This paper investigates the security issues of average consensus networks under false data injection attacks. Based on the intention of the adversary, the attacks to be analyzed are categorized into two types. The first type aims to rapidly diverge the states of the agents to infinity, while the second type seeks to mislead the states towards the adversary's desired values. A necessary and sufficient condition for Type-I attacks to bypass the anomaly detector is first provided, along with an algorithm for generating false data sequences. Subsequently, for Type-II attacks, the closed-form expression of the optimal attack is derived using dynamic programming. To address these vulnerabilities, a watermarking-based data transmission strategy is proposed by resorting to cryptographic pseudo-random sequences. The influence of watermarking parameters on detection performance across different attack scenarios is analyzed. It is demonstrated that the proposed strategy can effectively assist the anomaly detector in identifying stealthy attacks or mitigate its impact on the consensus networks by adjusting the watermarking parameters. A numerical example is provided to demonstrate the validity of the developed results.

This paper investigates the mixing scheme of social-learning imitation dynamics and self-reinforcing aspiration dynamics in spatial Prisoner’s Dilemma game, where agents update among three kinds of strategies (cooperation, defection, and extortion) through imitation or aspiration learning dynamics assigned in advance. Our results show that by introducing a few aspirants into a majority of imitators in the networked systems, the aspirants tend to adhere to cooperation strategy catalyzed by extortion strategy. Through mixing a proper proportion of these two learning dynamics, cooperative behavior easily emerges not only in regular lattice, but also in social networks. This may yield some insight into understanding the emergence of cooperation and optimizing performance of social systems.

In this paper, we investigate the multi-player equalizer strategy in the public goods game with threshold, a kind of key zero-determinant strategies in iterated games that can enforce opponents' long-term payoff to a fixed value. This paper studies the role of the equalizer strategy on the total amount of endowment in the particular scenario of the iterated multi-player game, where everyone will suffer a loss if the endowment does not exceed a threshold. Our results show that the threshold that the equalizer strategy can enforce to reach varies depending on the reward and risk factors. This also provides a potential clue on how humanity should reach a consensus to avoid the collective-risk social dilemma.

Identifying influential agents is an important issue in controlling the dynamical processes in complex networks, while centrality measurements are good ways to rank node’s influence. In this paper, we combine agents’ influence with their strategy-updating timescales to explore the effect of diverse influences on the emergence of cooperation in the evolutionary prisoner’s dilemma game. Through Monte Carlo simulation in five real-world social networks, we find that collective influence outperforms the basic centrality measurements such as degree and coreness in ranking agent’s influence, identifying the influential spreaders and promoting the evolution of cooperation. Moreover, collective influence with depth length plays an nontrivial role on the evolution of cooperation in networked systems.

Based on the Prisoner's Dilemma game, we study the effect of the diverse strategy-updating time scale on the evolution of cooperation under the normalized payoff framework. Agents can adjust their strategy-updating speed according to their fitness and collective influence, and this mechanism promotes the emergence of cooperation on Barabási-Albert scale- free networks. Moreover, agents with higher values of collective influence may have longer persistence-cooperation duration and diffuse their cooperative behaviors among neighbors efficiently. Through investigating the game-learning skeleton, we find that the heavy-tailed in-degree distribution emerges and influencers with proper depth length play an important role in maintaining cooperation.

In this paper, we study the evolution of cooperation in a stochastic game model where agents evolve in terms of some famous and important memory-two strategies, such as AllC, AllD, TFT and W SLS strategies. Comparing with memory-one strategies, it is found that the cooperation is easier to emerge in stochastic games with memory-two strategies. When agents remember more rounds of outcomes, cooperation can boost in noisy environment when some efficient transition rules work to reward mutual cooperation and punish defection. This may provide some potential clues to seek for efficient methods that maintain cooperation in multi-agent games.

Based on the celebrated Prisoner's Dilemma game, we study the roles of mutation mechanism for the evolution of cooperation with extortion strategies on clustered scale-free networks. It is shown that cooperation can be promoted under the influence of extortion strategies with small mutation rate. This is because that mutation helps the formation of alliance between extortion and cooperation strategies, and extortioners tend to locate on hubs and induce more small-degree neighbors becoming cooperators on high clustered scale-free networks. However, too smaller or too larger mutation rates will inhibit the emergence of cooperation, and the positive influence of mutation on the cooperation disappears on low clustered scale-free networks. This work may provide some clues to explore efficient methods to optimize performance on networked systems.

Based on the celebrated public goods game with group interaction, we study the evolution of cooperation on two kinds of scale-free networks with similar degree distribution and clustering coefficient. It is showed that there are different evolution routes in the structured population. The metric clusters existing on the popularity-similarity network let cooperation diffuse in local regions. Whereas, cooperators on the clustered scale-free network tend to invade hubs firstly, and then spread from hubs to leaves with a top-down pattern, which leads to the higher cooperation level on the clustered scale-free network than that on the popularity-similarity network.

The bounded rationality of agents plays an important role in the performance of complex systems. In this work, we explore the influence of bounded rationality on the evolution of cooperation, defection and extortion strategies on a regular lattice by applying the Fermi dynamics in the Prisoner's Dilemma game. It is found that the rationality level plays a non-trivial role in the emergence of cooperation with extortion in structured systems. On the one hand, for the perfect rationality case, it is difficult for cooperators to resist the invasion of defection. On the other hand, being too irrational breaks the stable structure between cooperators and extortioners, and results in the extinction of cooperation. Hence, there is a proper level of bounded rationality which can slow down the expansion of defective and extortionate behaviors, and promote the emergence of cooperation-extortion alliances, which can yield a better outcome to the whole system. This study may provide some clues to optimize the performance of multi-agent systems with bounded rationality.

Extortion strategies, which can let an individual's surplus exceed her opponent's by a fixed percentage, have played an important role in the understanding of the evolution of cooperation in the Prisoner's Dilemma game. In this paper, we combine individuals' extortion ability with their degrees, and study the influence of extortion diversity in the heterogeneous scale-free network. Our investigation shows that, when individuals' extortion factors are negative correlation with their degrees, these extortionate hubs play as catalysts to enhance the emergence of cooperative behavior. However, when the extortion factors are positively correlated with degrees, the effect of hub's catalyst is weaken.

Cooperation phenomena are ubiquitous in social systems. In this paper, based on the Prisoner's dilemma game model, we study the evolution of cooperation in two social networks, namely, the scientific collaboration network (SCN) and the “Pretty-Good-Privacy” (PGP) trust network. Our investigation shows that due to the existence of community structures in real social networks, small-degree individuals tend to follow their local hubs' behavior and would adopt their strategies in the long run. Hence, the community structure promotes the emergence of persistence behavior. This provides a clue to understanding the evolution of cooperation in social systems.

In this brief, we investigate pinning control for cluster synchronization of undirected complex dynamical networks using a decentralized adaptive strategy. Unlike most existing pinning-control algorithms with or without an adaptive strategy, which require global information of the underlying network such as the eigenvalues of the coupling matrix of the whole network or a centralized adaptive control scheme, we propose a novel decentralized adaptive pinning-control scheme for cluster synchronization of undirected networks using a local adaptive strategy on both coupling strengths and feedback gains. By introducing this local adaptive strategy on each node, we show that the network can synchronize using weak coupling strengths and small feedback gains. Finally, we present some simulations to verify and illustrate the theoretical results.

In this paper we study the effect of clustering coefficient on the evolution of cooperation in scale-free public goods games. Since the cooperator can feed back the investment to its cooperative neighbors through their common neighbor, the cooperative behaviors is easier to diffuse on the graph with triangle loops than that without loops. The feedback reciprocity mechanism of triangle discloses why the cooperation is enhanced in the high clustered scale-free networks. Since the clustering property is an important character in many real-world networks, our results may provide some insight into understanding the emergence and persistence of cooperation in the networked systems.

In this paper, we propose a decentralized adaptive pinning control scheme for synchronization of undirected networks using a local adaptive strategy to determine both coupling strengths and feedback gains. By applying this local adaptive strategy, we show that the network can achieve synchronization with small coupling strengths and feedback gains. We provide some simulations to verify and illustrate the theoretical results.

This paper studies the roles of small-world and degree heterogeneity features on the behavioral diversity in a structured population. The findings conclude that the collective behaviors are prone to the much higher diversity in a homogeneous structure due to the small-world effect, yet they are affected little in a scale-free structure. And the degree heterogeneity promotes the behavioral diversity a little while the population structure is homogeneous, but inhibits diversity while it is scale-free. Our work may be helpful for better understanding the collective evolutionary dynamic behaviors in a homogeneous or scale-free structured population.