HOW TO SHARE JOINT LIABILITY: A COOPERATIVE GAME APPROACH

Sharing damage that has been caused jointly by several tortfeasors is analyzed from a normative point of view. We show how damage can be apportioned on two distinct bases: causation and degree of misconduct. Our analysis uses the concept of potential damage on the basis of which we define a transferable utility game. Its core defines acceptable judgments as allocations of the total damage against which no group of tortfeasors can object. We show that weighted Shapley values define acceptable judgments and, vice versa, acceptable judgments reveal weights. Our paper illustrates how the cooperative approach may bring useful insights into legal questions. In particular, the Shapley value appears of special interest, being founded on axioms that are in line with fundamental principles of tort law.

[1]  M. Fernandez,et al.  A game theoretical approach to sharing penalties and rewards in projects , 2012 .

[2]  L. Shapley.  A Value for n-person Games , 1988 .

[3]  William Thomson,et al.  Cost allocation and airport problems , 2007 .

[4]  F. Parisi,et al.  The Efficiency of Comparative Causation , 2010 .

[5]  R. Posner,et al.  Joint and Multiple Tortfeasors: An Economic Analysis , 1980, The Journal of Legal Studies.

[6]  Frank S. Arnold,et al.  Causal Apportionment in the Law of Torts: An Economic Theory , 1980 .

[7]  G. Owen,et al.  A Simple Expression for the Shapley Value in a Special Case , 1973 .

[8]  E. Kalai,et al.  On weighted Shapley values , 1983 .

[9]  S. Shavell.  Torts in Which Victim and Injurer Act Sequentially , 1982, The Journal of Law and Economics.

[10]  Dov Monderer,et al.  Weighted values and the core , 1992 .

[11]  H. Young.  Monotonic solutions of cooperative games , 1985 .

[12]  Pierre Dehez,et al.  Allocation of Fixed Costs: Characterization of the (Dual) Weighted Shapley Value , 2011, IGTR.

[13]  L. Shapley,et al.  QUASI-CORES IN A MONETARY ECONOMY WITH NONCONVEX PREFERENCES , 1966 .

[14]  Robert J. Weber,et al.  Probabilistic Values for Games , 1977 .

[15]  Shlomo Weber,et al.  Strong tiebout equilibrium under restricted preferences domain , 1986 .

[16]  Frank S. Arnold,et al.  Causal Apportionment: Reply to the Critics , 1986, The Journal of Legal Studies.

[17]  R. Cooter.  Torts as the Union of Liberty and Efficiency: An Essay on Causation , 1987 .

[18]  A. Roth.  The Shapley value , 2005, Game Theory.

[19]  Lloyd S. Shapley,et al.  On balanced sets and cores , 1967 .

[20]  L. Shapley.  Cores of convex games , 1971 .

[21]  L. S. Shapley,et al.  Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts , 1979, Math. Oper. Res..

[22]  Yves Sprumont,et al.  Sharing a River , 2002, J. Econ. Theory.

[23]  L. Kornhauser,et al.  Sharing Damages among Multiple Tortfeasors , 1989 .

[24]  T. Mayer,et al.  The Economics of Clusters: Lessons from the French Experience , 2011 .

[25]  Tatsuro Ichiishi,et al.  Super-modularity: Applications to convex games and to the greedy algorithm for LP , 1981 .

[26]  Gregory Levitin,et al.  Active vs. Passive Defense against a Strategic Attacker , 2011, IGTR.

[27]  D. Schmeidler.  The Nucleolus of a Characteristic Function Game , 1969 .

[28]  Arantza Estevez-Fernandez.  A Game Theoretical Approach to Sharing Penalties and Rewards in Projects , 2008 .