Research On Zero-determinant Strategies And Networked Evolutionary Game Dynamics

From populations of the animal to the society of hunman,the large-scale cooper-ative behavior produced by agent interaction is the cornerstone of social development.Therefore,exploring the emergence and evolution mechanism of cooperative behavior is a problem of concern to economic,biological and social sciences.Game theory pro-vides a theoretical framework for its wide application.In game theory,the phenomenon of competition between agents is abstractly described,in which agents behavior can be characterized by strategies.Although classical memory-one strategies(such as tit-for-tat(TFT),generous tit-for-tat(GTFT),and win-stay-lose-shift(WSLS)strategy)are obtained theoretically,a large number of studies have shown that they exist in nature.In the past study of game theory,it is generally believed that the benefits between agents in iterated games are determined by the behaviors of all the players.In 2012,the zero-determinant strategy derived from Markov stochastic process theory allowed its users to unilaterally restrict the expected benifits of the players to satisfy a linear relationship.In particular,there are two subsets of zero-determinant(ZD)strategies:extortion strategy and submis-sive ZD strategy,in which the extortion strategy can obtain a payoff that no less than the opponent’s,while the submissive ZD strategy obtain always cooperation strategy and TFT strategy and can get into the co-cooperation with the cooperator.These two strategies have attracted a lot of attention from the scientists.This way of describing strategy behavior through payoff relationship provides a new perspective for strategy research in iterated game model.Complex systems in the real world can be abstracted as complex networks formed by interacting agents,such as protein networks and brain neural networks in the biological world,world wide web and wireless communication networks in social life,and social net-works and scientists’ cooperative networks constructed in human social behavior.These complex networks usually have complex topological and dynamic characteristics.Net-work evolutionary game is a theoretical tool to study the interaction between selfish agents in complex networks and explore the influence of network topology and strategy evolu-tion on cooperative behavior.Based on the network evolutionary game theory,we study the evolutionary dynamics of bounded rational agents after introducing zero-determinant strategy in terms of network topology and network evolution rules.The main contents are summarized as follows:Firstly,we explore the evolutionary dynamics of zero-determinant strategies on reg-ular graph,and study the influence of different microstructures on the evolutionary dy-namics of strategies in regular networks.By exploring the evolutionary dynamics of co-operation,defection and extorion strategies on the regular networks with the same degree distribution,the influence of different microstructures on the evolution of strategies is studied.We also proposes a strategy clique to analyze the dynamic changes in the strat-egy evolution and explain that exploitation strategy can promote cooperation to prevail in the network.Then we study the dynamics of submissive zero-determinant strategy and defection strategy in the regular graph,and the research shows that the submissive zero-determinant strategy can prevail in the regular network.Furthermore,when in the grid network are based on snowdrift game and Fermi dynamics,it is shown that submis-sive zero-determinant strategies can emerge in the grid network in the form of strategy clusters.Regular networks are formed by fixed rules and have special structural charac-teristics.This study provides a benchmark for exploring the evolutionary dynamics of zero-determinant strategies on more complex structures.Secondly,based on the iterated prisoner’s dilemma game,we explore the influence of topological characteristics on the evolution of submissive zero-determinant strategies in scale-free networks under both the accumulated payoff framework and normalized pay-off framework.Firstly,the influence of degree correlation on the evolution of submissive zero-determinant strategy in scale-free networks is studied.In assortative networks,the hubs makes it difficult for the submissive zero-determinant strategy to spread to the nodes with small degrees when the agent adopts the accumulated payoff,thus inhibiting the diffusion of submissive zero-determinant strategy in the assortative network.However,when the agent adopts the nomalized payoff to update her strategy,the nodes with small degree have more influence than hubs,but promote the emergence of submissive zero-determinant strategy in the assortative network.Next,we study the influence of clustering characteristics on the evolution of submissive zero-determinant strategies in scale-free net-works.By studying the evolution of submissive zero-determinant strategy in clustering scale-free networks,the results show that under the framework of accumulated payoff,the hubs in high clustering network is more likely to form clusters of submissive zero-determinant strategy to resist the invasion of defectors.However,under the normalized payoff framework,the clustering in scale-free network is difficult to maintain the sub-missive zero-determinant strategy clusters,which makes the submissive zero-determinant strategy in high clustering network are easily to be invaded by defectors.Finally,we study the evolutionary dynamics of zero-determinant strategy on the net-work under mixed evolutionary rules.When agents can choose aspiration evolution or replication dynamic to update strategy probability,compared with single evolutionary rules,mixed dynamics rules makes the cooperation strategy form a more stable alliance with extortion strategy to resist the invasion of defectors,and the agent driving force can make the defection strategy and extortion strategy turn into cooperative strategy,so that the cooperative behavior can surrive in the network.