Apportionment of liability by the stochastic Shapley value

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.