Sharing a Polluted River Network

Abstract

A polluted river network is populated with agents (e.g., firms, villages, municipalities, or countries) located upstream and downstream. This river network must be cleaned, the costs of which must be shared among the agents. We model this problem as a cost sharing problem on a tree network. Based on the two theories in international disputes, namely the Absolute Territorial Sovereignty (ATS) and the Unlimitted Territorial Integrity (UTI), we propose three different cost sharing methods for the problem. They are the Local Responsibility Sharing (LRS), the Upstream Equal Sharing (UES), and the Downstream Equal Sharing (DES), respectively. The LRS and the UES generalize Ni and Wang ("Sharing a polluted river", Games Econ. Behav., 60 (2007), 176-186) but the DES is new. The DES is based on a new interpretation of the UTI. We provide axiomatic characterizations for the three methods. We also show that they coincide with the Shapley values of the three different games that can be defined for the problem. Moreover, we show that they are in the cores of the three games, respectively. Our methods can shed light on pollution abatement of a river network with multiple sovereignties.JEL classification: C71, D61, D62.

Polluted river problems and games with a permission structure

“…These issues are considered initially by Ni and Wang (2007) for single spring rivers, and generalized by Dong, Ni, and Wang (2012) for rivers with multiple springs. They introduced the so-called cost sharing problem on a river network, shortly called polluted river problem, where besides a river structure, for every river segment a fixed cleaning cost is given.…”

“…Games with a permission structure model situations where players in a cooperative transferable utility game belong to some hierarchical structure where players need permission from some of their superiors before they can cooperate with other players. The polluted river problems correspond to games with a permission structure where the game is the inessential game where the worth of each coalition is the sum of the cleaning costs for all agents in the coalition (which is the Local Responsibility game used by Dong, Ni, and Wang (2012) to obtain the LRS method), and the digraph (permission structure) is the sink tree corresponding to the river structure with the arcs oriented from upstream to downstream agents.…”

“…Ni and Wang (2007) first consider this problem as cost sharing problems on a river network, shortly called polluted river problems. They consider rivers with one spring which was generalized by Dong, Ni, and Wang (2012) to rivers with multiple springs. They introduce and axiomatize three cost sharing methods: the Local Responsibility Sharing (LRS) method, the Upstream Equal Sharing (UES) method and the Downstream Equal Sharing (DES) method.…”

Power Measures and Solutions for Games Under Precedence Constraints

“…The river games of Ambec and Sprumont [27] consider the problem of allocating clean water among the agents (countries), living along the river. On the other hand, Dong et al [28] consider the cost allocation problem, where cleaning costs to clean a river from its pollution have to be allocated over the agents along the river. Applying precedence power solutions, we can consider different allocation rules, where the different power measures, on which the solutions are based, express the right of the agents on clean water (in case of allocating clean river water) or the responsibility of the agents in the pollution (in case of allocating cleaning costs).…”

Games with a permission structure - A survey on generalizations and applications

“…Applications of peer group games are, e.g. polluted river games (Ni and Wang (2007) and Dong et al (2012)), liability games (Dehez and Ferey 2013), the duals of airport games (Littlechild and Owen 1973), auction games (Graham et al 1990) and ATM games (Bjorndal et al 2004). From 24 Consider the game with permission structure (v, D) on N = {1, 2, 3} given by D = {(1, 2), (2, 3)} and v = u {3} .…”