To clean up the pollutants in cross-boundary rivers needs the collaborative actions among different agents involved. In our paper, we deal with the river pollution problem in a cooperative situation. We first introduce the adjacent downstream compensation method by considering the bargaining behavior between any two neighbour agents, which reconciles two famous doctrines in the international disputes, i.e., the Absolute Territorial Sovereignty theory and the Unlimited Territorial Integrity theory. Then we prove the coincidence of the adjacent downstream compensation method and the Shapley value of the corresponding responsibility game. By studying the concavity of the river pollution cost sharing game, we illustrate the stability of the adjacent downstream compensation method.

清理跨界河流中的污染物需要相关机构之间的协同行动。在本文中，我们以合作的方式处理河流污染问题。首先，我们通过考虑任何两个邻居代理人之间的讨价还价行为来介绍相邻的下游补偿方法，该方法与国际争端中的两个著名学说，即绝对领土主权理论和无限领土完整理论相协调。然后，我们证明了相邻下游补偿方法与相应责任博弈的Shapley值的一致性。通过研究河流污染成本分摊博弈的凹度，我们说明了相邻下游补偿方法的稳定性。