The Evolution Of Cooperation In Repeated Public Goods Game

Competitive behaviors between living beings are ubiquitous in the real world. According to Darwinism, fitter individuals are more likely to survive. Without any mechanisms, the fitness of cooperators is lower than that of non-cooperative ones. Individuals will tend to choose to defect in competitions. A fundamental aspect of all biological systems is cooperation. Cooperative interactions are required for many levels of biological organization ranging from single cells to groups of animals. Cooperation in a competitive world is a conundrum. How to explain the emergence and maintenance of cooperation between selfish individuals has received increasing attention of many scientists with various backgrounds. Evolutionary game theory provides a powerful theoretical foundation to explore this problem. This thesis is absorbed in the evolution of cooperation in repeated public goods game played in the well-mixed population, and the main results are as follows:We explore the effect of punishment and reward on the evolution of cooperation in well-mixed population. Before the game, everyone should show his attitude towards the cooperators and the defectors at a cost to themselves, rewarding or punishing, no matter what they will do. Neither rewards nor punishment alone has effect on the evolution of cooperation. In the relation of the two regimes, the cooperation level increases as the selection expands in strength. Our results show that in the game with rewards and punishment the players rewarding have advantages over the ones punishing.In the condition of noise, we institute a new model to seek the evolution of adaptive players in well-mixed population basing on the variation in behavior. We bring the tit for tat property into the multi-player interaction and denote that an individual cooperates with others at a certain probability which shows the variation in behavior. We characterize the population dynamics by the Moran process with frequency-dependent selection which describes natural selection: more successful players are more likely to be copied. We show that although the influence of the noise will prevent the development of cooperation in the public goods game, tit for tat will promote it because of the variation in behavior.Moreover, on the basis of the model above we introduce the nonlinearity and the different scales of group. What's more, different kinds of nonlinearity have absolutely diverse effects on the evolution of cooperation. Our results show that under the circumstance of variation in behaviors and the property of tit for fat, synergy nonlinearity promotes the development of cooperation while the discount nonlinearity impedes it. What's more, there is a moderate number of players in a group in the public goods game with discount nonlinearity.We construct a theoretical model to delve into the evolution of different strategies in well-mixed public goods game while the punishment is based on a threshold value. In one round game, individuals contribute different investments at a corresponding cost to themselves, while the punishment is in allusion to the players whose cost is below the certain threshold value. When the threshold value of punishment is moderate, the total contribution to the public pool will be maximum and cooperators with the contribution little larger than the threshold value are most likely to thrive.