Empirical Study Of Evolutionary Game On Treelike Networks

Evolutionary game theory on the network is one of the basic dynamics in complex system. The prisoner’s dilemma game is one of the most representative problems among related researches of the evolutionary game models. First, the topology structure of the network itself decides the level of cooperation; second, the selection mechanism of the cooperative nodes will affect the whole dynamical process of the evolutionary game. There are a large number of treelike structures in real complex system, such as rivers, galaxies and the national organization, with few systemic researches on treelike networks. Moreover, the previous studies of the prisoner’s dilemma usually choose cooperative nodes randomly at the initial time, which is hard to reflect real situations in networks.This thesis starts from the treelike network, on which we study the characteristics of the prisoner’s dilemma game. At the same time, a fitness evaluation mechanism with memory is introduced into the prisoner’s dilemma game to deeply understand the effect of memory for cooperative behavior. In addition, the evolutionary game model can be used to the empirical analysis of Spartina alterniflora treelike network. Inter discipline study can be promoted through applying the game theory to ecology. Followings are the main contributions of the thesis:1. This thesis builds three treelike network structures with different degree distribution characteristics, analyzes the structure characteristics. Based on the common constructing algorithms of network models, three kinds of treelike networks——BA scale-free treelike network with power law degree distribution, the complete binary treelike network with degree values in the set of{1,2,3} and the small-world fractal treelike network with exponential distribution are built. These three kinds of network models not only include the most common scale-free and small-world characteristics in complex systems, but also cover the prominent binary structure, which is special in the configuration of tree structure.2. We study an evolutionary version of the Prisoner’s Dilemma game and introduce a fitness evolutionary mechanism with memory into treelike networks. Initially, the distribution of strategies among the nodes in the network obeys two different rules:distributed randomly and distributed in accordance with the nodes’degree. The simulation results find that the cooperation frequency fc decreases as the advantage of defectors over cooperators increases when the cooperative nodes are selected randomly and the construction algorithms make no special effect on the results; the cooperative nodes’degree plays the dominating role when the cooperative nodes are selected based on the nodes’ degree.3. Based on the spatial configuration of Spartina alterniflora, we construct the empirical network, the clonal plant multiple relation treelike network, to explore the evolutionary game characteristics. First, we study the structure properties of Spartina alterniflora, which reflect the ecological strategy that avoiding competition between each other. Second, the evolutionary Prisoner’s Dilemma game is introduced into the Spartina alterniflora treelike network. Initially, the distribution of strategies among the nodes in the "network obeys three different rules:distributed randomly, with fc decreasing with the increasing of b, in accordance with different types of Spartina alterniflora biological units and the nodes’ degree, the nodes with larger degree play an important role. In addition, the fitness evolutionary mechanism with memory is also introduced to analyze the effect of memory in empirical treelike network. Finally, we consider the public goods game with only two strategies and with voluntary participation to analyze the relationship between the frequency of different strategies and the initial distribution of cooperative nodes, in that way we get the evolutionary game dynamics characteristics of Spartina alterniflora clonal plant empirical network.