolus;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • K13 - Law and Economics - - Basic Areas of Law - - - Tort Law and Product Liability; Forensic Economics
    • K49 - Law and Economics - - Legal Procedure, the Legal System, and Illegal Behavior - - - Other

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