This research applies cooperative game theory—specifically, the bankruptcy model—to address conflicts arising from the scarcity of water resources shared by multiple agents. This case study addresses potential outcomes of five allocation rules applied to the apportionment of water between two agents in the Missouri River. Currently, there is no interstate compact to apportion Missouri River and frequent disputes between upstream and downstream states occur. Upstream states favor managing reservoir water levels to support reservoir recreation and downstream states want water for the downstream navigation channel. The five allocation rules studied are (1) Proportional Sharing, (2) Constrained Equal Awards, (3) Constrained Equal Losses, (4) Sequential Sharing based on Proportional Sharing, and (5) a proposed Modified Constrained Equal Awards rule. The results of the analysis of apportionment during four dry years in the 2000s show that the best approaches are the proposed Modified Constrained Equal Awards Rule and the Proportional Sharing Rule.

The Missouri River is the longest river in North America and flows from the semi-arid western states to the relatively moist Midwest. An integrated system of large reservoirs, constructed in the mid-20th century, provides important water storage, hydroelectricity and flood control benefits. This system has been managed by the US Army Corps of Engineers which has traditionally followed its original mandate to support navigation and flood control. As water uses and societal values have evolved, the management of the river has slowly evolved, and the Army Corps of Engineers has adopted adaptive management to incorporate biological uncertainties into its decision-making. Other evolution, including the incorporation of economic incentives into water management, has failed to occur.