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An Axiomatic Analysis of Joint Liability Problems with Rooted -Tree Structure

Author

Listed:
  • Takayuki Oishi

    (Aomori Public University, Japan)

  • Gerard van der Laan

    (VU University Amsterdam, the Netherlands)

  • René van den Brink

    (VU University Amsterdam, the Netherlands)

Abstract

For joint liability problems concerning tort law, a legal compensation scheme may be based on lower and upper bounds of compensation for injury and on case-system consistency. Introducing several properties inspired from this observation, we analyze compensation schemes axiomatically under the situation where causation of the cumulative injury appears in multiple sequences of wrongful acts. The situation underlying the model 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. This unique compensation scheme is the nucleolus of an associated liability game.

Suggested Citation

  • Takayuki Oishi & Gerard van der Laan & René van den Brink, 2016. "An Axiomatic Analysis of Joint Liability Problems with Rooted -Tree Structure," Tinbergen Institute Discussion Papers 16-042/II, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20160042
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    File URL: http://papers.tinbergen.nl/16042.pdf
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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Dehez, Pierre & Ferey, Samuel, 2013. "How to share joint liability: A cooperative game approach," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 44-50.
    7. 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.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Liability problems; Tort law; Rooted-tree graph; Axiomatization; Nucleolus;

    JEL classification:

    • 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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