The Kura-Araks Basin is facing problems with insufficient water availability for all needs and poor water quality, which results in high rates of waterborne diseases. The riparians of the basin struggle with management of water resources within their national borders, as well as internationally, across the basin. With international rivers, interdependency among countries is created, where the upstream country can impact the quantity and quality of water downstream. This study focuses on the upstream-downstream relationship with the Kura River between Azerbaijan and Georgia. The analysis uses a game theoretical framework, which incorporates several issues in the negotiation space. Specifically, water quantity and water quality are analyzed separately and combined into an aggregated isolated game. The analysis compares the aggregated isolated game, where the outcome of each game is negotiated separately, with an interconnected game, where the two games are jointly negotiated. Using realistic parameters, results show that due to the repeated nature of some of the payoffs, cooperation is unlikely to be achievable in each game independently, since at least one country has an incentive to deviate. In contrast, the interconnected game can achieve full cooperation and increase the welfare of both countries.