The Research On Emergence And Evolution Of Cooperation In Self-questioning Spatial Public Goods Game

Cooperation exists both in biological and social system, so it is one of the mostimportant issues to research the emergence and the evolution of cooperative behaviors inthe evolutionary biological and social theory. Game theory, particularly the evolutionarygame theory, provides an effective theoretical framework for the scientists to study theissue. According to the Darwinian’s principle, the individual will defect to maximize itsbenefits, which obviously can’t explain the widespread cooperation phenomenon in thereal world. The emergence and maintenance of cooperative behavior in selfish groupsbecomes a hot issue concerned by scholars in many fields.Considering the fact of the interaction among individuals and the different evolvingrules in social systems, we investigate the emergence and evolution of cooperation inspatial Public Goods Game. The works are as follows:1. In real social systems, agents not only learn and imitate the outstandingachievements of others, but sometimes they also reflect on their own behavior. Previously,researchers have proposed a self-questioning mechanism in the Snowdrift Game. Here westudy self-questioning mechanism in the classic Public Goods Game, and find theself-questioning mechanism can better promote cooperative behavior at the smallermultiply factor r and the cooperative frequency as a function of r has center symmetrynature. The self-questioning mechanism is often essential in dealing with practicalproblems, so it can help understanding and explaining the emergence of cooperation in thenature.2. Considering the incentive effects of finishing the work in advance are oftenemployed in reality, likewise, the present discounted effect of the future profits by finishingthe work sooner can also promote the cooperative level. Some researchers haveconstructed a time-rewarding function in the Snowdrift Game before. Here we use the time-rewarding expression in the model of classic Public Goods Game to represent theeffect of the present discounted effect, thus the time-rewarding Public Goods Game modelis constructed and evolves under the self-questioning mechanism. Results indicate that thetime-rewarding can apparently promote the cooperation over a wide range of r, and thereexists a “frozen interval” so that the cooperation frequency wanders at the lowest level.The Citizen’s health insurance, public transport, environmental issues, etc. belong to thiskind of problems. Results suggest that the time-rewarding Public Goods Game is closer tothe result of the people’s judgment, and it can avoid the tragic that the defector eventuallyoccupy the entire network in original model，So it has both theoretical and practicalguiding significance for the optimization of the social environment and the globalwarming.3. We research on the effect of the multiplication factor to the cooperative evolutionin Voluntary Public Goods Game. Some researchers had ever considered the groupdiversity-depreciation of the public goods caused by the surroundings in the original PublicGoods Game. However, we study the depreciation effect of multiplication factor in theVoluntary Public Goods Game. Results show that the depreciation effect can effectivelypromote the cooperative evolution in the Voluntary Public Goods Game, and there exists amoderate value r range which can promote the system to reach the highest level ofcooperation.