A Study Of Pollution Control Games With Continuous And Bayesian Continuous Updates

In the classic differential game model,it is usually assumed that in the initial stage of the game,the player knows the information about the whole time interval of the game,but in real life,it is often impossible to know the information on the whole time interval.Therefore,the concept of continuous updating is introduced,it not only perfects the existing dynamic and differential game framework but also more in line with the settings of real life.In the differential game with continuous updating,it is assumed that at each instant the player only knows the information for a fixed length of time without knowing the information on the whole time interval.In fact,life is full of uncertain factors,unknown parameters can be described as random variables,and Bayesian updating has become an important tool for studying unknown parameters.This paper uses a continuous updating method to study the impact of pollution emissions on the environment and national benefits firstly.Using the method of Pontryagin maximum principle,it is found that the cooperative strategy with continuous updating of players and the corresponding cooperative state trajectory in the game.When studying the cooperative model of pollution control problems,the emphasis is on constructing ? class characteristic function with continuous updating,and the Shapley value is used as the optimal cooperation criterion.Finally,through numerical simulation,the pollution state,the characteristic function,and the Shapley value of the classic differential game and the differential game with continuous updating are visually compared.When studying a pollution control model with unknown parameters,it is assumed that the profit of each player depends on its emissions(or productivity),and the emissions of the player have cross-effects.This paper creatively uses the conjugate prior method to obtain the analytical form of the posterior distribution at each stage.When constructing the equilibrium strategy of the model,the classical Bayes theorem and Hamilton-Jacobi-Bellman equation are used to obtain the Bayesian feedback Nash equilibrium strategy of the player in the game.Finally,simulations are used to analyze and compare the equilibrium strategies and pollution status of players in the classic dynamic game and the game with Bayesian continuous updating.