Coupled constraint Nash equilibria in environmental games

The focus of this paper is on how to model and solve an environmental compliance problem using [Rosen, J.B., 1965. Existence and uniqueness of equilibrium points for concave n-person games. Econometrica 33 (3), 520–534] seminal idea of coupled constraint equilibrium. First, Rosen's results about the existence and uniqueness of a Nash normalised equilibrium for coupled constraint games are explained. These results are then combined with a numerical approach to game solutions based on the Nikaido–Isoda function. A river basin pollution game, which is a model for a common nonpoint source pollution problem, is solved numerically using this approach. In the game, the agents face a joint constraint on the total pollution, which defines a coupled constraint set in the combined strategy space. This makes the game special in terms of the strategy spaces. Unlike for standard games where they are defined separately for each player, here we have a joint constraint on the combined strategy space of all players. Hence, the game needs coupled constraint equilibrium as the solution concept. Static and (open-loop) dynamic equilibria are computed for the basin problem under the discussed equilibrium concept. All equilibria are instructive for the legislator, in that they contain information on how to choose the “optimal” charges, under which agents obey the constraints.