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In this article, the evolution of prisoner's dilemma game with volunteering on interdependent networks is investigated. Different from the traditional two-strategy game, voluntary participation as an additional strategy is involved in repeated game, that can introduce more complex evolutionary dynamics. And, interdependent networks provide a more generalized network architecture to study the intricate variability of dynamics. We have showed that voluntary participation could effectively promote the density of co-operation, that is also greatly affected by interdependent strength between two coupled networks. We further discussed the influence of interdependent strength on the densities of different strategies and found that an intermediate interdependence would play a bigger role on the evolution of dynamics. Subsequently, the critical values of the defection temptation for phase transitions under different conditions have been studied. Moreover, the global oscillations induced by the circle of dominance of three strategies on interdependent networks have been quantitatively investigated. Counter-intuitively, the oscillations of strategy densities are not periodic or stochastic, but have rich dynamical behaviors. By means of various analysis tools, we have demonstrated the global oscillations of strategy densities possessed chaotic characteristics. [ABSTRACT FROM AUTHOR]

In this article, based on interdependent networks, the effect of self-organized interdependence on the evolution of cooperation is studied. Different from the previous works, the interdependent strength, which can effectively improve the fitness of players, is taken as a kind of limited resources and co-evolves with players’ strategy. We show that the self-organization of interdependent strength would spontaneously lead to power law distribution at the stationary state, where the level of cooperation in system can be significantly promoted. Furthermore, when intermediate quantity of interdependence resources existing in system, the power law distribution is most evident with the power β ≈ 1.72, meanwhile the level of cooperation also reaches the maximum value. We discuss the related microscopic system properties which are responsible for the observed results and also demonstrate that the power law distribution of interdependence resources is an elementary property which is robust against the governing repeated games and the initial resources allocation patterns. [ABSTRACT FROM AUTHOR]

In reality, complicated situations usually include multiple game scenarios, which cannot be effectively described by a single game model. Hence, how to model and reveal the cooperative behaviors in complex multiple game environments is a meaningful topic. In this article, by using switching control, a spatial multigame model with reciprocal reward and reputation mechanism is proposed, where a specific game scenario at each time step is determined by current individuals' behaviors and the game type. Besides, the allocation of limited resources is co-evolved with the evolution of cooperation, which can be regarded as the results of the game and meanwhile affect the while game processes. The evolution dynamics of the proposed model is detailly discussed and the mutual influence of reputation mechanism, reward reciprocity and resource allocation on cooperative behaviors is quantitatively studied. Finally, in order to illustrate the robustness of the analyzed results, its impact on the cooperative behaviors in single PD and SD games are comparatively discussed. • Spatial multigame using switching control. • Reciprocal reward and reputation mechanism in multigame. • Co-evolution of multigame combined with limited resource allocation. [ABSTRACT FROM AUTHOR]

• A signal propagation model for financial granular network is constructed. • Theoretical proofs of fluctuation propagation on financial granular network. • Quantitative analysis of the fluctuation propagation in real financial data sets. Financial markets are usually affected by various factors, such as breaking news or the release of important economic data, which would interrupt normal fluctuations and cause the abruptly increasing of volatility. How the financial markets behave under the impact of sudden external stimulations is of great significance for the analysis and prediction of financial prices. In this article, combining the theory of complex networks with granular computing, the financial granular complex network is constructed, based on which the propagation of fluctuation patterns after the occurrence of abnormal changes are studied. Here, the so-called "abnormal changes" are defined as the sudden and fierce fluctuations of financial prices, which are the non-trivial phenomena commonly existing in financial markets. By constructing the dynamical equations of pattern propagation, the evolution trajectories and the intrinsic characteristic of abnormal volatility patterns in financial granular network are quantitatively and qualitatively discussed. Results reveals the behaviors of the financial granule networks after the occurrence of abnormal fluctuations, and the impact of network topology on the propagation of fluctuation patterns is proved theoretically. In order to verify the validity of theoretical analysis, the empirical studies are carried out by using the real financial data deriving from foreign exchange and stock markets. [ABSTRACT FROM AUTHOR]

• A novel spatial multigame model with environment and resources. • Self-organized dynamics from the perspective of resource allocation and environmental factors. • Position-based pinning control mechanism is involved. In reality, environment has the considerable effect on the decision making of individuals. Meanwhile, individuals with different amount of resources could have distinct responses to environmental impacts. In this article, based on spatial multigame model, the mutual effect of environment and resources allocation on cooperation is studied. Firstly, the fitness of individuals in multigame is redefined by using environmental factor and limited resources are introduced into the model coevolving with individual strategy. Secondly, the relationship between resource quantity and strategy selection is studied, where the influence of the environmental factor and resources on cooperative behaviors has been discussed in detail. Thirdly, the evolutionary dynamics of cooperation clusters are discussed such that the characteristics of resource allocation in multigame model are further analyzed. Finally, in order to deeply reveal the impact of resources on the evolution behaviors of the multigame system, position-based pinning control mechanism is involved to control the speed of resource change and the corresponding evolutionary processes are discussed. [ABSTRACT FROM AUTHOR]