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In this paper, we study the effects of reputation-based investment strategy on cooperation in the spatial public goods games. The investment of one player to a particular group depends on the reputation of the group organizer. We define a player’s reputation as the frequency of cooperation in the past few time steps. Our results show that the cooperation level can be remarkably enhanced if a player invests more in the group organized by a higher-reputation leader. We explain this phenomenon by analyzing the income gap between cooperators and defectors at the interface that separates clusters of the two competing strategies. To have an intuitive understanding, we plot the snapshots of spatial distributions of players with different reputation. The effects of the memory length are also studied.

Education is not only a guarantee of personal knowledge, but also a topic of national importance. In this paper, we analyzed the scientific papers published by authors from China and the United States in 239 educational journals over a period of 20 years (2000–2019). We first extracted the topic of each paper via the Latent Dirichlet allocation model, which demonstrated significant differences in specific sub-fields between both countries. Next, we constructed two networks of scientific collaboration among the educators of each country. By analyzing these networks’ topological properties, we show both countries’ differences and common features. Regarding individuals, Chinese educators collaborate widely, whereas American educators are more likely to collaborate in certain groups. Regarding groups, there exists an optimal team size for producing highly popular papers in both countries.

We study group formation in the spatial public goods game with continuous strategies. An active group will become inactive with high (low) probability if the collective contribution is below (above) a threshold value. Meanwhile, an inactive group recovers to be active with some probability. We have found that the cooperation level and the average payoff of players are maximized at moderate values of the threshold and the recovery rate. Spatial distributions of strategies and active groups are plotted to understand the evolution of cooperation.

An interesting phenomenon is often observed in realistic systems. In the process of games, if the expected payoff from game interactions is not achieved, players would refuse to participate in the games. Inspired by this fact, we propose an aspiration-induced dormant mechanism, in which players quit the games and become dormant if their payoffs are less than the aspiration level. After a dormant period, they continue to play the game with others. Our results indicate an intermediate aspiration value, leading to the highest cooperation level in the spatial prisoner’s dilemma games. The effects of the dormant period are also studied.

Migration plays an important role in the evolution of cooperation. Previous studies concerning mobile population often assumed that all agents move with the identical velocity. In this paper, we propose a payoff-driven migration in which the velocity of an agent depends on his/her payoff. A parameter α is introduced to adjust the influence of payoff, when α = 0 means that agents all move with the identical velocity while α > 0 means that the lower the payoff is, the faster the moving speed is, and vice versa. For the prisoner’s dilemma game, we find that in comparison with the case that agents all move with the same speed, cooperation could be promoted strongly when payoff-dependent velocity is considered. Remarkably, the cooperation level is not a monotonic function of α , and there exists an optimal value of α which can lead to the maximum cooperation level. For the snowdrift game, the cooperation level increases with α .

In this paper, we study a heterogeneous donation game in geographical small-world networks. Cooperators provide benefits to their neighbors at some costs. Defectors pay no cost and do not distribute any benefits. The total contribution of a cooperator is fixed and he/she distributes his/her contribution unevenly to his/her neighbors. The amount that a cooperator contributes to a neighbor depends on their geographical distance. Our results show that, the cooperation level reaches the highest when cooperators give distant neighbors more help, but only to a certain extent. We analyze the time evolution of cooperator clusters and the length of cooperative links. Besides, we study the effects of the density of shortcuts on cooperation.

We study the collective motion of self-propelled agents with the restricted view. The field of view of each agent is an annulus bounded by the outer radius r and inner radius α r , where α ​is a tunable parameter. We find that there exists an optimal value of α leading to the highest degree of direction consensus. This phenomenon indicates that there exists superfluous communication in the collective motion of self-propelled agents and short-range interactions hinder the direction consensus of the system. The value of optimal α decreases as the absolute velocity increases, while it increases as the outer radius r and the system size increase. For a fixed value of α , direction consensus is enhanced when the absolute velocity is small, the outer radius or the system size is large.

The design of routing strategies for networks of mobile nodes has received increasing attention in recent years. In this paper, we propose an adaptive routing strategy that incorporates geographical distance with local traffic information through a tunable parameter h . It is found that there exists an optimal value of h , leading to the maximum traffic throughput of the network. The optimal value of h decreases as the moving speed increases and increases as the communication radius increases. The dependence of the throughput on the moving speed and the communication radius is also studied. Our results show that for a wide range of the parameters, the throughput decreases as the moving speed increases. However, when the value of the parameter is set to be one, the maximum throughput is obtained at a moderate speed. Moreover, we find that the throughput increases with the communication radius.

We introduce a deterministic win-stay-lose-shift rule into the spatial public goods game, according to which a player will change its current strategy only if its payoff is below a predefined aspiration level. Simulation results on the square lattice and scale-free network indicate that the aspiration level greatly affects the evolution of cooperation. For small multiplication factors, the frequency of cooperation increases to 0.5 as the aspiration level increases. For large multiplication factors, intermediate levels of aspiration prove optimal for the successful evolution of public cooperation. Some qualitative analyses are provided to explain the above results. Besides, we have found that there exists a ping-pong vibration of cooperation at some specific values of multiplication factors and aspiration levels.

In this paper, we study an aspiration-induced migration model, in which each individual plays the prisoner’s dilemma game with those being within a circle of radius r centered on himself/herself. An individual will migrate to a randomly chosen place with the velocity v if his/her payoff is below the aspiration level. We report that cooperative behavior is favored when the aspiration level and interaction radius are moderate, and the migration velocity is slow.

An evolutionary prisoner’s dilemma game with players adjusting their learning motivation is studied. At each time step, each player can adjust his/her learning motivation according to the difference between the current payoff and payoff aspiration. Greater payoff aspiration means stronger learning motivation, and vice versa. We find that the density of cooperation in a spatial prisoner’s dilemma game is enhanced when the learning motivation mechanism is considered. Meanwhile, we show that proper noise can not only induce the highest cooperation level but also can maintain the cooperation phenomenon even though there is more temptation to defect.

In this paper, we bring an unequal payoff allocation mechanism into evolutionary public goods game on scale-free networks and focus on the cooperative behavior of the system. The unequal mechanism can be tuned by one parameter α : if α > 0 , the hub nodes can use its degree advantage to collect more payoff; if α 0 , numerous non-hub nodes will obtain more payoff in a single round game. Simulation results show that the cooperation level has a non-trivial dependence on α . For the small enhancement factor r , the cooperator frequency can be promoted by both negative and positive α . For large r , there exists an optimal α that can obtain the highest cooperation level. Our results may sharpen the understanding of the emergence of cooperation induced by the unequal payoff allocation mechanism.

Considering the difference between the actual and expected payoffs, we bring a stochastic learning updating rule into an evolutionary Prisoners Dilemma game and the Snowdrift game on scale-free networks, and then investigate how the expectation level A and environmental noise κ influence cooperative behavior. Interestingly, numerical results show that the mechanism of promoting cooperation exhibits a resonance-like fashion including the coaction of A , κ and the payoff parameters. High cooperator frequency is induced by some optimal parameter regions. The variation of time series has also been investigated. This work could be of particular interest in the evolutionary game dynamics of biological and social systems.

In real-life networks, incomers may only connect to a few others in a local area for their limited information, and individuals in a local area are likely to have close relations. Accordingly, we propose a local preferential attachment model. Here, a local-area-network stands for a node and all its neighbors, and the new nodes perform nonlinear preferential attachment, π ( k i ) ∝ k i α , in local areas. The stable degree distribution and clustering-degree correlations are analytically obtained. With the increasing of α , the clustering coefficient increases, while assortativity decreases from positive to negative. In addition, by adjusting the parameter α , the model can generate different kinds of degree distribution, from exponential to power-law. The hierarchical organization, independent of α , is the most significant character of this model.