A dynamic game for managing a conservative pollutant in an estuary

A two-person non-zero asymmetric discrete time infinite dynamic game is developed to address pollution management in an estuary. The game is between two cities on an estuary which need to reduce their pollutant loadings to within acceptable bounds while maximizing their net benefits. The game is asymmetric because one of the cities is adjacent to a park which benefits both cities. A tax is used as the pollution abatement method. A feedback Nash equilibrium is found which solves the game of the two cities. The strategies of the two players depends on the tax rate and on the concentration of the pollutant in the estuary. Realistic state dynamics are incorporated using a box model to model the flow of the estuary rendering the state space two-dimensional. A bicubic spline interpolation with a combination of policy iteration and successive approximation is implemented to solve the game. The acceptable bounds are fuzzified and a dynamic game with a fuzzy constraint is introduced. Fuzzy dynamic programming is used to solve the game with a fuzzy constraint.