The mechanism of alliance promotes cooperation in the spatial multi-games

In reality, individuals often tend to enhance their competitiveness by forming alliances with the partners sharing the same view. Motivated by this phenomenon, we propose a novel model considering the mechanism of alliance to investigate the evolution of cooperation in the spatial multi-games, in which the intensity of alliance could be adjusted by a parameter μ. In detail, the focal individual will contribute the ratio μ of his own payoff as a cost of the alliance, and then expect to gain the equal portion of average benefits of the neighbors holding the same strategy, which means that the individual fitness can be tuned by the intensity of alliance. Through extensive numerical simulations, one could find that the mechanism of alliance can significantly promote the prosperity of cooperation. Moreover, the larger the value of μ, the stronger the intensity of alliance, which could lead to the higher the level of cooperation. In particular, the evolutionary dynamics presents a complex situation when the co-changes of the intensity of alliance μ and sucker's payoff δ are commonly considered. Furthermore, we also verify the robustness of the proposed mechanism by using the diversity of the intensity of alliance and different network topologies. The current results are conducive to comprehending the emergence and persistence of cooperation within the real-world population.     

Payoff-based accumulative effect promotes cooperation in spatial prisoner’s dilemma

We study the effect of accumulative payoff on the evolution of cooperation in the evolutionary prisoner’s dilemma on a square lattice. We introduce a decaying factor for the accumulative payoff, which characterizes the extent that the historical payoff is accumulated. It is shown that for fixed values of the temptation to defect, the density of cooperators increases with the value of the decaying factor. This indicates that the more the historical payoff is involved, the more favourable cooperators become. In the critical region where the cooperator density converges to zero, cooperators vanish according to a power-law-like behaviour. The associated exponents agree approximately with the two-dimensional directed percolation and depend weakly on the value of the decaying factor.     

Reputation-based strategy persistence promotes cooperation in spatial social dilemma

Understanding the emergence and maintenance of cooperation in social dilemma has received a lot of attention. In previous research, many scholars found that the reputation mechanism can promote cooperation, and the variation of reputation is consistent. However, in reality, according to both one's current action and past experiences, every individual's impression from others is modified to varying extent everyday. In other words, the length of duration of the same performance influences the diverse scale of their own reputation fluctuation. Therefore, a reputation-based strategy persistence mechanism, in which the increment of current reputation is determined by the persistence of last strategy, is proposed. Moreover, we introduce a parameter α to illustrate the impact of strategy persistence on reputation variation. The results of simulation show that the new mechanism paves the way for cooperation in evolutionary game, and the smaller α is, the better the mechanism performs.     

Evaluating fitness by integrating the highest payoff within the neighborhood promotes cooperation in social dilemmas

In this paper, we propose a modified fitness evaluation mechanism, which integrates the environmental factors into the focal player’s fitness calculation, to investigate the evolution of cooperative behaviors in the prisoner’s dilemma game. Here, the fitness of a player is computed by combining the individual raw payoff and the highest payoff within the neighborhood, which is regulated by a single parameter termed as trust level η$\eta$. We show, compared to the traditional version (η=0$\eta =0$), that the cooperation level can be highly enhanced for η>0$\eta >0$. Meanwhile, we illustrate the dynamical evolution of cooperators on the square lattice, and for different defection parameters b$b$ the _FC−K$F_C-K$ curves are utilized to investigate the impact of noise during the strategy updates. Likely, the role of pursuing the highest payoff within the neighborhood also favors the survival of cooperators in the spatial snowdrift game. In addition, the sensibility of knowing the external factors is often not identical for all individuals and we consider the distributed trust level in which η$\eta$ is a distributed parameter, and the results indicate that pursuing the highest payoff in the neighborhood is also inspiring as a consequence of its positive effect on cooperation. The current results are highly instructive for us to further understand the maintenance and emergence of cooperation under the framework of evolutionary game theory.     

Dynamic allocation of investments promotes cooperation in spatial public goods game

In this paper, we introduce a dynamic allocation investment mechanism into the spatial public goods game. In the model, if a cooperator i$i$ collects more payoffs from one group centered on the player j$j$ in the last round, he will put more investments to the group in the next round. The intensity of investment is controlled by a tunable parameter α$\alpha$. Simulation results show that the emergence of cooperation is remarkably promoted, and a larger α$\alpha$ induces a higher cooperation level. These interesting phenomena are then extensively explained by pairwise investments, average payoffs and evolution snapshots.     

Elimination mechanism promotes cooperation in coevolutionary prisoner’s dilemma games

We propose an elimination mechanism in the study of the evolutionary prisoner’s dilemma games on evolving networks. It assumes that after each round of playing, players whose payoffs are below a certain threshold will be eliminated from the game and the same number of new nodes will be added to the network to maintain the size of the network constant. Numerical results show that moderate values of elimination threshold can result in a maximum cooperation level in the evolutionary prisoner’s dilemma game. Moreover, the elimination mechanism can make the network structure evolve into a high heterogeneity in degree distribution, which is considered to be helpful in promoting cooperation in evolutionary games. The present study may provide new insight for understanding the evolution of cooperation in light of the law ‘survival of the fittest’ in nature.     

Role of memory effect in the evolution of cooperation based on spatial prisoner's dilemma game

We investigate the impact of memory effect on the evolution of cooperation in the spatial prisoner's dilemma game, in which each player will record his own strategies during the previous M game rounds (here, M is also named as the memory length). At each time step, each individual will update his current strategy according to the Fermi-like probability which will be multiplied by a pre-factor, and this factor will be correlated with the fraction of previous strategy states identical with the individual strategy to be updated. The numerical simulation results demonstrate that the memory length will largely influence the cooperation level at the stationary state, and it is clearly shown that the intermediate value of M will optimally favor the emergence of cooperation and the dynamical evolution, and characteristic patterns also support these conclusions. In addition, we depict the full cooperation phase diagrams and find that the cooperation region will be broadened under the case of moderate M values. The current results also indicate that the limited memory may be enough for us to design the effective promotion mechanism and further understand the emergency of cooperation taking place upon many networked populations.     

Adaptive co-evolution of strategies and network leading to optimal cooperation level in spatial prisoner’s dilemma game

We study evolutionary prisoner's dilemma game on adaptive networks where a population of players co-evolves with their interaction networks. During the co-evolution process, interacted players with opposite strategies either rewire the link between them with probability $p$ or update their strategies with probability $1-p$ depending on their payoffs. Numerical simulation shows that the final network is either split into some disconnected communities whose players share the same strategy within each community or forms a single connected network in which all nodes are in the same strategy. Interestingly, the density of cooperators in the final state can be maximised in an intermediate range of $p$ via the competition between time scale of the network dynamics and that of the node dynamics. Finally, the mean-field analysis helps to understand the results of numerical simulation. Our results may provide some insight into understanding the emergence of cooperation in the real situation where the individuals' behaviour and their relationship adaptively co-evolve.     

Evolution of cooperation in the spatial public goods game with the third-order reputation evaluation

In this letter, in order to deeply explore the role of individual reputation in the evolutionary game dynamics, we present a new third-order reputation evaluation model to discuss the evolution of cooperation in the spatial public goods game. In the current model, we should not only consider the strategy (cooperation, C or defection, D) of a focal player, but also take his own reputation and his opponent's reputation status into account. Among them, the individual reputation will be divided into being good and bad according to the specified threshold, and the good player will be endowed with the more influential strategy transfer ability, which further helps to create the clusters of cooperative and good players within the population and then fosters the cooperation. A large plethora of experimental simulation results indicate that four rules under the third-order reputation mechanism can lead to the promotion of cooperation when compared to the traditional public goods game model. The current work is conductive to a better understanding of the persistence and emergence of collective cooperation in real-world systems.     

社交网络中基于贝叶斯和半环代数模型的节点影响力计算机理

本文综合考虑网络结构及节点间的互动等关键因素, 提出了一种节点影响力分布式计算机理. 首先根据节点交互行为在时域上的自相似特性, 运用带折扣因子的贝叶斯模型计算节点间的直接影响力; 然后运用半环模型来分析节点间接影响力的聚合; 最后根据社交网络的小世界性质及传播门限, 综上计算出节点的综合影响力. 仿真结果表明, 本文给出的模型能有效抑制虚假粉丝导致的节点影响力波动, 消除了虚假粉丝的出现对节点影响力计算带来的干扰, 从中选择影响力高的若干节点作为传播源节点, 可以将信息传播到更多数目的节点, 促进了信息在社交网络中的传播. 关键词： 社交网络 影响力 贝叶斯 半环代数     

Formation of PAHs and soot platelets: multiconfiguration theoretical study of the key step in the ring closure–radical breeding polyyne‐based mechanism

Polyynes of general formula H? (C?C? )_nH are known to play a significant role in combustion and pyrolysis, possibly being intermediates in the formation of polycyclic aromatic hydrocarbons (PAHs) and soot. They have also been detected in astrophysical investigations. The key step in the polyyne‐based radical breeding mechanism for PAH growth is a cyclization, put forward by Krestinin, which implies disruption of electron couples, plausibly expected to be energy demanding. We explore the electronic features and energy requirements of such a process by quantum mechanical multiconfiguration methods (CASSCF and CASPT2). The features of the wavefunction are analyzed, and the free energy barriers are estimated over a wide range of temperatures, for three molecular models. The initial radical adduct A, generated by H ^. , HC?C ^. (ethynyl), or HC?C? C ^. H₂ ( propargyl ) addition to butadiyne (BD, HC?C? C?CH), undergoes a cyclization with the generation of two new radical centers. However, in most of the cases, one of these new singly occupied sp² orbitals has some overlap with the unpaired electron lobe already existent in A: some sort of bonding builds up and consequently the triradical character cannot be large. Only one model suggests a possible role of the radical breeding mechanism during combustion. Copyright © 2009 John Wiley & Sons, Ltd.