Emergence Of Cooperation On The Complex Networks Study On The Inhomogeneity In Spatial Public Goods Games

Cooperation is ubiquitous both in animal and social systems, researching the emergence and the evolution of cooperative behavior is one of the most important issues in the evolutionary biological science and social theory. Game theory, especially the evolutionary game theory, provides an effective theoretical framework for the scientists to study this issue. Given the complexity of the actual social networks as well as the complicated interacted forms of the individuals, study of game theory on the complex networks has a rapid development recently.In this thesis, we generalize the development of game theory, and introduce the basics of the classical game theory and traditional evolutionary game theory. Studies of evolutionary game theory on the complex networks are mainly elaborated including the topology of network, game evolving rules and so on. Considering the fact of the diversity of interaction among the individuals, we investigate the impact of inhomogeneity on the evolution of cooperative behavior on the spatial public goods games, the work are as follows:1. Individual inhomogeneity. Preferential selection rule is introduced into the public goods games. The term preferential selection is realized that one player will select a neighbor from its neighborhood with the probability dependent on the payoff of this neighbor, i.e., the higher the payoff, the higher the probability is. It is found that compared with the original version with the stochastic selection, preferential selection can remarkably promote cooperation, and it is in favor of forming the cooperative clusters and the spread of the cooperation during the whole population.2. Group inhomogeneity-spatial diversity of the value of public goods. Multiplication factor embodies the value of the public goods'feedback to the public, and the value of the public goods is diverse in the real social system. We discuss the impact of three different distributions of multiplication factor in spatial public goods games, and find that compared with the classical version, cooperative level is remarkably improved for all the distributions in which uniform distribution enables the best enforcement on almost the range of the parameters. Besides, it is proved that there exits an optimal diversity inducing the best cooperation for the cases of exponential distribution and power-distribution. Furthermore, it is shown that cooperation in the case of power-law distribution is most tolerant to the noise.3. Group diversity-depreciation of the public goods. In reality, the value of the public goods will be reduced or even lost because of the surroundings or the reason of themselves, we construct a model to describe this phenomenon: critical mass (CM) as maximum affordability index is introduced into the public goods games, it is assumed that if the number of cooperators in a one unit group reaches the index, each individual enjoys the best payoff of the public goods, otherwise, the multiplication factor decreases, and the payoff is calculated according to the form of classical payoff function. The simulation results show that it plays different behavior for different values of critical mass (CM), and there exits an optimal critical mass enabling the overall cooperative level at some value of multiplication factor. Furthermore, it is proved that the exit of the critical mass is irrelative to the interacted topology of the regular network, and the system always gets the global cooperative level at CM=G-1, where G is the size of one unit group.4. Group diversity-depreciation of the public goods caused by the surroundings. The multiplication factor represents the value of the public goods, and the surroundings will influence the value of the public goods, so our model is described as follows: The multiplication factor in a single group is related with the numbers of cooperators in this group as a function of whereβ0 is a tunable parameter. It is found that compared with the original version (β0), the cooperative level is remarkably improved, and there exist moderate values ofβinducing the best cooperation. Besides, the cooperative flat of optimalβbroadens as the multiplication factor increases. Moreover, impact of noise on cooperation is investigated, and it is proved that variation of cooperation with the noise not only depends on the values of r, but also has the relation with the values ofβ, and cooperation in the case ofβ1.0 dominates on almost the range of noise for each values of r. We investigate the initial distribution of the multiplication factor forβ1.0, and find that the initial distribution can be depicted as Gaussian distribution.