Tagged Spatial Evolution Dynamics Model

Evolutionary game theory is developed on the basis of Darwin's theory of biological evolution as a new research field. It is used to research the changes in individuals over time in a group when combining evolutionary dynamics and game theory in traditional economics. Evolutionary game theory is a strong theoretic tool to study the cooperation between the groups. Nowak and May introduce the concept of spatial grid firstly. Based on this, extensive field of spatial network is developed, like Evolutionary Game on complex networks, Evolutionary game between effective population and so on.The first chapter describes the evolutionary game theory and related theoretical background knowledge, meanwhile explains the related rules between prisoner's dilemma and Nash Equilibrium and spatial game. The second chapter introduces several related evolutionary dynamics models, also describes the evolution of the lattice dynamics and the dynamics model based on indirect reciprocity and direct reciprocity.Based on the above theoretical knowledge and by considering the group system of an individual distributed in the grid, this paper establishes two evolutionary dynamics models. Firstly, we have studied the effect of fixed tag on the evolution dynamics of the Prisoner's Dilemma. Secondly, we have studied the impact of change tag on the evolution dynamics. A detailed description as follows:1) For fixed tags, each individual carries with a recognizable, inheritable tag. We use the prisoner's dilemma model to study the influence of a fixed tag on the cooperation degree of the individuals in the population. Initially, the amount of each tag is a normal distribution, and with the increase of tag types, the cooperation degree when system is stable becomes higher; When the betrayer's income increasing, the proportion of cooperation is stepped fall. In the beginning, if the amount of each tag is a evenly distribution according to the probability, The average proportion of cooperation is higher than normal distribution when the system becomes stable with changing tag types; And also, when the tag type is more than one, the curve of the cooperation degree still shows a stepped fall.2) For changed tags, each individual not only carries with a recognizable, inheritable tag, but also carries with ability to endure and learning probability. Similarly, we use the prisoner's dilemma model to study the influence of a change tag on the cooperation degree of the individuals in the population. The results show that when the learning probability is 0.1, the cooperation degree of the population is negatively correlated with the capacity; and when the ability to endure is 0.2, the cooperation degree of the population is positively correlated with the capacity...