Nash Equilibria Of Dynamical Game For Two Classes Of Population Dynamics

The natural environment and resources is the bases for human development, especially renewable resources, which have main effect for human survival and progress.Under the premise of ensuring the ecological balance and resource to exist for a long time, study of the development and utilization of resources in order to get the best benefit problem is certainly has practical significance.In recent years, domestic and foreign scholars study resource management problem, and many important results are obtained. Early studies mainly consider only one developer monopoly situation, and for the two developers competition situation research not much,This paper mainly discusses the Nash equilibria of dynamical game for Size population model and periodic population model. According to the contents, it is divided into three chapters:In the first chapter, it introduces the background, the present study situation of population dynamics system at home and abroad and the preparative theories.In the second chapter, a dynamical game in the exploitation of periodic age-dependent population resources is considered. The existence of Nash equilibria is established by Kakutani’s fixed point theorem for multivalued mappings, and the structure of equilibria is described by normal cones and adjoint system techniques.In the third chapter, structure of Size population model with dynamic game Nash equi-librium and optimal control problems is researched.