Sustainable cooperation on the hybrid pollution-control game with heterogeneous players

This paper considers a hybrid pollution-control differential game with two farsighted players and one myopic player. Both the seasonal regime shifts in the state dynamics and the players' heterogeneous preferences are introduced into the model. The strategies under cooperative, noncooperative and partially cooperative scenarios are obtained by utilizing the Pontryagin's Maximum Principle. Under all feasible coalition structures, the convergence of the state variable is proved. A new sustainably--cooperative optimality principle is proposed according to the coalition structures, which belongs to the imputation set. The prerequisite for the existence of time-consistency in the sustainably-cooperative optimality principle is explicitly obtained. The seasonal imputation distribution procedure (IDP) is designed to maintain the time-consistentcy (dynamic stability) of cooperation over time.