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How to share joint liability: a cooperative game approach

  • DEHEZ, Pierre

    ()

    (Université catholique de Louvain, CORE, Belgium)

  • FEREY, Samuel

    ()

    (BETA, University of Lorraine, Nancy, France.)

Sharing a damage that has been caused jointly by several individuals - called tortfeasors - is a difficult problem that courts often face. Even if there are basic principles and rules to apportion damages among them, legal scholars are still looking for a systematic apportionment method. We analyze that question from a normative point of view, using the theory of cooperative games that offers an axiomatic approach to surplus or cost sharing. We show how this kind of damage can be apportioned on two distinct basis, causation and degree of misconduct. Our analysis is based on the concept of potential damage. The potential damage associated to a subset of tortfeasors is the monetary value of the damage that they would have caused without the participation of the other tortfeasors. It is distinct from the additional damage associated to a subset of tortfeasors that is given by the difference between the total damage and the potential damage of the complementary subset. We distinguish two situations of joint liability, the simultaneous case where the damage would not have occurred in the absence of any one of the tortfeasors and the sequential case where the sequence of acts that has produced the damage is known. In the simultaneous case, the potential damage of an individual tortfeasor is by definition zero. In the sequential case, the only information needed is the immediate damage each tortfeasor has caused, depending on his or her position in the sequence. A judgment specifies for each tortfeasor an amount to be paid. That amount should not exceed his or her additional damage but should not fall below his or her potential damage. This defines two natural bounds, an upper bound and a lower bound, that we extend to subsets of tortfeasors. A judgment is fair if the contribution of any subset of tortfeasors is inferior to his potential damage and superior to his additional damage. Particular fair judgments are then obtained by assigning weights to tortfeasors to reflect difference in degrees of misconduct. In game theoretic terms, potential damages define a transferable utility game whose core defines fair judgments. We show that weighted Shapley values define fair judgments and, vice versa, fair judgments reveal weights. Our paper illustrates how the cooperative approach may bring useful insights into legal questions. The Shapley value appears of particular interest in a legal context because it is founded on axioms that are in line with the fundamental principles of tort law.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2012023.

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Date of creation: 21 Jul 2012
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Handle: RePEc:cor:louvco:2012023
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  1. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
  2. Ambec, Stefan & Sprumont, Yves, 2000. "Sharing a River," Cahiers de recherche 0006, GREEN.
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  6. Pierre Dehez, 2011. "Allocation Of Fixed Costs: Characterization Of The (Dual) Weighted Shapley Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 141-157.
  7. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer, vol. 21(1), pages 27-39.
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  9. Duranton, Gilles & Martin, Philippe & Mayer, Thierry & Mayneris, Florian, 2010. "The Economics of Clusters: Lessons from the French Experience," OUP Catalogue, Oxford University Press, number 9780199592203, March.
  10. 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.
  11. Pierre Dehez, 2011. "Allocation of fixed costs: characterization of the (dual) weighted Shapley value," Working Papers of BETA 2011-03, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  12. repec:cup:cbooks:9781107013940 is not listed on IDEAS
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