Research Of Cooperative Emergence Mechanism Of Donation Behavior On Correlation Network

Cooperative behaviors as well as other altruistic behaviors exist everywhere in the real word. For instance, as we all know, male spider will be eaten by the female spider after mating. Otherwise, many people risk their lives to save others who are in distress. These altruistic behaviors all exhibit selfless spirit and such altruism is inseparable during the course of building a harmonious society. The urgent need for a good atmosphere of harmonious society has caused many scholars of different fields pay attention to altruistic behavior. Game theory provides the modeling foundation and analytical method to investigate how altruistic behaviors influence the cooperation between individuals.As a mathematical research method, game theory abstracts some concrete issues and then studies the development rules and characteristics inside them. It provides an extremely effective systematic framework for researching the emergence and evolution among individuals in the social life. Game theory considers that individual is absolutely rational which means that individuals always maximize their profits under certain constraint conditions. At the same time, the individual will have conflicts during their cooperation. In this paper, the game model we adopt is a typical model of game theory namely the prisoner’s dilemma game. The reason why we chose it is that the prisoner’s dilemma as a research prototype of reciprocal altruism has attracted wide attention. In addition, the prisoner’s dilemma demonstrates the conflict between the interests of individuals and those of the collective. While Complex networks provide a systematic framework for describing the game relationship between individuals.There are a variety of complex networks in the real world, not only in nature but also in human society. We consider individuals which are involved in the game as nodes in the network and the edges are their game relationship. The actions of individuals in the network will be influenced and restricted by the network layout, the game rules and the actions of the neighbors. However, the vast majority of network in the real world will not be as random network, nor the rules of the network as the same as the absolute determination of the relationship. Therefore, this paper uses the WS small world network as the basis of our research; it can express some of the characteristics of the network from the real point of view.In order to study the relationship between altruistic behavior and individual cooperation emergence mechanism on complex network, in this paper, we adopt the prisoner’s dilemma game on correlation network to simulate individual how to choose their own strategy when there is a conflict between individual interests and group interests, and individuals autonomously chooses whether to make a donation to disadvantaged groups and whether to learn adjacent individuals’ strategy. We implement repeated prisoner’s dilemma game on the network until the stable state. Finally, we count the cooperation circumstances of individual and analysis the effect of donation Behavior and other factors on cooperation. The optional strategy of individual in our investigative mechanism has only two situations: cooperation and defection. In addition, each individual can only interact with their neighbors.Theoretical analysis and simulation results show that donation behavior can promotes cooperation in prisoner’s dilemma on correlation network. The cooperation rate becomes higher as the increasing of the degree of correlation between two networks namely correlation probability. At the same time, the value of T in the profits matrix which we call defection temptation also plays a vital role in cooperation. Once T increases to upper limit threshold, defectors’ profits will occupy dominant position and then cooperator will disappear. Conversely, defectors will disappear once T decreases to lower limit threshold. Compared with the threshold that individuals tend to choose defection strategy in a single network, correlation network enhance this threshold which means that individual remains cooperation even though T take a larger value. In addition, the donation probability determines the cooperation degree and donation ratio determines the difficulty situation of the cooperation degree. Finally, the cooperation rate will become higher as the increasing of the probability of adding edges into WS small-world network.