The Evolution Of The Zero-determinant Strategy And Network Reconstruction

Game theory is an important method to study the mechanism of selfish individual altruistic behavior,and it is also an important way to explore human cooperative behavior.The game research on network combining the game theory and complex networks,depicts players’ relationship by a network,which makes it close to the real system.On the other hand,acquisition of network structure is a prerequisite for researching mechanism of group cooperation,epidemic controlling and prevention,community detection and dynamical evolutionary mechanism.However,it is usually difficult to obtain all nodes’ relationship,that is,the network structure is unknown.How to reveal the hidden structure and analyze its dynamic evolutionary behavior basing on observable data? It has been another important topic in the field of network data analysis.Based on the theories of complex network,stochastic process,optimization and game theory,this paper studies the feature of the zero-determinant strategy,its evolution behavior in complex network and reconstructs networks reversely based on evolutionary game data.The three topics interconnect and restrict each other.The theoretical analysis of zero-determinant strategy provides theoretical support for the study of evolutionary behavior on the network,and network reconstruction provides the connection of nodes for researching game evolution in empirical systems.Meanwhile researching the evolution behavior of zero-determinant strategy on network provides reference for detecting its feature and making effective measure to reconstruct the network with a high precision.The specific research contents include the following aspects:Firstly,aiming at the game between extortion strategy(a subclass of zerodeterminant strategy)and cooperation strategy,the paper gives the instantaneous distribution and their time-varying payoffs in the previous state and analyzes how to reach the steady state quickly,which provides real dynamic benefits for the players who frequently update their strategies.Moreover,if the extortion strategy plays games with evolutionary player,it is proved analytically that evolutionary player must evolve into a cooperator if both defect at previous move.And simulations show that the evolutionary player must become an unconditional cooperator although they have different evolutionary speeds in four cases,which verifies the zero-determinant strategy is a catalyst for cooperation again.Secondly,the evolution of the zero-determinant strategy on square grid.For rational group,the paper studies the single invasion of zero-determinant strategy and allcooperative strategy and discusses the expansion conditions of new mutants.On the other hand,how the rationality degree and extortion factor affect the evolution is discussed on the bounded rational group.It is found that the group’s evolution with different rational have great differences under different extortion factor in the rational homogeneous group.In the heterogeneous rational population,the strong rational group will lead the weak rational group to choose the beneficial strategy so that the strategies of the group can be synchronized,but the evolutionary process is related to the ratio of the strong rational players and the extortion factor.Finally,the paper compares the returns of two strategies and analyzes the causes.The paper can advise the extortioner take a proper extortion factor for his scores,along with improving the group’s cooperation.Thirdly,the evolution of extortion strategy on scale-free network.According to the features of the punishment and extortion strategy,a combination strategy is proposed for the Hub nodes on scale-free network.One Hub node can act as a leader with such strategy.He can improve the level of group’s cooperation,and his incomes is obviously higher than the average of the group.Furthermore,it is robust to the temptation of betrayal and competitive strategy.At the same time,its application is very flexibility.Fourth,the evolution of zero-determinant on the dynamic network.Consider games with elimination,the individual adjusts his strategy according to the opponent’s previous strategies,then decides whether to terminate their games.Firstly,two functions of zerodeterminant strategy are explored through analyzing the change in results brought by it.They are the catalytic for cooperation and preventing individuals from being obsoleted.Then,whether the elimination rate of a node is affected by its initial strategy and degree is analyzed.It can be found that small nodes tend to be eliminated,and the influence of the initial strategy is related to zero-determinant strategy.When it participates the games,the nodes with initial cooperation are conducive to survival.When it doesn’t participate games,the good strategy for nodes is defection strategy.Fifth,the reconstruction of the whole and part of network is studied based on evolutionary game via complex network,optimization theory and zero-determinant strategy.Firstly,the paper proposes two compressed sensing models.After analysis of their features a combined reconstruction method is presented based on sample size and the node’s degree.The influence to the reconstruction accuracy is analyzed on the networks with different types,different sizes,different densities,initial strategies and their number,and it is also compared with Compressed Sensing and LASSO on accuracy and run speed.It can be found that the combined method has an obvious advantage on large and sparse network.Moreover,the participation of strategies,such as zerodeterminant strategy and Win stay lost shift,which can improve group’s cooperation,can greatly improve the accuracy of network reconstruction.It validates and applies the zero determinant strategy’s cooperation catalyst again and explores its new function.Then,empirical analysis on several real networks strengthens the advantages of the combined Compressed Sensing.Finally,the robustness of the combinatorial method for noise samples is discussed,and the method is also extended to coupled oscillation systems.The innovation of the paper is as follows:Firstly,different with research focusing on the steady state,the paper analyzes the dynamic behavior of zero-determinant strategy in the early stage of the game.For the zero-determinant strategy is a mixed strategy with memory-one and players update their strategies frequently so the steady state can’t be achieved quickly,it is more critical to grasp the instantaneous distribution and instantaneous returns.The paper analyzes the instantaneous returns of both players and how to approach the stable state quickly,which provides theoretical guidance for the players to grasp the information and make decision in the early stage of the game.Secondly,according to group betrayal caused by low return to the cooperator,the paper makes improvements from strategy and game mechanism respectively,which changes the main theme of the game from group betrayal to group cooperation.From the perspective of strategy: a combination strategy is proposed by exploring the features of zero-determinant strategy and punishment strategy.The combined strategy can enable the Hub node to lead the individuals cooperate with each other.It provides an effective strategy to the leader for a high cooperation in the real games.From the perspective of game mechanism: the player is given the right of elimination,and he adjusts his relationship with his opponent according to the previous behavior of the opponent,and then adopts the appropriate strategy.The games on the dynamic network are more realistic than on the static network,so it can reasonably interpret the cooperation behavior in the nature and human society.Moreover,the zero-determinant strategy is introduced into the game mechanism,and a new feature of the zerodeterminant strategy is discovered----protecting the individual’s game right.Thirdly,two network reconstruction models are constructed.And it needn’t give threshold to identify the neighbors with model Ⅱ.And the combined model not only has a high reconstruction accuracy,but also runs fast.In addition,the influences on the reconstruction accuracy from the strategies are discussed,which provides a new research perspective for improving the accuracy of network reconstruction.The zero-determinant strategy and punishment strategy are combined on the magnifying node,and the zero-determinant strategy is applied to the,which turns group defection into group cooperation and explores the new functions of the strategy.To sum up,the paper theoretically gives the income function of the zero determinant strategy and their distribution during the early stage.Next,a combined strategy of zerodeterminant strategy and punishment strategy is proposed and applied on large degree node for a high cooperation.In addition,for more individuals to participate in the game and cooperate with each other,we introduce zero-determinant strategy into dynamic games with elimination right.Finally,two network reconstruction models are constructed to solve the problems of low precision of reconstruction withing few samples and subjectivity of threshold respectively.The introduction of zero-determinant strategy into network reconstruction is helpful to recognize,understand and use it wisely.It provides more channels to reconstruct the internal relationships hidden in the real world with fewer samples...