A Tripartite Game Analysis of Environmental Pollution Control Based on Complicated Intergovernmental Relations

An excellent ecological environment is conducive for improving economic benefits and social benefits. The environmental pollution control requires the cooperation of governments at all levels and a large amount of capital investment. However, under the system with Chinese characteristics, the intergovernmental relations present complex and dynamic characteristics: the central government is authoritative, the local governments are obedient and self-interested, and the environmental pollution control usually involves multiple government departments, while it has strong externality, which makes it easy to breed “free rider” behavior in the process of environmental pollution control. Therefore, the cross-regional environmental pollution control cooperation model of governments at all levels is a complex and worthwhile research problem. Based on this, the paper studies a tripartite game problem of environmental pollution control from both horizontal and vertical intergovernmental relations. The Hamilton–Jacobi–Bellman equation was used to obtain the optimal effort strategy, environmental pollution control level, and environmental pollution losses under the Nash game model, the Stackelberg game model, and the Cooperative game model. The results show the following: firstly, the governments’ environmental pollution control efforts are positively related to their own execution ability and influence ability and negatively related to the cost coefficient; secondly, from the perspectives of environmental pollution control level and environmental pollution losses, the Cooperative game model is superior to the Nash game model and the Stackelberg game; thirdly, this paper analyzes the relationship between the loss-bearing ratio, the special financial funds, the effort level of government, and the environmental pollution control level; finally, the conclusions are verified by numerical analysis, which proves the validity of the models.

On the numerical solution of a free end-time homicidal chauffeur game

A functional formulation of the classical homicidal chauffeur Nash game is presented and a numerical framework for its solution is discussed. This methodology combines a Hamiltonian based scheme with proximal penalty to determine the time horizon where the game takes place with a Lagrangian optimal control approach and relaxation to solve the Nash game at a fixed end-time.

A Nash-game approach to joint data completion and location of small inclusions in Stokes flow

International audience We consider the coupled inverse problem of data completion and the determination of the best locations of an unknown number of small objects immersed in a stationary viscous fluid. We carefully introduce a novel method to solve this problem based on a game theory approach. A new algorithm is provided to recovering the missing data and the number of these objects and their approximate location simultaneously. The detection problem is formulated as a topological one. We present two test-cases that illustrate the efficiency of our original strategy to deal with the ill-posed problem. Nous étudions le problème de détection des petites inclusions immergées dans un fluide visqueux et incompressible, lorsque le mouvement de celui-ci est régi par les équations de Stokes. Des données du type Cauchy seront ainsi fournies seulement sur une partie frontière de l’écoulement.A cet égard, nous essayons de développer une méthode originale basée sur une approche de théorie des jeux, pour résoudre notre problème inverse. Un nouvel algorithme a été donc présenté traitant simultanément la question de la reconstruction des données manquantes avec celle de détection d’objets. La notion de gradient topologique a été utilisée afin de déterminer le nombre d’objets présents et leurs localisations approximatives. Dans cet objectif, une étude numérique présentée, a été effectuée pour prouver l’efficacité de la méthode.