We study partial coalition formation and the strategic timing of membership of an IEA for environmental issues in the Coalitional Bargaining Game (CBG) of Gomes (Econometrica 73:1329–1350, 2005). We apply the CBG to a specific river sharing problem with two symmetric upstream agents, each at a tributary, and one downstream agent located at the junction of tributaries. We identify five regions in the parameter space of a discount factor and a productivity parameter for water. In one region the grand coalition always forms immediately. In two other regions, immediate formation of the grand coalition and gradual coalition formation both occur with positive probability. In another two regions only gradual coalition formation occurs. In one of these latter regions, a region with discount factors close to one, both upstream agents form a monopoly with positive probability. Formation of the monopoly persists in the limit as the discount factor goes to one.