The Study Of Game Dynamics Driven By Cooperative Mechanisms

Cooperation prevails in ecological and social systems,which is essential to the evolution of population and the prosperity of society.However,cooperation comes with a cost.Cooperative individuals burden self losses due to public benefits,contrary to selfish individuals’ profit-seeking nature.In order to solve such social dilemmas,cooperative mechanisms are applied to adjust the benefits between individuals and the public.This adjustment results in the phenomenon that individuals can maximize the public benefits while chasing their benefits.This thesis studies several cooperative mechanisms acting on the individual,group and interacting environment by constructing different replicator dynamics.With corresponding game dynamics,this thesis depicts and investigates individual behaviors influenced by factors in cooperative mechanisms,such as incentive mechanisms,group resource allocation,interacting environment transition.These quantitative analyses provide a theoretical foundation for cooperative mechanism design and system performance improvement.This thesis is composed of four parts as follows:1.Among cooperative mechanisms acting on the individual,this thesis studies the game dynamics driven by peer pressure and incentive mechanisms.Peer pressure is the punishment to defectors under the stress of social norms.It changes the payoff function of defectors.Incentive mechanisms reward cooperators and set up social norms.Based on the evolutionary public goods game,this thesis constructs a replicator equation of the frequency of cooperators.It is used for studying the relationship between stable(unstable)equilibrium points with peer pressure,the number of participants in public goods games and cooperation rewards,respectively.In a structured population,this thesis studies the reciprocal effect of local interaction with peer pressure.It points out that a heterogeneous population structure brings more peer pressure to defectors,which leads to cooperation prevailing in the population.2.Among cooperative mechanisms acting on the group,this thesis studies the game dynamics driven by group competition mechanisms.The fraction of cooperators in one group defines the group reputation.Influenced by cooperative social norms,groups with good reputations can take advantage in group competitions.With the definition that one group state is the distribution of numbers of cooperators,this thesis proposes a model named group state replicator dynamic model that reflects the evolution of cooperation in a group-based population accompanied by group competition mechanisms.Based on the model,this thesis investigates the dynamics of group state and analyzes the efficiency of the group competition mechanism.This thesis also studies the influence of group social status on its group state.It finds out that a heterogeneous group linked structure can help cooperators survive when the average enhancement factor is small but prohibits the promotion of cooperation in a cooperation-friendly environment.3.Among cooperative mechanisms acting on the interacting environment,this thesis studies the game dynamics driven by game transition mechanisms.In stochastic games with multiple interacting environments,joint actions and interacting environments are correlated.By representing the transition of joint actions and interacting environments as a Markov chain,this thesis proposes a model named state-transition replicator dynamics to reflect the dynamics of strategies in stochastic games.Based on the replicator dynamics,this thesis illustrates that unbalanced transition probabilities can lead to mutual cooperation in a cooperation back interacting environment,even if individuals face the same prisoner’s dilemmas in each interacting environment.Moreover,this thesis gives the minimum value of payoffs that cooperation back interacting environment needs to be higher than others for mutual cooperation in all interacting environments.4.For the stochastic game,this thesis studies the game dynamics driven by zero-determinant game transition probabilities and zero-determinant strategies.With the two-environment,two-individual,two-action stochastic game,this thesis derives zero-determinant game transition probabilities and strategies,which lead to a linear relationship between expected payoffs of individuals.Such game transition probabilities and strategies can force an individual to choose cooperative behaviors unilaterally.This thesis points out that if the payoffs in different interacting environments have no intersection,zero-determinant game transition probabilities exist.For equalizer and extortionate transition probabilities,this thesis analyzes their characteristics and performances in state-transition replicator dynamics.This thesis also gives the existence condition of zero-determinant strategies.It shows that zero-determinant game transition probabilities and zero-determinant strategies cannot coexist in one stochastic game.This thesis gives their features for extortionate and generous strategies.It shows that the generous strategy is the dominant one if both individuals apply zero-determinant strategies.