  This paper investigates the game theory of resource-allocation situations
where the "first come, first serve" heuristic creates inequitable, asymmetric
benefits to the players. Specifically, this problem is formulated as a
Generalized Nash Equilibrium Model where the players are arranged sequentially
along a directed line graph. The goal of the model is to reduce the asymmetric
benefits among the players using a policy instrument. It serves as a more
realistic, alternative approach to the line-graph models considered in the
cooperative game-theoretic literature. An application-oriented formulation is
also developed for water resource systems. The players in this model are
utilities who withdraw water and are arranged along a river basin from upstream
to downstream. This model is applied to a stylized, three-node model as well as
a test bed in the Duck River Basin in Tennessee, USA. Based on the results, a
non-cooperative, water-release market can be an acceptable policy instrument
according to metrics traditionally used in cooperative game theory
