Effects Of Environmental Feedback And Resource Allocation In Networked Game Dynamics

Cooperative behavior is widely existed in real biological,social and economic systems.Cooperative behavior plays a crucial role in the normal operation of these systems.The evolutionary game theory whose aim is to understand the evolution and pervasiveness of cooperation in biological and social systems.More specifically,the goal is to answer how natural selection can favor costly,cooperative behaviors that benefit others.Researches are concerning the process of emergence and dissipation of cooperative behavior,therefore in recent decades,they building models by plenty of observations and experiments to reproduce these phenomena,analyze the phase transition and propose reasonable explanation.Real-world systems are often characterized by bi-directional feedback between incentives in environmental and strategic interactions.Recently,more and more attention has been paid to the interplay between the environment and the individuals’ collective behavior.In this dissertation,we mainly discuss the extension of the theoretical framework of the game dynamics of environmental feedback to the alternating evolution of coordination and anti-coordination,and to the three-strategy voluntary participation game model,and the game dynamics of a population with spatial structure is preliminarily investigated by considering the environmental feedback mechanism.In addition,we consider the influence of the selection intensity environment on the level of cooperation in the group,and consider the criticality of resource allocation.The main research contents and achievements are summarized as follows.In the first chapter,the basic concepts of evolutionary game theory,development history,typical game types,analysis methods,network structure,and the consideration of environmental feedback mechanism are systematically introduced.In the second chapter,we use the environmental feedback dynamics to correlate the coordination game and the anti-coordination game.Interestingly,the dynamic phenomenon of alternating rotation of coordination and anti-coordination is successfully observed in our model.We derive theoretically and numerically the conditions for the arising and stability of these stable states.We also find that there are two regions that do not overlap or intersect and are not affected by the relative feedback parameter.The demarcation of the two regions is determined by the payoff matrix parameter.However,stochastic noise plays a crucial role,and the introduction of a tiny stochastic noise can have a significant effect that the left and right regions can cross each other.The rotation of the emergence and demise of hippies(new products,technology or opinions),and the emergence and dominance of hippies can form a closed trajectory,which can be transformed to each other.The probability distribution of the sojourn time staying in a region is well approximated by a power law with an exponential cutoff,which is very robust under different relative feedback speed and different stochastic noise variances.These results are important for us to understand many phenomena in real social systems,for example,the alternating rotation of innovation and imitation.In the third chapter,we extend the theoretical framework of game-environment feedback dynamics to the evolutionary three-strategy games,namely the voluntary prisoner’s dilemma game.In this present work,a generalized linear environment dependent payoff structure be considered,meanwhile,the environment is influenced by the configuration of the population strategy states.Although the model feature is changed slightly,we observe quite rich dynamics in the stationary states,such as two-strategy coexistence state,three-strategy coexistence state,persistent oscillations of strategies and environment,internal saddle point and unstable spiral phenomenon.We derive theoretically and numerically the conditions for the arising and stability of these stable states.Remarkably,we find that which kind of stationary state is finally achieved is mainly determined by the relative feedback strength of the environment and the payoff matrix,while it is almost unaffected by the relative feedback speed and the initial frequency of strategies.In the fourth chapter,we incorporate environmental feedback mechanisms into spatially structured populations.We find that in structured populations,the persistent oscillations in the environmental feedback mechanism become weaker,and in particular,the environmental state becomes almost constant.The spatial structure prevents the system from transitioning between states.In particular,the spatial structure makes the strategies cluster to prevent the invasion of the other strategy,and even for the weak prisoner’s dilemma,the spatial structure not only prevents the invasion of the other strategy,but also prevents the recovery of the system environment state.In the fifth chapter,we focus on the effect of selection intensity environment on the level of population cooperation.The results show that under the environment of strong selection intensity,the evolution of cooperative strategy is strongly driven by aspiration,and significantly increase the cooperative strategy proportion compared with the results under weak selection environment.In addition,there is a critical cost-benefit ratio,which makes the proportion of cooperative strategy decrease sharply.The critical cost-benefit ratio decreases as the value of aspiration increase.However,when the selection intensity was weak,the aspiration value has a little effect on the proportion of cooperative strategies.Furthermore,the theoretical results are verified by Monte Carlo numerical simulation and the results are qualitatively consistent for different system sizes and different system structures.The apparent difference in the level of cooperation between strong and weak selection environments will be crucial to our basic understanding of human behavior and may lead to new insights into human self-evaluation.In the sixth chapter,we study the critical unfairness under the dominant cooperative strategy on the extended snowdrift game,involving the concept of resource allocation.Both theoretical and numerical simulation results show that the larger the resource is,the larger the critical proportion of benefits that defectors can obtain.But the trend becomes slower and slower,and there is a saturated value.This corresponds to the limitation of real resources,for example,land,capital,manpower,etc.,are not infinitely increasing but limited.Moreover,the greater the system connectivity,the smaller the critical proportion.In other words,this kind of inequality is stronger in the social structure with fewer connections,and weaker in the social structure with more connections.We also reveal that introducing incentives and punishments makes it harder for cooperators to get a fair share of the profits.That is,bosses may use reward and punishment to increase the extent of exploitation on their employees.These results are important for us to understand many phenomena in real social systems.The conclusion of this dissertation and some prospects for the future works in this field is given in the last chapter.