An Endogenous Approach to the Polluted River Problem

Polluting agents situated along a river must collectively clean it to meet a minimum water quality standard. Since cleaning operations are costly, it is crucial to allocate these expenses fairly. This paper introduces the Upstream Prorata Sharing method, which endogenously assigns responsibility to each agent based on the potential costs their pollution imposes on downstream river segments. We present three distinct axiomatic characterizations grounded in different principles. First, we explore fairness properties, which address scenarios where some agents reduce their cleanup costs. Next, we examine merging properties, analyzing the implications of two agents combining into a single entity. Finally, we propose a redistribution property, which quantifies how much an agent should contribute to cleaning downstream segments.