A Discrete-Time Dynamic Game of Seasonal Water Allocation

We present a method for the derivation of feedback Nash equi- libria in discrete-time finite-horizon nonstationary dynamic games. A partic- ular motivation for such games stems from environmental economics, where problems of seasonal competition for water levels occur frequently among heterogeneous economic agents. These agents are coupled through a state variable, which is the water level. Actions are strategically chosen to max- imize the agents individual season-dependent utility functions. We observe that, although a feedback Nash equilibrium exists, it does not satisfy the (exogenous) environmental watchdog expectations. We devise an incentive scheme to help meeting those expectations and calculate a feedback Nash equilibrium for the new game that uses the scheme. This solution is more environmentally friendly than the previous one. The water allocation game solutions help us to draw some conclusions regarding the agents behavior and also about the existence of feedback Nash equilibria in dynamic games. The paper draws from Refs.1–2. Its earlier version was presented at the Victoria International Conference 2004, Victoria University of Wellington, Wellington, New Zealand, February 9–13, 2004. We thank the anonymous referee and Christophe Deissenberg for insightful comments, which have helped us to clarify its message. We also thank our colleagues Sophie Thoyer, Robert Lifran, Odile Pourtalier, and Vladimir Petkov for helpful discussions on the model and techniques used in this Paper. Gratitude is expressed to the Kyoto Institute for Economic Research, Kyoto University, for this author's support in the final stages of the paper preparation