Research On The Evolution Of Cooperation Based On Hypergraph And Mobile Populations

Rational agents are always inclined to select defective behaviors according to the principle of Darwinian natural selection.However,cooperative phenomenon is ubiquitous in both natural system and human society.How to understand and explain the spontaneous emergence and maintenance of cooperation among selfish agents in social dilemmas still remains a challenge,and it has attracted the continuous attention of researchers from diverse fields.Under the powerful theoretical framework of evolutionary game theory,large amounts of researches,involving different structured populations(such as the square lattice,random network,small-world network and scale-free network)and various social dilemmas(including the prisoner’s dilemma game,snowdrift game and public goods game),have arisen.In recent years,the evolutionary dynamics on hypergraphs and the evolution of cooperation in mobile populations have received more and more attention.In this dissertation,based on evolutionary game theory,we have studied the evolution of cooperation on hypergraphs and mobile populations.The main contents of this dissertation are as follows:(1)Based on hypergraphs,the evolution of cooperation in the spatial public goods game with heterogeneous multiplication factors is explored.In addition to the original public goods game model with the homogeneous multiplication factors,we also consider three distributions with different heterogeneity strengths of heterogeneous multiplication factors,including the uniform distribution,exponential distribution and power-law distribution.The results show that,the fractions of cooperators in the public goods game corresponding to the above four distributions increase with the order of the uniform hypergraph.Further,compared with the results of the original spatial public goods game on hypergraphs,the introduction of the heterogeneity of the multiplication factors can significantly facilitate the evolution of cooperation in the public goods game on hypergraphs,and the power-law distribution enables the best cooperation level.In addition,the effect of the hyperlinks on the evolution of cooperation is explored and the above conclusions are robust to the number of hyperlinks.It is also found that the increase of the number of hyperlinks will restrain the emergence of cooperation.(2)The effects of mobile populations on the evolution of cooperation in a spatial prisoner’s dilemma game considering position persistence is investigated in the two-dimensional plane.The position persistence period is introduced to characterize the time duration that mobile individuals stay in their present position.When = 1,agents will consider migration at each time and the model reduce to a traditional mobile population model;when → ∞,agents will remain in the initial positions and the model becomes a static one that without considering migration mechanisms.Compared with the static model,the migration mechanism can effectively improve the level of cooperation.At the same time,within a certain period of position persistence,the cooperation level increases with the increase of the position persistence,while longer period of position persistence no longer significantly increases the cooperation level of the system.The influence of individuals’ interaction radius on the evolution of cooperation is studied,and it is found that there exists an optimal interaction radius for different position persistence periods,which leads to the highest cooperation level.