Dynamic Analysis And Control Strategy Of The Supervision Game In Environmental Pollution

The supervision mechanism of environmental regulation is critical to reduce the risk of the uncontrollable pollution and to ensure the performance of environment policies. The dynamics and complexity of the environmental pollution commonly invalidates the prediction and control strategies in real life. Therefore, it is essential to investigate the environmental supervision mechanism. Game theory is an effective methodology to resolve the conflicts on the environmental resources. However, the related ressarch works up to date mainly focus on finding the equilibrium states using traditional game theory, regardless of the uncertainties induced by the bounded rationality in the dynamic gaming procedure. The recent studies on the application of evolutionary game mostly pay attention to the existence of the Evolutionary Stable Strategy, in spite of the discussion about the control strategies. Researches on multi-person game focused on the "cooperative pollution" firms, neglecting the fact that the competitions between firms are more common. Thus, the objective of this thesis is to investigate the dynamic procedure of supervisory game and to optimize the penalty mechanism to control the over-pollution behavior of firms.This thesis investigates the dynamics analysis of evolutionary procedure of supervisory game and the optimization of punishment strategy as a control method. The long term dynamic supervisory relationship between government and polluting firms is modelled using game theory. The dynamic systems analysis methodology combined with System Dynamics (SD) are used to study the effects of environment policies, especially the penalty mechanism, on the Nash equilibrium and the complex dynamic gaming procedure. An optimized punishment strategy is proposed in a differential game framework.In particular, this thesis firstly develops a System Dynamic model for mixed-strategy game between the government and the polluting firm, without or with the consideration of information delay. For the case without information delay, it takes both game players a long time to reach the Nash equilibrium. For the case with information delay, a double penalty is proposed to deal with the unreachable Nash equilibrium. As a critical stable state, the Nash equilibrium might be unreachable by any small perturbation. So the dynamic analysis of paths to the equilibrium state is more significant than the Nash equilibrium itself.Subsequently, considering the bounded rational of decision-makers, the dynamic evolutionary procedure of two-player asymmetric game model is investigated. A dynamic penalty is suggested to deal with the problem that there does not exit evolutionary stable strategy (ESS) under the condition of static payoff matrix. Theory analysis and computer simulation validate the dynamic penalty.This thesis further considers the competitive relationships between the polluting firms. The dynamic procedure of multi-person asymmetric evolutionary game model is developed. The penalty factor k, which indicates the limit of fine, is closely related with the volatility of the dynamic evolutionary procedure. The static penalty has a better effect on the restrain of environmental pollution, while the dynamic one can stabilize the fluctuation during the evolutionary game procedure.Lastly, it is considered, within the framework of a differential game, that the enforcement of regulator using an appropriate penalty can force a polluting firm to act in a socially optimal way. Two different penalty mechanisms, one with the suspension of production (SOP) and the other without SOP (NSOP), are discussed. A completely restraining penalty (CRP), which relates to both players' strategies, is identified to reduce the probability of the firm's pollution behaviors.