Comment on ‘Sharing a polluted river’

In Ni and Wang (2007) two solutions are given to determine the division of the cost of cleaning a river among the agents located along the river. For each solution the authors give three different motivations, namely (i) an axiomatic characterization, (ii) the solution is the Shapley value of an appropriately defined cooperative TU-game, and (iii) the solution belongs to the Core of the associated game. In this comment we argue that the results (ii) and (iii) follow directly from more general results on inessential and auction or dual airport games. We also provide some alternative axiomatizations without the Additivity axiom. Finally, we state more general results for these cost allocation methods that follow immediately from well-known results on cooperative games.