Research On Cooperative Evolution Of Prisoner’s Dilemma Game On Complex High-Order Network

The flourishing of the real world is inseparable from the cooperation of individuals,but the act of cooperation often represents dedication and giving a part of self-interest,which is inconsistent with the nature of human selfishness.Therefore,in order to explore the emergence and maintenance of cooperative behavior,many researchers around the world have made a lot of research through the theory of evolutionary games on complex networks.The theory of network reciprocity holds that the interaction behavior of most individuals in reality always exists in different interaction networks,and different interaction networks will have different impacts on the emergence and evolution of cooperation.Based on different networks and evolutionary rules,the establishment of models to simulate various phenomena in the real world,explain and even predict the causes and trends of events,is an important research direction in evolutionary games.To study the evolutionary results of the prisoner’s dilemma when based on different evolutionary models.In this dissertation,two novel evolutionary game models are established,focusing on the influence of ordinary lattice networks and simplicial complex networks on the evolution of prisoner’s dilemma.1.The reputation mechanism with the punishment mechanism is combined in the lattice network,focusing on the influence of different punishment time on the evolution of cooperation.In the model,uniform reputation threshold will be set,and if an individual’s reputation falls below the reputation threshold,they will be punished and punishment time is .A large number of simulation results show that we can adjust the punishment time to make the cooperation in the system relatively optimal.In addition,and successfully explain the reason why the punishment time affects the steady-state cooperation level through the evolutionary step diagram and the evolutionary snapshot diagram.Different punishment times will affect the mutually beneficial symbiotic relationship between the punished cooperators and the unpunished cooperators,and then affect the overall level of cooperation.Finally,we test the robustness of the evolutionary model.The simulation results show that the robustness of the model in this paper is relatively good in different common networks.2.The simplicial complex formed by the combination of 1-simplex and 2-simplex as the network model,and adjust the proportion of 2-simplex in the network by mixing proportion .The individual will play that double or multiple prisoner’ dilemma game in 1-simplex or 2-simplex.In this way,to explore the cooperative evolutionary impact of non-pairwise interactions on the prisoner’s dilemma.A large number of simulation results show that simplicial complex network can promote the evolution of cooperation,and the cooperation level in the system can be relatively optimal by adjusting the mixing ratio .Furthermore,we explain the reason of this phenomenon through the 2-simplex strategy proportion diagram and the complex network distribution diagram.The individual performs the multi-prisoner dilemma in 2-simplex,and make the strategy relatively unified in a small range,and gradually expands the cooperative group to resist the defectors invasion,and finally achieves dynamic stability.