Research On The Influence Of Time-dependent Effect On Group Game Behavior On Complex Networks

As Marx said,people are the sum of all social relations,and everyone is in different social relations and social networks,and the decisions made by individuals in this network are closely related to personal interests and social interests.Cooperation can pool the limited wisdom and resources of individuals.It is an important factor in promoting the development of human civilization and the cornerstone of social development.However,since it is contrary to the theory of evolution,explaining the emergence of cooperation and revealing the mystery of cooperative evolution has always been a big problem.Therefore,exploring the factors influencing the evolution of cooperation is of great value in understanding and promoting human development.Punishment of defection has long been recognized as an effective mechanism to promote cooperation,but there is limited research on how punishment mechanism affects cooperation evolution and how punishment mechanism interacts with other factors that affect cooperation.Complex networks can abstract social relationships in real life,and game theory is a method guide for individuals to make choices.Therefore,combining game theory with complex network theory,using game theory as a framework and complex network theory as a tool to study the evolution of cooperative behavior has gradually become a hot topic.In real life,games and cooperation are often influenced by time factors.The delay of punishment or incentives and the fluctuation of rewards over time are important factors affecting the evolution and stability of network cooperation.Related research is also very limited.Based on the background and research above,this paper constructs a model combining complex network and evolutionary game theory to explore the impact of punishment mechanisms and time-dependent effects on group game behavior on complex networks.Specific work is as follows:1.This paper chooses NW small-world network and BA scale-free network as the network model,and constructs a complex network model of the public goods game.Then,two third-party punishment mechanisms are introduced,namely the public pool punishment mechanism and the peer punishment mechanism.Under the punishment mechanism,the model has three strategies,namely punishment,cooperation and defection.By adjusting the profit coefficient and the noise factor,the impact of these two third-party punishment mechanisms on the public goods game on complex networks is explored under two different network models.The experimental analysis found that no matter what kind of punishment mechanism,the promotion of cooperation effect is significant.Under the same model and parameters,peer punishment can promote cooperation better than public pool punishment,while noise factor and cooperator density are inversely correlated.Under the premise of the punishment mechanism,the cooperation effect of BA network is better than that of NW network,and the cooperation effect of BA network is inversely correlated with the edge coefficient.2.This paper introduces the initial policy selection preference of large-degree nodes.After discovering the influence of the initial strategy distribution of the large-degree nodes on the network,the model introduces the initial strategy selection preference of the large-degree nodes,which represents the probability that the large-degree nodes will become the punisher in the initial material selection.Experimental analysis found that: the higher the preference,the better the cooperation effect of the network,and the more stable the strategy distribution in the equilibrium state of the network.3.This paper introduces the oscillator function of the profit coefficient and the punishment delay,and uses these two factors to explore the influence of time-dependent effects on group game behavior on complex networks.(1)This paper considers the income oscillation function of sinusoidal fluctuations to simulate the income fluctuations in reality,and introduces four parameters of benchmark income,amplitude,frequency and time offset as influencing factors.Through experimental analysis,it is found that after the NW small world network introduces the oscillating revenue function,the evolution of the group strategy will also fluctuate sinusoidally with the oscillating function.By adjusting the four influencing factors,it is found that the increase of amplitude has an inhibitory effect on cooperation,while the base income and vibration frequency have no positive or negative effect on cooperation.In contrast,in the BA scale-free network,with the introduction of the oscillating revenue function,the distribution of each strategy will eventually reach equilibrium after a small fluctuation in a short period,and the oscillating is beneficial to cooperators.By adjusting the time offset,we conclude that the time offset does not affect network equilibrium.(2)This paper introduces a punishment delay in the NW network public goods game model with a punishment mechanism to simulate that the punishment cannot be realized immediately in reality.By adjusting the punishment delay,it is found that the punishment delay has an inhibitory effect on the cooperation effect,and the upper limit of the inhibition is the cooperation effect without punishment mechanism.Moreover,the marginal inhibitory utility decreases as the punishment delay increases.In summary,by introducing the punishment mechanism and time factor into the game model,this paper better simulates real investment and game scenarios,and provides a basis for understanding the generation and evolution of cooperative behavior and the impact of time-dependent effects on evolutionary games with punishment mechanisms.The theoretical basis provides certain guidance for people’s economic behavior in real life,and can provide help to better avoid losses.