Statistical Experiment And Evolutionary Dynamics Of Cooperative Behavior Under Asymmetric Mechanism

As a common altruistic behavior,the emergence and evolution of cooperation has always attracted the attention of scholars in many fields,and it is one of the frontier scientific issues.Existing researches showed that the evolution of cooperative behav-ior can be attributed to five rules: direct reciprocity,indirect reciprocity,kin selection,group selection,and network reciprocity.However,the proposal of five rules acqui-esced in the homogeneity of the population,and asymmetry,as a phenomenon common in nature,has not been taken into consideration.In order to explore the impact of asym-metry on behavioral dynamics and human behavioral decision-making,in this paper,we establish the evolutionary game dynamics models and design an asymmetric human behavior statistical experiment.Through evolutionary game theory,methods of statis-tical physics,replicator dynamic equations,Markov processes,and statistics methods such as modeling and clustering,we study the game of two species with asymmet-ric symbiosis and the game of human behavior under asymmetric initial wealth,and provide some meaningful conclusions for learning the evolution of behaviors in asym-metric environments.The research content is mainly divided into the following four parts.First,in the study of the asymmetric parasitic relationship on the two-layer inter-dependent networks,we discuss the survival of two species with asymmetric parasitic relationship and the evolutionary dynamics of cooperative behavior.Through the con-ditional parasitic relationship,the interdependent networks can establish asymmetric coupling and directly affect payoffs of the agents.The simulation results show that cooperators in the upper network almost disappear,and more than half of the nodes in the lower network are occupied by cooperators when the dilemma strength is small.Conversely,when the dilemma strength increases,the situation is just the opposite.Co-operators in the upper layer can even occupy the entire network,while cooperators and defectors in the lower layer are evenly matched and achieving stable coexistence.In addition,after considering the parasitic relationship of different strategies separately,we find that defectors are almost always in the dominant position when the parasitic relationship only exists between cooperators,and cooperators is instead to have the opportunity to dominate when the parasitic relationship exists only between defectors.Second,in the study of asymmetric parasitic relations on a single-layer network,we discuss the evolutionary games between two species with asymmetric parasitic re-lations.On the square lattice,regardless of the values of the additional cost of the host,the additional benefits of the parasite,and the temptation to defect,the host cooperators always exist,and the host and the parasite can always coexist,which is caused by cycle dominance.The simulation results on the random small-world network are similar to that on the square lattice,except that they exhibit larger oscillations in some parameter spaces than on the lattice.However,the evolution of strategies on the random regular network is more unstable,including multiple steady states and oscillations.Third,in the study of asymmetric symbiosis on a single-layer network,we dis-cuss the evolution of cooperative behaviors of two species under multiple symmetric and asymmetric symbiosis relationships.While agents within the species are engaged in the prisoner's dilemma game,different species measure their inter-species relation-ships through changes in their payoffs.We consider two well-mixed populations in-cluding infinite population and finite population,as well as the structural population on the regular square lattice.In the infinite population,the entire population is eventually occupied by defectors.In the finite population,the population always maintains the coexistence of four strategies through cycle dominance.In the structural population,phase transitions are more complicated.When dilemma strength is low,cooperators always exist,and different species can coexist when there is little difference in asym-metric inter-species payoffs.When dilemma strength is high,different species can also coexist when the difference in payoffs between species is not very large,but the parame-ter space for cooperators to survive is limited.Coexistence can be achieved among four strategies only when the interactive payoffs between two species are similar and both are negative.The occurrence of this coexistence is caused by cycle dominance,which is consistent with the reasons in the finite population.Although cooperative behavior cannot be maintained in an infinite population,in most cases in a finite population and a structured population,cooperators can still be active in the system when the temptation to defect is high.Finally,in the behavior experimental study on asymmetry,we discuss the impact of asymmetric initial wealth on human behavior.The experiment is mainly divided into two experimental groups with different initial wealth and a control group with the same initial wealth.In the experimental group,we only allow interactions between players with different initial wealth.The difference between the two experimental groups is the difference in initial wealth.By recruiting college students,we carry out corresponding experiments and obtain the real decision-making informations.The experimental re-sults show that the level of cooperation is higher when the initial wealth is the same for everyone.The asymmetry of initial wealth inhibits the emergence of cooperative behavior,and the greater the asymmetry,the lower the cooperation rates.However,for the two groups with different initial wealth,there is no significant difference in their behavior in the same session.The only difference is that the party with the lower initial wealth has a benefit proportional to the level of cooperation,that is,players with the higher cooperation rates,whose payoffs are also higher.As the experimental rounds in-creases,it indirectly leads to the convergence of wealth differences.Through statistical modeling and clustering analysis,we further find that a relatively large proportion of conditional cooperators and emotional conditional cooperators is an important reason for showing the pro-social behavior in the symmetry session.