Evolutionary Games And Controllability On Complex Networks

Complex network has provided a new method in studying the complex system. In the network, nodes represent the individuals, and edges represent the interactions among individuals. A lot of complex systems can be modeled as networks, including the Inter-net, World Wide Web and some other technology networks, protein interaction networks, food webs and some other biological networks and social networks. Researches about various dynamics on networks, such as games, the spread of disease, controllability and other researches can not only make people to deeply understand the actual dynamic pro-cess in the systems, but also can guide people on how to control them. The exploring of various mechamics in evoltionary games can guide us to promote the cooperation among individuals in real systems, while the controllability can offer us a method to achieve the full control of system by minimum cost.The emergence and maintenance of the cooperation behaviors among selfish indi-viduals have always been a challenge for the social dilemma, because in these dilemmas, the collective interest is in conflict with the individuals’interest. Although the mutual cooperation can obtain high collective benefits, but defection can also bring high own benefits. The study of evolutionary games can help us to understand the choice of the individuals in the real systems and the evolution of cooperation for the whole systems. By introducing these various mechanisms and factors, we can understand the effect of these mechanisms on the cooperative behavior in the networks and promote the cooper-ation behavior. Then, we can induce the emergence of cooperation. The ultimate goal of research on complex networks and complex systems is still how to control them, and the first question we met is to judge controllable. In recent years, the research on net-work control has offered us the judgement of whether a complex network is controllable and how much is the minimal number of driver nodes we need to achieve full control of network. In this paper, the main work is as follows.Individuals behave differently in different environments, such as in the public goods game, the individuals contribute to the group only if there have other individuals who are also willing to contribute. We introduce the weigthed conditional strategies to dis-tinguish the effect of individuals with different contribution conditions on the group contribution behavior. We find that, for lower mutiplication, the most cautious individ- uals can survive in unweigthed model. However, for large weights in weigthed model, more strategies can survive in networks. In other words, the introduction of weights is helpful to the survival of conditional strategies. On the contrary, for higher multiplica-tion, uncautious cooperators are more likely to survive in networks.In the realistic case, not everyone needs to engage in the game in each round. Gen-erally, in many empirical cases, players are inclined to not participate in the game for longer time (rather than one round). After a certain period, they can come back to the normal interactions. Inspired by this fact, we propose the silence strategy and silence pe-riod into the prisoner’s dilemma game. Different from the voluntary participation model in which the loner can gain the low payoff, the silence player, who does not participate in games, neither gains the payoff nor provides payoff to others within the silence period. Moreover, considering that the player also has consumption in the games, we introduce silence strategy based on the consumption mechanism. The probability of selecting si-lence depends on the surplus payoff controlled by consumption level. Interestingly, we have unveiled that the introduction of silence can greatly promote cooperation for the low consumption level. This promotion behavior is supported by the rockscissor-paper cycle. In the most early stages, cooperators are exploited by defectors. Due to lack of benifit, cooperators turn to silence players quickly. After the silence period, the surviv-ing cooperation clusters, which have larger payoff, attract numerous silent individuals (around the clusters) to penetrate into the clusters as cooperation members. However, if we further enlarge the consumption level, this cycle will disappear. Under the large consumption level, though the defection is still restrained, the silence strategy will ab-solutely take up the system. This means that there exists an optimal cooperation at intermediate consumption level, which is robust against the silence period.The interdependent network is used to explore the cascading failures, spreading and other dynamics, in which a node in one network is interdependent to other nodes in an-other network. The dependency relation is also used to study the cooperation behaviors, and it has been demonstrated that interdependent networks can spread the cooperation. Motivated by the fact that individuals behave differently when facing the various inter-action objects, we introduce a dependency relation into the spatial prisoner’s dilemma games. Specifically, a fraction of individual pairs is selected randomly to depend with each other. This dependency relation can bring an extra payoff to the individual which is between the payoff of mutual cooperation and temptation to defect. The motivation of this setup is that the dependency relation ought to be stronger than ordinary cooperation but it cannot induce the defection between the dependent individuals. It is found that the dependency relation hinders the cooperation on the regular ring networks, while it can-not affect the cooperation on random networks and scale-free networks.The only case that it can promote is the square lattice networks. Whether the dependency relation can affect the cooperation is determined by the homogeneous or heterogeneous of degree.Recent experimental studies have demonstrated that the cooperation can be greatly enhanced in dynamic social networks. The higher cooperation level is contributed by the breaking and rewiring processes which reflect the response to defection. Here we focus on the pattern of response to defection induced by the continuous defection be-haviors, while a occasional defection is neglected. The usage of this setup is motivated by the fact that the limitation of social relationship determines the candidate whom the individuals can rewire the new links with them are relatively fixed. In other words, rewiring a new link the individual with a randomly selected individual is hard, which is consistent with the real situation that the personal social circle is finite. In this paper, we investigate the cooperation on the dynamic networks induced by the continuous de-fection behaviors. The individual chooses to break the links with neighbours who have already continuously adopt defection strategy for several steps, meanwhile, the broken links will be rewired after the breaking operation the same steps. The simulation results show that the cooperation level is enhanced greatly on the dynamic networks by pas-sively isolating the defectors. The breaking and rewiring operation induce the networks can hold in the pure cooperation state even for large tempt to defection. In particular, we find that the faster response to defection is more conductive to the cooperation behavior. Moreover, the fraction of individuals with maximum degree equals to the cooperation level in stable state, which bridges the evolutionary games and networks’s structures.Conformity behaviors are quite common in society and animal communities. Some laboratorial experiments have revealed that, people and animals highly tend to follow majority in their groups. Hence, we explore controllability of complex networks with conformity behaviors by relying on the exact controllability theory. We explore the controllability of a variety of regular and complex networks with conformity, finding some interesting results that are different from the prediction of structural controllability theory. Finally, We present an example of steering a small social network, in which evolutionary games take place to several target states by controlling driver nodes with minimum number.