Migration is a common behavior in both biology and human societies for seeking more suitable environments or driven by greater benefits. Under the theoretical framework of evolutionary games, migration has been proved to be an effective mechanism for promoting cooperation. In this work, we introduce the migration based on historical payoffs into an evolutionary public goods game in two-dimensional space. Specifically, we introduce a parameter α to account for the ambition of individuals. During the evolution, individuals compare their current payoffs with the threshold values determined by the historical payoffs obtained in last round and the parameter α , and then decide whether to migrate. In particular, if the current payoff is greater than the threshold value, the individual will remain in his position, otherwise he will move in a randomly chosen direction with the migration speed v . The results show that cooperation could be promoted by the historical-payoff–dependent migration when compared with the situation of random migration, and there exists an optimal α which is most favorable to cooperation. Moreover, we provide some phenomenological explanations based on the characteristic snapshots of strategy pattern during the evolution. We also study the effects of the synergy factor r and the migration speed v on cooperation, and find that the moderate values of v could facilitate cooperation best. Besides, the robustness of the results has been tested by investigating the model in a sparse population and in a larger range of α , respectively.

Migration based on historical payoffs promotes cooperation in continuous two-dimensional space

We explore the evolution of human mobility behavior based on public goods game. By using mean field method, the population distribution in different regions is theoretical calculated. Numerical simulation results show that the correlation between the region’s degree and its final population is not significant under a larger human migration rate. Human mobility could effectively promote cooperative behavior and the population balance of different regions. Therefore, encouraging individuals to migrate may increase the total benefits of the whole society. Moreover, increasing the cooperation cost could reduce the number of cooperators, and that would happen to the correlation between the region’s degree and its final population. The results indicate the total population could not dramatically rise with the region’s degree under an unfair society.

The evolution of human mobility based on the public goods game

We studied the effect of population density in a spatial public goods game. We found that the effect on the evolution of cooperation is very complex when the strategy learning and mobility of players in a long range are considered in a two-dimensional lattice. As the learning range is larger than the mobility range, the system is driven to enter into a cooperation state for a low population density, because a small local group is beneficial to sustain a high level of cooperation. As population density increases to a moderate range, the mobility of players from a domain invaded by defectors supports the evolution stability of cooperation. When the mobility range is larger than the learning range, a formation of compact domains of cooperators promotes cooperation as the population density becomes high.

Xiao Yao

Papers

Promotion of Cooperation in a Spatial Public Goods Game with Long Range Learning and Mobility