Application Of Heterogeneous Differential Game Model In Pollution Control

The players are always homogeneous when using differential games to solve pollution control problems.However,differential games are able to solve more specific practical problems after introducing heterogeneous assumptions in differetial games.For instance,differential games with asymmetric time horizons can used to analyse the influence on regional pollution when factory relocations take place.And differential games with multiple states are able to study emissions of different factories,when there are multiple pollution taxes.A two-player differential game with different time horizons is studied in this paper.The game is used to analyse the effect of factory relocation on regional pollution.The Nash Equilibrium is obtained by using the Pontryagin's maximum principle,and the equation of the state pollution is derived after that.The method for constructing the characteristic function is maximum-minimum principle.And the cooperation solution researched in this game is Shapley value.The simulation not only shows the difference of state pollution between cooperation and non-cooperation,but also compares the difference of players' strategies in these two cases.Moreover,the time consistency of the cooperation is studied,and the imputation distribution procedure over Shapley value is also been calculated.As for the differential game with two states,the Nash Equilibrium is studied at first.And the equilibrium is used to research the influence on pollution when factories encounter two different pollution taxes.When constructing the characteristic function of coalitions in this game,the assumption is that all the other players choose their Nash Equilibrium strategies in the initial non-cooperative game.The Shapley value is viewed as the solution of the cooperative game.At last,the influenece on state pollution and players' payoffs are shown by using the simulation.