Asymmetric Nash Solutions in Trans-boundary River Sharing Problems

As mentioned in Chapter 1, the main issues in trans-boundary river basins are scarcity of water and externalities from upstream to downstream. For instance, excessive water consumption of upstream countries might deprive the right of water consumption for downstream countries. Another prominent issue is that upstream countries could pollute the trans-boundary river carelessly without taking into account the downstream countries' benefits. Unfortunately, the property rights of water in trans-boundary river basins are not properly defined. Therefore, some particular characteristics of the river sharing problem such as the externalities of pollution from upstream to downstream and the absence of clearly defined property rights in international river situations have drawn interests from researchers to study the river sharing problem. Giannias and Lekakis (1996) and Kilgour and Dinar (2001) analyze the river sharing problem between two or more countries along an international river that is linear, i.e., a river where agents are located subsequently from upstream to downstream. The model in the first reference distinguishes between upstream and downstream, is deterministic and has both water quantity and water quality. The second reference analyzes a stochastic model of water quantity among several countries. Both studies characterize the unique allocation that maximizes utilitarian welfare. Ambec and Sprumont (2002) mark the start of embedding legal principles from International Water Law in the river sharing problem. They translate the legal principles of Absolute Territorial Sovereignty (hereafter, ATS) and Unlimited Territorial Integrity (hereafter, UTI) into their model. ATS is applied to every group of agents and imposes conditions of core stability. UTI is also applied at the group level, but it is an aspirational approach. It is impossible that distinct groups of countries can simultaneously achieve their group aspiration levels. As appropriate requirements, Ambec and Sprumont (2002) propose group ATS and that no group attains a welfare above its group aspiration level. For a linear river with insatiable agents, they show that the downstream incremental solution is the only welfare distribution that satisfies these