Evolution Of Cooperation And Game Dynamics On Complex Networks

Cooperation is ubiquitous on many levels of biological organizations and is of vital im-portance to their development.However,cooperation often weakens one's own advantage in the competition for survival.Understanding how cooperation emerges from and evolves in a population consisting of selfish individuals has long been an important and challenging issue.Evolutionary game theory on complex networks provides a powerful framework for ex-ploring the evolution of cooperation and the competition between strategies,where complex networks represent population structures and games describe interactions between individuals.Under this framework,resorting to the methodology from network science,stochastic process and statistical physics,we mainly investigate how population structures,individuals'behavior patterns and interacting environments influence evolutionary dynamics.The principal results and innovations are as follows:First,we study how population structures affect the evolution of cooperation.By model-ing interactions and strategy dispersal with two independent networks,we make clear underly-ing mechanisms of spatial reciprocity(spatial structure promotes the evolution of cooperation).Only when one's interaction partners overlap its'role models,spatial reciprocity emerges.The more frequently an individual interacts with its role models,the stronger the spatial reciprocity is.Our findings are applicable to both two-player and multiplayer interactions,and theoret-ically clarify how structural clusters on social networks,strong social ties,and asymmetry between interaction structure and strategy dispersal structure influence the evolution of coop-eration.Based on above findings,we propose an algorithm to strengthen spatial reciprocity by individuals adjusting their social ties.Next,we study how behavior diversity affect the evolution of cooperation in pairwise in-teractions,where individuals adopt different strategies against different opponents.We have shown that regardless of population structures,behavior diversity can boost cooperation re-markably.Even a small fraction of individuals taking behavior diversity are enough to stabi-lize cooperation in a high level.From the perspective of network dynamics,compared with individuals competing over nodes,behaviors diffusing along edges provides more advantages for the evolution of cooperation.Further,we study how behavior diversity in multiplayer public goods games(investment diversity and payoff allocation diversity)affects the evolution of cooperation.We find that the success of cooperators relies heavily on the correlation between one's investment in a game and its benefit allocated from the same game.In most cases,the positive correlation,i.e.a greater investment in games with a larger share of benefits,facilitates a cooperative society.We study evolutionary multiplayer games on networks with edge diversity,where edge types indicate genetic similarity,geographic proximity,and difference in interacting environ-mental states.When the edge type indicates whether or not two collected individuals perform the same task,we find that division of labor can promote cooperation remarkably.When games on different edges are diverse(indicate different interacting environmental states),the evolu-tionary process can be approximated by interactions under a transformed and unified game.Finally we investigate the evolutionary dynamics when individuals'behaviors and inter-acting environments are correlated.We find a simple rule for the evolution of cooperation on networks:cooperation is favored over defection if the ratio of the benefit provided by a co-operative behavior,b,to the corresponding cost,c,exceeds k-k~?,which means b/c>k-k~?,where k is the average number of neighbors and k~?captures the effects from environmental feedbacks.Even if cooperation is disfavored in each environmental state,allowing for a tran-sition between them can result in a favorable outcome for cooperation.Even small variations in different environmental states can promote cooperation markedly.