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Apportionment of liability by the stochastic Shapley value

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  • Kim, Jeong-Yoo
  • Lee, Seewoo

Abstract

If multiple defendants are jointly liable for a plaintiff's harm, the court must determine the apportionments of the damages among them. Recently, in a series of papers, Dehez and Ferey (2013) and Ferey and Dehez (2016a,b) took a cooperative game theory approach, and used the Shapley value and the weighted Shapley value to determine the shares especially in the case of sequential acts. In this paper, we argue that their allocation rule is not strictly fair if we take even a small random error into account. We alternatively propose the stochastic Shapley value which extends the definition of the Shapley value to stochastic cooperative games and show that it satisfies ex post efficiency, symmetry, dummy, feasibility and fairness.

Suggested Citation

  • Kim, Jeong-Yoo & Lee, Seewoo, 2019. "Apportionment of liability by the stochastic Shapley value," International Review of Law and Economics, Elsevier, vol. 60(C).
    • Handle: RePEc:eee:irlaec:v:60:y:2019:i:c:s014481881930153x
    DOI: 10.1016/j.irle.2019.105860
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    References listed on IDEAS

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    1. Spier, Kathryn E, 1994. "A Note on Joint and Several Liability: Insolvency, Settlement, and Incentives," The Journal of Legal Studies, University of Chicago Press, vol. 23(1), pages 559-568, January.
    2. Rodica Brânzei & Vito Fragnelli & Stef Tijs, 2002. "Tree-connected peer group situations and peer group games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(1), pages 93-106, March.
    3. Kahan, Marcel, 1996. "The incentive effects of settlements under joint and several liability," International Review of Law and Economics, Elsevier, vol. 16(4), pages 389-395, December.
    4. Suijs, Jeroen & Borm, Peter, 1999. "Stochastic Cooperative Games: Superadditivity, Convexity, and Certainty Equivalents," Games and Economic Behavior, Elsevier, vol. 27(2), pages 331-345, May.
    5. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    6. 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.
    7. Jeong-Yoo Kim & Joon Song, 2007. "Signal Jamming in Pretrial Negotiation with Multiple Defendants," Journal of Economics, Springer, vol. 91(2), pages 177-200, June.
    8. Feessa, Eberhard & Muehlheusser, Gerd, 2000. "Settling multidefendant lawsuits under incomplete information," International Review of Law and Economics, Elsevier, vol. 20(2), pages 295-313, June.
    9. Dehez, Pierre & Ferey, Samuel, 2013. "How to share joint liability: A cooperative game approach," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 44-50.
    10. Daniel Granot, 1977. "Cooperative Games in Stochastic Characteristic Function Form," Management Science, INFORMS, vol. 23(6), pages 621-630, February.
    11. A. Charnes & Daniel Granot, 1977. "Coalitional and Chance-Constrained Solutions to n -Person Games, II: Two-Stage Solutions," Operations Research, INFORMS, vol. 25(6), pages 1013-1019, December.
    12. Kornhauser, Lewis A & Revesz, Richard L, 1994. "Multidefendant Settlements: The Impact of Joint and Several Liability," The Journal of Legal Studies, University of Chicago Press, vol. 23(1), pages 41-76, January.
    13. Samuel FEREY & Pierre DEHEZ, 2016. "Overdetermined Causation Cases, Contribution and the Shapley Value," LIDAM Reprints CORE 2755, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    More about this item

    Keywords

    Fairness; Joint liability; Stochastic cooperative game theory; Stochastic Shapley value; Threshold case;
    All these keywords.

    JEL classification:

    • K41 - Law and Economics - - Legal Procedure, the Legal System, and Illegal Behavior - - - Litigation Process

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