Prisoner＇s Dilemma Game with Nonlinear Attractive Effect on Regular Small-World Networks

We investigate a spatial Prisoner＇s Dilemma game with nonlinear attractive effect on regular small-world networks. The players located on the sites of networks can either cooperate with their neighbours or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbours with a probability proportional to .A^α denoting the attractiveness of the neighbour, where .4 is the collected payoff and ^α （-〉0） is a free parameter characterizing the extent of nonlinear effect. Then each player adopts its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density pc of cooperators in the stationary state for various values of α and the rewiring probability q of the network. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect for the same network structures. We also point out that long-range connections either enhance or inhibit the cooperation, which depends on the value of α and the payoff parameter b.     

Prisoner's Dilemma Game on Clustered Scale-Free Networks under Different Initial Distributions

The evolutionary prisoner＇s dilemma game is investigated under different initial distributions for cooperators and defectors on scale-free networks with a tunable clustering coefficient. It is found that, on the one hand, cooperation can be enhanced with the increasing clustering coefficient when only the most connected nodes are occupied by cooperators initially. On the other hand, if cooperators just occupy the lowest-degree nodes at the beginning, then the higher the value of the clustering coefficient, the more unfavorable the environment for cooperators to survive for the increment of temptation to defect. Thereafter, we analytically argue these nontrivial phenomena by calculating the cooperation probability of the nodes with different degrees in the steady state, and obtain the critical values of initial frequency of cooperators below which cooperators would vanish finally for the two initial distributions.     

Evolutionary snowdrift game with disordered environments in mobile societies

We investigate an evolutionary snowdrift game on a square $N=L\times L$ lattice with periodic boundary conditions, where a population of $n_{0}$ ($n_{0}\leq N$) players located on the sites of this lattice can either cooperate with or defect from their nearest neighbours. After each generation, every player moves with a certain probability $p$ to one of the player's nearest empty sites. It is shown that, when $p=0$, the cooperative behaviour can be enhanced in disordered structures. When $p>0$, the effect of mobility on cooperation remarkably depends on the payoff parameter $r$ and the density of individuals $\rho$ ($\rho=n_{0}/N$). Compared with the results of $p=0$, for small $r$, the persistence of cooperation is enhanced at not too small values of $\rho$; whereas for large $r$, the introduction of mobility inhibits the emergence of cooperation at any $\rho<1$; for the intermediate value of $r$, the cooperative behaviour is sometimes enhanced and sometimes inhibited, depending on the values of $p$ and $\rho$. In particular, the cooperator density can reach its maximum when the values of $p$ and $\rho$ reach their respective optimal values. In addition, two absorbing states of all cooperators and all defectors can emerge respectively for small and large $r$ in the case of $p>0$.     

Evolutionary prisoner’s dilemma game on highly clustered community networks

This paper studies the evolutionary prisoner's dilemma game on a highly clustered community network in which the clustering coefficient and the community size can be tuned. It finds that the clustering coefficient in such a degree-homogeneous network inhibits the emergence of cooperation for the entire range of the payoff parameter. Moreover, it finds that the community size can also have a marked influence on the evolution of cooperation, with a larger community size leading to not only a lower cooperation level but also a smaller threshold of the payoff parameter above which cooperators become extinct.     

Finite Size Effect on the in-Medium Chiral Condensate at Finite Density

The in-medium quark condensate is studied with an equivalent quark mass approach that has the advantage of no need for extra assumptions on the current mass derivatives of model parameters with respect to the quark current mass. It is found that the ratio of the quark condensate in a medium to that in a vacuum depends not only on density but also on the finite size. With decreasing volume, it decreases to a minimum, and then saturates at a radius of about 1 fro. The condensate approaches to its bulk value when the volume becomes infinitely large, and it decreases finearly with increasing density if the density is extremely low.     

Electron states scattering off line edges on the surface of topological insulator

We study the local density of states （LDOS） for electrons scattering off the line edge of an atomic step defect on the surface of a three-dimensional （3D） topological insulator （TI） and the line edge of a finite 3D TI, where the front surface and side surface meet with different Fermi velocities, respectively. By using a S-function potential to model the edges, we find that the bound states existed along the step line edge significantly contribute to the LDOS near the edge, but do not modify the exponential behavior away from it. In addition, the power-law decaying behavior for LDOS oscillation away from the step is understood from the spin rotation for surface states scattering off the step defect with magnitude depending on the strength of the potential. Furthermore, the electron refraction and total reflection analogous to optics occurred at the line edge where two surfaces meet with different Fermi velocities, which leads to the LDOS decaying behavior in the greater Fermi velocity side similar to that for a step line edge. However, in the smaller velocity side the LDOS shows a different decaying behavior as x-1/2, and the wavevector of LDOS oscillation is no longer equal to the diameter of the constant energy contour of surface band, but is sensitively dependent on the ratio of the two Fermi velocities. These effects may be verified by STM measurement with high precision.     

Integrating the environmental factor into the strategy updating rule to promote cooperation in evolutionary games

Many previous studies have shown that the environment plays an important role for social individuals.In this paper,we integrate the environmental factor,which is defined as the average payoff of all a player’s neighbours,with the standard Fermi updating rule by introducing a tunable parameter,ω.It is found that the level of cooperation increases remarkably,and that the cooperators can better resist the invasion of defection with an increase in ω.This interesting phenomenon is then explained from a microscopic view.In addition,the universality of this mechanism is also proved with the help of the small-world network and the random regular graph.This work may be helpful in understanding cooperation behaviour in species from unicellular organisms up to human beings.     

Pupil apodization for increasing data storage density

We introduce a technique for increasing density in optical data storage systems. This technique is based on the use of a superresolving filter at the pupil of a confocal readout system. The main characteristic of this confocal readout system is that the light beam traverses twice through the pupil filter. We describe how to analyze the system performance for general filters, but we focus the study on filters with no focus displacement. Although the storage density attainable depends on the filter characteristics, we show that the storage density can be easily duplicated.     

Locally Rotationally Symmetric Bianchi Type-Ⅰ Model with Time Varying Λ Term

We investigate the locally rotationally symmetric （LRS） Bianchi type-Ⅰ cosmological model for stiff matter and a vacuum solution with a cosmological term proportional to R^-m （R is the scale factor and m is a positive constant）. The cosmological term decreases with time. We obtain that for both the cases the present universe is accelerating with a large fraction of cosmological density in the form of a cosmological term.     

Modified Holographic Ricci Dark Energy in Chameleon Brans–Dicke Cosmology and Its Thermodynamic Consequence

The objective of this paper is to discuss the Chameleon Brans–Dicke gravity with non-minimally matter coupling of scalar field. We take modified Holographic Ricci dark energy model in this gravity with its energy density in interaction with energy density of cold dark matter. We assume power-law ansatz for scale factor and scalar field to discuss potential as well as coupling functions in the evolving universe. These reconstructed functions are plotted versus scalar field and time for different values of power component of scale factor n. We observe that potential and coupling functions represent increasing behavior, in particular, consistent results for a specific value of n. Finally, we have examined validity of the generalized second law of thermodynamics and we have observed its validity for all values of n.     

Evolution of cooperation in lattice population with adaptive interaction intensity

We study the evolutionary Prisoner’s Dilemma game among individuals endowed with adaptively interaction intensity. Individuals adjust their interaction intensity according to the rules “payoff increase-high intensity, payoff decrease-low intensity”: if an individual’s payoff increases compared with that in the previous generation, he raises his interaction intensity; otherwise, he reduces the probability of interaction. We find that if individuals can adjust their interaction intensity with a proper scale, cooperation can be promoted. Interestingly, individuals with low interaction intensity usually hold the boundary of cooperator cluster. Such spatial distribution can alleviate the exploitation from defectors to cooperators since the interaction between cooperators and defectors is weakened. We hope our work can yield some insight into investigation of the evolution of cooperation in structured population.     

Cooperation in N-person evolutionary snowdrift game in scale-free Barabási-Albert networks

Cooperation in the N-person evolutionary snowdrift game (NESG) is studied in scale-free Barabási-Albert (BA) networks. Due to the inhomogeneity of the network, two versions of NESG are proposed and studied. In a model where the size of the competing group varies from agent to agent, the fraction of cooperators drops as a function of the payoff parameter. The networking effect is studied via the fraction of cooperative agents for nodes with a particular degree. For small payoff parameters, it is found that the small-k agents are dominantly cooperators, while large-k agents are of non-cooperators. Studying the spatial correlation reveals that cooperative agents will avoid to be nearest neighbors and the correlation disappears beyond the next-nearest neighbors. The behavior can be explained in terms of the networking effect and payoffs. In another model with a fixed size of competing groups, the fraction of cooperators could show a non-monotonic behavior in the regime of small payoff parameters. This non-trivial behavior is found to be a combined effect of the many agents with the smallest degree in the BA network and the increasing fraction of cooperators among these agents with the payoff for small payoffs.     

Effects of average degree on cooperation in networked evolutionary game

We study effects of average degree on cooperation in the networked prisoner's dilemma game. Typical structures are considered, including random networks, small-world networks and scale-free networks. Simulation results show that the average degree plays a universal role in cooperation occurring on all these networks, that is the density of cooperators peaks at some specific values of the average degree. Moreover, we investigated the average payoff of players through numerical simulations together with theoretical predictions and found that simulation results agree with the predictions. Our work may be helpful in understanding network effects on the evolutionary games.     

Prisoner’s Dilemma Game with Cooperation-Defection Dominance Strategies on Correlational Multilayer Networks

As multilayer networks are widely applied in modern society, numerous studies have shown the impact of a multilayer network structure and the network nature on the proportion of cooperators in the network. In this paper, we use Barabási–Albert scale-free networks (BA) and Watts and Strogatz networks (WS) to build a multilayer network structure, and we propose a new strategy-updating rule called “cooperation-defection dominance”, which can be likened to dominant and recessive traits in biogenetics. With the newly constructed multilayer network structure and the strategy-updating rules, based on the simulation results, we find that in the BA-BA network, the cooperation dominance strategy can make the networks with different rs show a cooperative trend, while the defection dominance strategy only has an obvious effect on the network cooperation with a larger r. When the BA network is connected to the WS network, we find that the effect of strategy on the proportion of cooperators in the network decreases, and the main influencing factor is the structure of the network. In the three-layer network, the cooperation dominance strategy has a greater impact on the BA network, and the proportion of the cooperators is enhanced more than under the natural evolution strategy, but the promotion effect is still smaller than that of the two-layer BA network because of the WS network. Under the defection dominance strategy, the WS layer appears different from the first two strategies, and we conclude through simulation that when the payoff parameter is at the middle level, its cooperator proportion will be suppressed, and we deduce that the proportion of cooperators and defectors, as well as the payoff, play an important role.     

Evolution of Cooperation in Public Goods Games

We investigate the evolution of cooperation with evolutionary public goods games based on finite populations, where four pure strategies: cooperators, efectors, punishers and loners who are unwilling to participate are considered. By adopting approximate best response dynamics, we show
that the magnitude of rationality not only quantitatively explains the experiment results in [Nature (London) {\bf 425} (2003) 390], but also it will heavily
influence the evolution of cooperation. Compared with previous results of infinite populations, which result in two equilibriums, we show that there merely exists a special equilibrium and the relevant high value of bounded rationality will sustain cooperation. In addition, we characterize that loner's payoff plays an active role in the maintenance of cooperation, which will only be warranted for the low and moderate values of loner's payoff. It thus indicates
the effects of rationality and loner's payoff will influence the cooperation. Finally, we highlight the important result that the introduction of voluntary participation and punishment will facilitate cooperation greatly.     

Preferential selection promotes cooperation in a spatial public goods game

We introduce a preferential selection mechanism into a spatial public goods game where players are located on a square lattice. Each individual chooses one of its neighbors as a reference with a probability proportional to , where P_y is the neighbor’s payoff and A (≥0) is a tunable parameter. It is shown that the introduction of such a preferential selection can remarkably promote the emergence of cooperation over a wide range of the multiplication factor. We find that the mean payoffs of cooperators along the boundary are higher than that of defectors and cooperators form larger clusters as A increases. The extinction thresholds of cooperators and defectors for different values of noise are also investigated.     

The roles of heterogeneous investment mechanism in the public goods game on scale-free networks

The public goods game is an important theoretical model for investigating the emergence of cooperation in the multi-player social dilemma. It has been proven that scale-free networks can significantly promote cooperation, but fail to sustain cooperation when the player obtains the normalized payoff. In this paper, we introduce heterogeneous investment mechanism into the public goods game on scale-free networks, and study the evolution of cooperation in both cases of accumulated and normalized payoff. Our research reveals that the heterogeneous investment mechanism can obviously facilitate cooperation as the adjusted parameter α increases. The increase of α allows cooperators to emerge under lower values of r. In the case of accumulated payoff, cooperators always firmly occupy the hubs, and the population keeps high cooperation level. In the case of normalized payoff, the increase of α changes the situation that the hubs are easily invaded by defectors, and inhibits the spread of defectors.     

Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs

We study the evolution of cooperation modeled as symmetric 2x2 games in a population whose structure is split into an interaction graph defining who plays with whom and a replacement graph specifying evolutionary competition. We find it is always harder for cooperators to evolve whenever the two graphs do not coincide. In the thermodynamic limit, the dynamics on both graphs is given by a replicator equation with a rescaled payoff matrix in a rescaled time. Analytical results are obtained in the pair approximation and for weak selection. Their validity is confirmed by computer simulations.     

Effect of community structure on coevolutionary dynamics with dynamical linking

We investigate the effect of community structure on the evolution of cooperation in the prisoner’s dilemma and the snowdrift game with dynamical linking. We show both analytically and numerically that cooperators are generally more favorable on community networks than on networks without community structure, and in particular, there exists an optimal intermediate value of the model parameter leading to the easiest fixation of cooperators. We show that our results are robust with respect to the initial number of cooperators and are valid for a wide range of the ratio of time scales associated with linking and strategy dynamics. Since community structure is ubiquitous in real social networks, our results may provide new insights into the evolution of cooperation in real world.