The Research Of Cooperation On Group Game With Multi-layer Complex Network

Complex networks can be used to describe various complex systems in reality.Realistic interactions are usually complex and diverse,which can be represented by a multi-layer network,such as multi-layer social networks,multi-layer power networks,etc.Gaming behavior is common in social life,such as playing chess,business negotiations,etc.Between game theory and complex networks,there is a good relationship.Therefore,it can be said that if the discovery of complex networks provides convenience for describing individual relationships,then the discovery of game theory makes it possible to explore the reasons for the emergence of rational individual cooperation.In conclusion,the combination of complex networks and game theory is a hot topic in current researches.In recent years,an increasing number of researchers have used a combination of complex networks and game theory to explore the reasons for the emergence of cooperative behavior.However,most evolutionary games focused on single-layer networks in previous studies.In fact,the reason why it is difficult to explain the complexity of real networks on single-layer networks is that the environment people lived is multiple.It means that networks are often interdependent or interconnected.The limitations of these studies are either the use of square lattices networks or two-player games,where square lattices networks lack some practical significance and more two-person games cannot explain common multi-person interaction phenomena,such as the preparation of public facilities,the treatment of environmental pollution,and so on.Moreover,some existing game learning rules do not represent people's decisionmaking process well.For instance,strategic decisions will be affected by personal characteristics in some cases.In order to solve these problems and enrich research results,this paper proposes a model on multi-layer complex networks called “public goods game with selection preferences”(PGG-SP)model to help people make better decisions in different social dilemmas by combining multi-layer networks with multiplayer games.Based on the above,the main contributions of this article are summarized as follows:(1)By simulating real-world network conditions,this paper builds single-and double-layer complex networks based on improved small-world networks and scale-free networks,respectively.By comparing the differences in the evolutionary behavior of group games on different types of networks,it is demonstrated that individuals will be more stable and collaborative to reach cooperation under a multi-layer network environment.Subsequently,the reasons for this phenomenon are further discussed by changing the key parameters in the multi-layer network.(2)In order to overcome the shortage of previous strategy learning methods which individual characteristics are not be considered,this paper proposes a model called PGG-SP.In this model,an individual's preferred characteristics will be included which represents the probability that an individual tends to cooperate in the game.Individuals will take into account both benefits and preference attributes when learning strategies.Thus,this assumption better conforms with the process of making decisions in a practical scenario.(3)To imitate dynamic social interaction between individuals,a dynamic double-layer network is designed which realizes the co-evolution behavior of game strategy and network topology.It proves that the adaptive adjustment of the strategy and structure can credibly enhance cooperation and maintain stability.In addition,we construct a dynamic heterogeneous double-layer network to depict some practical scenarios.To verify the role of the multi-layer network in group games,four types of multi-layer networks are applied in this paper.In addition,the corresponding game results are compared between single-layer,multi-layer,static,and dynamic networks by using Monte Carlo simulation experiment methods.Taking the double-layer network as an example,the results show that the increase of the enhancement factor promotes the emergence of cooperation in the group game more than the single-layer network,and the level of cooperation is consistent when the sum of the enhancement factors of the two layers is fixed.In addition,variations in various structural parameters cause different effects on cooperation.Meanwhile,the phenomenon of coordinated development and strategy convergence of the double-layer network has appeared in the evolution process.Moreover,the results show the level of cooperation in dynamic double-layer networks is higher than static double-layer networks and it is also more stable than dynamic single-layer networks.In short,multi-layer networks have shown the characteristics of promoting the emergence of cooperation in group games from all levels.Accordingly,it can more accurately reflect the production process of cooperation in the real world.