Universal scaling for the dilemma strength in evolutionary games

Why would natural selection favor the prevalence of cooperation within the groups of selfish individuals? A fruitful framework to address this question is evolutionary game theory, the essence of which is captured in the so-called social dilemmas. Such dilemmas have sparked the development of a variety of mathematical approaches to assess the conditions under which cooperation evolves. Furthermore, borrowing from statistical physics and network science, the research of the evolutionary game dynamics has been enriched with phenomena such as pattern formation, equilibrium selection, and self-organization. Numerous advances in understanding the evolution of cooperative behavior over the last few decades have recently been distilled into five reciprocity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity. However, when social viscosity is introduced into a population via any of the reciprocity mechanisms, the existing scaling parameters for the dilemma strength do not yield a unique answer as to how the evolutionary dynamics should unfold. Motivated by this problem, we review the developments that led to the present state of affairs, highlight the accompanying pitfalls, and propose new universal scaling parameters for the dilemma strength. We prove universality by showing that the conditions for an ESS and the expressions for the internal equilibriums in an infinite, well-mixed population subjected to any of the five reciprocity mechanisms depend only on the new scaling parameters. A similar result is shown to hold for the fixation probability of the different strategies in a finite, well-mixed population. Furthermore, by means of numerical simulations, the same scaling parameters are shown to be effective even if the evolution of cooperation is considered on the spatial networks (with the exception of highly heterogeneous setups). We close the discussion by suggesting promising directions for future research including (i) how to handle the dilemma strength in the context of co-evolution and (ii) where to seek opportunities for applying the game theoretical approach with meaningful impact.     

Emergence of cooperation in spatial public goods game with conditional participation

Conditional interactions are common in both human and animal societies. To understand the impacts of this feature on the evolution of cooperation, we propose a modified public goods game combined with conditional interactions in terms of the aspiration payoffs. Through simulations, we find that the function of the fraction of cooperators and the synergy factor is non-monotonic. This indicates that a large synergy factor is not always in favor of the promotion of cooperation. In addition, for a high aspiration, the typical coexistence state of cooperators and defectors could disappear, and the system demonstrates a sharp transition from the complete defection state to the complete cooperation state as the synergy factor increases. Furthermore, an interesting critical phenomenon is found in a finite system, i.e., the system can randomly evolve into a complete defection state or a complete cooperation state. An explanation of these evolutionary outcomes is provided in this paper, which is in agreement with the simulation results.     

Integrating neighborhoods in the evaluation of fitness promotes cooperation in the spatial prisoner’s dilemma game

A fundamental question of human society is the evolution of cooperation. Many previous studies explored this question via setting spatial background, where players obtain their payoffs by playing game with their nearest neighbors. Another undoubted fact is that the environment plays an important role in the individual development. Inspired by these phenomena, we reconsider the definition of individual fitness which integrates the environment, denoted by the average payoff of all individual neighbors, with the traditional individual payoffs by introducing a selection parameter u. Tuning u equal to zero returns the traditional version, while increasing u bears the influence of environment. We find that considering the environment, i.e., integrating neighborhoods in the evaluation of fitness, promotes cooperation. If we enhance the value of u, the invasion of defection could be resisted better. We also provide quantitative explanations and complete phase diagrams presenting the influence of the environment on the evolution of cooperation. Finally, the universality of this mechanism is testified for different neighborhood sizes, different topology structures and different game models. Our work may shed light on the emergence and persistence of cooperation in our life.     

Evolution of cooperation among mobile agents

We study the effects of mobility on the evolution of cooperation among mobile players, which imitate collective motion of biological flocks and interact with neighbors within a prescribed radius R. Adopting the the prisoner’s dilemma game and the snowdrift game as metaphors, we find that cooperation can be maintained and even enhanced for low velocities and small payoff parameters, when compared with the case that all agents do not move. But such enhancement of cooperation is largely determined by the value of R, and for modest values of R, there is an optimal value of velocity to induce the maximum cooperation level. Besides, we find that intermediate values of R or initial population densities are most favorable for cooperation, when the velocity is fixed. Depending on the payoff parameters, the system can reach an absorbing state of cooperation when the snowdrift game is played. Our findings may help understanding the relations between individual mobility and cooperative behavior in social systems.     

叶黄素聚集体吸收光谱的实验分析与理论模拟

分子聚集体表现出单分子所不具备的特有功能,利用吸收光谱对聚集体分子结构特性的研究是理解其电子和能量转移功能的基础。实验中利用紫外-可见分光光度计,检测了叶黄素在乙醇溶液中的单体吸收谱和在1∶1乙醇水溶液中的聚集体吸收谱。并通过对叶黄素单体吸收谱的高斯分解,获得了激发态的振动能级结构参数。理论上采用时间相关函数描述的吸收谱线和Frenkel激子模型,通过模拟单分子吸收光谱,获得了叶黄素分子的激发能、特征模振动频率、Huang-Phys因子等参数。再利用这些参数进行了聚集体分子光谱的模拟,分析了叶黄素聚集体的分子结构影响光谱变化的原因。结果表明,(1) 分子间的相互作用是决定吸收光谱峰位移动的主要原因,实验中叶黄素H-聚集体的吸收光谱较单体蓝移了77 nm,模拟显示相互作用在2 000 cm-1附近;(2) 聚集体分子个数越多,聚集协作效应越大,吸收光谱半高宽变小,同时吸收峰进一步蓝移;(3) 环境的无序度对吸收光谱的半高宽也存在较大的影响,无序度越大,吸收光谱半高宽越大。实验结果为进一步研究聚集体在生物系统和材料系统中的功能提供了理论依据。     

Motif structure and cooperation in real-world complex networks

Networks of dynamical nodes serve as generic models for real-world systems in many branches of science ranging from mathematics to physics, technology, sociology and biology. Collective behavior of agents interacting over complex networks is important in many applications. The cooperation between selfish individuals is one of the most interesting collective phenomena. In this paper we address the interplay between the motifs’ cooperation properties and their abundance in a number of real-world networks including yeast protein-protein interaction, human brain, protein structure, email communication, dolphins’ social interaction, Zachary karate club and Net-science coauthorship networks. First, the amount of cooperativity for all possible undirected subgraphs with three to six nodes is calculated. To this end, the evolutionary dynamics of the Prisoner’s Dilemma game is considered and the cooperativity of each subgraph is calculated as the percentage of cooperating agents at the end of the simulation time. Then, the three- to six-node motifs are extracted for each network. The significance of the abundance of a motif, represented by a Z-value, is obtained by comparing them with some properly randomized versions of the original network. We found that there is always a group of motifs showing a significant inverse correlation between their cooperativity amount and Z-value, i.e. the more the Z-value the less the amount of cooperativity. This suggests that networks composed of well-structured units do not have good cooperativity properties.     

Permanence of a discrete nonlinear N-species cooperation system with time delays and feedback controls

A discrete nonlinear N-species cooperation system with time delays and feedback controls is considered in this paper. Sufficient conditions which ensure the permanence of the system are obtained. It is shown that these conditions are weaker than those of Chen [F.D. Chen, Permanence of a discrete N-species cooperation system with time delays and feedback controls, Appl. Math. Comput. 186(2007) 23-29], that is, our investigation shows that the additional condition in Chen’s paper is not necessary.     

改进的粒子群算法在虚拟企业合作伙伴选择中的应用

根据虚拟企业合作伙伴选择的原则,给出了合作伙伴选择的多目标决策模型,用定量的方法对合作伙伴进行描述.同时,给出了改进的二进制粒子群优化算法,并对本文的多目标优化问题进行求解.通过仿真试验测试,证明该方法是可行性.     

Diversity of contribution promotes cooperation in public goods games

In most previous studies of public goods game, individuals conventionally donate their contributions equally to the games they participate in. We develop an extended public goods game model, in which individuals distribute their contributions based on the groups’ qualities. Namely, the individuals are allowed to increase their investment to the superior groups at the expense of the nasty ones. The quality of a group is positively correlated with its cooperation level. In numerical simulations, synchronized stochastic strategy updating rule based on pairwise comparison for a fixed noise level is adopted. The results show that the high-quality group preference mechanism can greatly improve cooperation, compared with conventional models. Besides, the system with stronger preference toward high-quality groups performs better. Investigation of wealth distribution at equilibrium reveals that cooperators’ wealth appreciates with the increase of preference degree when cooperators take up the same fraction of the population.