Sharing the cost of cleaning up a polluted river

Abstract

Consider a group of agents located along a polluted river where every agent must pay a certain cost for cleaning up the polluted river. Following the model of Ni and Wang (2007), we propose the class of α-Local Responsibility Sharing methods, which generalizes the Local Responsibility Sharing (LRS) method and the Upstream Equal Sharing (UES) method. We first show that the UES method is characterized by relaxing independence of upstream costs appearing in Ni and Wang (2007). Then we provide two axiomatizations with endogenous responsibility of the α-Local Responsibility Sharing method, one using this weak independence axiom (taken from the UES method) and one using a weak version of the no blind cost axiom (taken from the LRS method). Moreover, we also provide an axiomatization with exogenous responsibility by introducing α-responsibility balance. Finally, we define a pollution cost-sharing game, and show that, interestingly, the Half Local Responsibility Sharing (HLRS) method coincides with the Shapley value, the nucleolus and the τ -value of the corresponding pollution cost-sharing game. This HLRS method can be seen as some kind of middle compromise of the LRS and UES methods.