The evolution of cooperation in public good game with deposit

The emergence of cooperation still remains a fundamental conundrum in the social and behavior sciences. We introduce a new mechanism, deposit mechanism, into theoretical model to explore how this mechanism promotes cooperation in a well-mixed population. Firstly, we extend the common binary-strategy combination of cooperation and defection in public good game by adding a third strategy, namely, deposit cooperation. The players with deposit cooperation strategy pay a deposit in advance to obtain the benefits of public good at a lower contributions compared with the players with cooperation strategy, when the provision of public good is successful. Then, we explore the evolution of cooperation in the public good game with deposit by means of the replicator dynamics. Theoretical computations and stimulations show that the deposit mechanism can promote cooperation in a well-mixed population, and the numbers of equilibrium point are determined by variables of public good game. On the one hand, when the coexistence of cooperators and defectors is the stable equilibrium point in the evolutionary system, increasing the threshold of public good and adopting the weak altruism way for share benefits can enhance the level of cooperation in the population. On the other hand, if the coexistence of deposit cooperators and defectors is the stable equilibrium point, it is effective to promote the deposit cooperation by lowering the values of discount and deposit, and raising the threshold of public good.     

双复杂网络间的演化博弈

复杂网络的演化博弈是社会结构与稳定的重要模型. 基于单网络演化博弈模型, 提出了一种双复杂动态网络的演化博弈模型, 考虑双复杂网络在两个不同收益矩阵的囚徒困境博弈下增长, 当两个网络没有相互联系时, 发现增长网络中的空间互利性所导致的平均合作水平的突变, 推广了前人的结论. 在两个网络有相互联系时, 平均合作水平可以两者出现高度同步. 在网络的收益系数达到一定时, 才实现较高的合作水平. 增加网络内连接数量时, 自然选择不利于网络的合作, 而公平选择却有利于网络的合作, 说明了更新策略的影响. 当增加网络间连接数量时, 两个网络合作水平都下降. 当保持网络间和网络内的连接比例不变时, 网络的平均度越大, 平均合作水平越小. 本文发现了背叛领袖的存在, 并揭示了双网络模型下背叛领袖对平均合作水平的影响及其与合作领袖的互动机理, 这结果给出社会结构, 稳定和演化的重要信息和启示.     

Interaction stochasticity may hinder cooperation in the spatial public goods game

We propose an analytic model to explore the effect of interaction stochasticity on the evolution of cooperation in spatial public goods game. The results show that whether cooperation can dominate in populations crucially depends on the player's probability of opting-out. Stochastic opting-out enhances cooperation as long as the probability of opting-out is less than a threshold depending on the graph's degree. Otherwise the promoting effect of spatial structures on cooperation is hindered even neutralized by stochastic opting-out. Moreover, there exists an intermediate optimal probability with which the advantage of cooperation over defection is maximized in the evolutionary race. Interestingly, the optimal probability is related to the percolation threshold of the underlying graph. Our findings illustrate that spatial structures may not facilitate cooperation when stochastic opting-out is allowed, and provide a link between physics and social sciences.     

On fairness,full cooperation,and quantum game with incomplete information

Quantum entanglement has emerged as a new resource to enhance cooperation and remove dilemmas. This paper aims to explore conditions under which full cooperation is achievable even when the information of payoff is incomplete.Based on the quantum version of the extended classical cash in a hat game, we demonstrate that quantum entanglement may be used for achieving full cooperation or avoiding moral hazards with the reasonable profit distribution policies even when the profit is uncertain to a certain degree. This research further suggests that the fairness of profit distribution should play an important role in promoting full cooperation. It is hopeful that quantum entanglement and fairness will promote full cooperation among distant people from various interest groups when quantum networks and quantum entanglement are accessible to the public.     

Impacts of memory on a regular lattice for different population sizes with asynchronous update in spatial snowdrift game

Memory is an important factor on the evolution of cooperation in spatial structure. For evolutionary biologists, the problem is often how cooperation acts can emerge in an evolving system. In the case of snowdrift game, it is found that memory can boost cooperation level for large cost-to-benefit ratio r, while inhibit cooperation for small r. Thus, how to enlarge the range of r for the purpose of enhancing cooperation becomes a hot issue recently. This paper addresses a new memory-based approach and its core lies in: Each agent applies the given rule to compare its own historical payoffs in a certain memory size, and take the obtained maximal one as virtual payoff. In order to get the optimal strategy, each agent randomly selects one of its neighbours to compare their virtual payoffs, which can lead to the optimal strategy. Both constant-size memory and size-varying memory are investigated by means of a scenario of asynchronous updating algorithm on regular lattices with different sizes. Simulation results show that this approach effectively enhances cooperation level in spatial structure and makes the high cooperation level simultaneously emerge for both small and large r. Moreover, it is discovered that population sizes have a significant influence on the effects of cooperation.     

To cooperate or to defect? Altruism and reputation

The basic difficulty in cooperation theory is to justify the cooperation. Here we propose a new approach, where players are driven by their altruism to cooperate or not. The probability of cooperation depends also on the co-player’s reputation. We find that players with positive altruism cooperate and meet cooperation. In this approach, payoffs are not relevant.     

Cooperation and charity in spatial public goods game under different strategy update rules

Human cooperation can be influenced by other human behaviors and recent years have witnessed the flourishing of studying the coevolution of cooperation and punishment, yet the common behavior of charity is seldom considered in game-theoretical models. In this article, we investigate the coevolution of altruistic cooperation and egalitarian charity in spatial public goods game, by considering charity as the behavior of reducing inter-individual payoff differences. Our model is that, in each generation of the evolution, individuals play games first and accumulate payoff benefits, and then each egalitarian makes a charity donation by payoff transfer in its neighborhood. To study the individual-level evolutionary dynamics, we adopt different strategy update rules and investigate their effects on charity and cooperation. These rules can be classified into two global rules: random selection rule in which individuals randomly update strategies, and threshold selection rule where only those with payoffs below a threshold update strategies. Simulation results show that random selection enhances the cooperation level, while threshold selection lowers the threshold of the multiplication factor to maintain cooperation. When charity is considered, it is incapable in promoting cooperation under random selection, whereas it promotes cooperation under threshold selection. Interestingly, the evolution of charity strongly depends on the dispersion of payoff acquisitions of the population, which agrees with previous results. Our work may shed light on understanding human egalitarianism.     

Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism

We introduce a stochastic win-stay-lose-shift (WSLS) mechanism into evolutionary Prisoner’s Dilemma on small-world networks. At each time step, after playing with all its immediate neighbors, each individual gets a score to evaluate its performance in the game. The score is a linear combination of an individual’s total payoff (i.e., individual gain from the group) and local contribution to its neighbors (i.e., individual donation to the group). If one’s actual score is not larger than its desired score aspiration, it switches current strategy to the opposite one with the probability depending on the difference between the two scores. Under this stochastic WSLS regime, we assume that each focal individual gains its fixed score aspiration under the condition of full cooperation in its neighborhood, and find that cooperation is significantly enhanced under some certain parameters of the model by studying the evolution of cooperation. We also explore the influences of different values of learning rate and intensity of deterministic switch on the evolution of cooperation. Simulation results show that cooperation level monotonically increases with the relative weight of the local contribution to the score. For much low intensity of deterministic switch, cooperation is to a large extent independent of learning rate, and full cooperation can be reached when relative weight is not less than 0.5. Otherwise, cooperation level is affected by the value of learning rate. Besides, we find that the cooperation level is not sensitive to the topological parameters. To explain these simulation results, we provide corresponding analytical results based on mean-field approximation, and find out that simulation results are in close agreement with the analytical ones. Our work may be helpful in understanding the cooperative behavior in social systems based on this stochastic WSLS mechanism.     

Evolution of Cooperation in Evolutionary Games for Heterogeneous Interactions

When a population structure is modelled as a square lattice,the cooperation may be improved for an evolutionary prisoner dilemma game or be inhibited for an evolutionary snowdrift game.In this work,we investigate cooperation in a population on a square lattice where the interaction among players contains both prisoner dilemma game and snowdrift game.The heterogeneity in interaction is introduced to the population in two different ways:the heterogenous character of interaction assigned to every player(HCP) or the heterogenous character of interaction assigned to every link between any two players(HCL).The resonant enhancement of cooperation in the case of HCP is observed while the resonant inhibition of cooperation in the case of HCL is prominent.The explanations on the enhancement or inhibition of cooperation are presented for these two cases.     

Effect of habitat destruction on cooperation in public goods games

We explore the evolution of cooperation in a public goods game where the habitat destruction is taken into account. A model of ordinary differential equations is proposed, in which incorporate the habitat destroyed. And we focus on the impact of different levels of habitat destruction on cooperation. Our results show that the fraction of cooperation receives the biggest boost for moderate habitat destruction, and decreases to zero very quickly for a higher degree of habitat destruction. Similarly, our results suggest that low or moderate habitat degradation can promote the evolution of cooperators, and once habitat degradation is too severe, the fraction of cooperators will decline dramatically. Furthermore, we investigate the cooperation level with different multiplication factor, and results demonstrate that the cooperation increases monotonously with the increasing of the multiplication factor. Our findings may provide many more insights for understanding the emergence and maintenance of cooperation in the complex biological and social systems.     

Influence of the variance of degree distributions on the evolution of cooperation in complex networks

We study how initial network structure affects the evolution of cooperation in a spatial prisoner’s dilemma game. The network structure is characterized by various statistical properties. Among those properties, we focus on the variance of the degree distribution, and inquire how it affects the evolution of cooperation by three methods of imitation. For every method, it was found that a scale-free network does not always promote the evolution of cooperation, and that there exists an appropriate value of the variance, at which cooperation is optimal.     

Dynamic Evolution with Limited Learning Information on a Small-World Network

This paper investigates the dynamic evolution with limited learninginformation on a small-world network. In the system, the information amongthe interaction players is not very lucid, and the players are not allowedto inspect the profit collected by its neighbors, thus the focal playercannot choose randomly a neighbor or the wealthiest one and compare itspayoff to copy its strategy. It is assumed that the information acquaintedby the player declines in the form of the exponential with the geographicaldistance between the players, and a parameter V is introduced to denote theinspect-ability about the players. It is found that under the hospitableconditions, cooperation increases with the randomness and is inhibited bythe large connectivity for the prisoner's dilemma; however, cooperation ismaximal at the moderate rewiring probability and is chaos with theconnectivity for the snowdrift game. For the two games, the acuminous sightis in favor of the cooperation under the hospitable conditions; whereas, themyopic eyes are advantageous to cooperation and cooperation increases withthe randomness under the hostile condition.     

Evolution of global cooperation and ethnocentrism in group-structured populations

Global cooperation becomes more and more important in times of increased environmental awareness. However, exploiting out-group members allows ethnocentrism to be advantageous over global cooperation. The debate on which strategy, global cooperation or ethnocentrism, is more likely to persist with the increasing trend of globalization, is ongoing from the evolutionary perspective. To shed some light on this issue, we explore the influences of global migration and leadership on the emergence of global cooperation and ethnocentrism. It is found that global migration can enhance ethnocentrism while has little effect on global cooperation. Interestingly, the enforcement of leadership, under which leaders punish defectors, can facilitate global cooperation such that it accounts for a higher fraction than ethnocentrism in equilibrium state.     

Way of Breaking Links in the Evolution of Cooperation

We investigate how the way of breaking links and establishing links impacts cooperation by comparing four coevolutionary rules. In the rules, a player chooses to break an existing link according to his environment, and the establishment of a new link depends on the environment of the potential neighbor. It is found that the way of breaking links plays a key role in promoting cooperation. The way of establishing links has a negligible effect on cooperation, but determines the population structure. Our results may provide some insights into understanding the evolution of cooperation.     

Effect of Growing Size of Interaction Neighbors on the Evolution of Cooperation in Spatial Snowdrift Game

In this paper,we study the influence of the size of interaction neighbors(k) on the evolution of cooperation in the spatial snowdrift game.At first,we consider the effects of noise K and cost-to-benefit ratio r,the simulation results indicate that the evolution of cooperation depends on the combined action of noise and cost-to-benefit ratio.For a lower r,the cooperators are multitudinous and the cooperation frequency ultimately increases to 1 as the increase of noise.However,for a higher r,the defectors account for the majority of the game and dominate the game if the noise is large enough.Then we mainly investigate how k influences the evolution of cooperation by varying the noise in detail.We find that the frequency of cooperators is closely related to the size of neighborhood and cost-to-benefit ratio r.In the case of lower r,the augmentation of k plays no positive role in promoting the cooperation as compared with that of k = 4,while for higher r the cooperation is improved for a growing size of neighborhood.At last,based on the above discussions,we explore the cluster-forming mechanism among the cooperators.The current results are beneficial to further understand the evolution of cooperation in many natural,social and biological systems.     

Nuclear exoticism

Extreme states of nuclearmatter (such that feature high spins, large deformations, high density and temperature, or a large excess of neutrons and protons) play an important role in studying fundamental properties of nuclei and are helpful in solving the problem of constructing the equation of state for nuclear matter. The synthesis of neutron-rich nuclei near the nucleon drip lines and investigation of their properties permit drawing conclusions about the positions of these boundaries and deducing information about unusual states of such nuclei and about their decays. At the present time, experimental investigations along these lines can only be performed via the cooperation of leading research centers that possess powerful heavy-ion accelerators, such as the Large Hadron Collider (LHC) at CERN and the heavy-ion cyclotrons at the Joint Institute for Nuclear Research (JINR, Dubna), where respective experiments are being conducted by physicists from about 20 JINR member countries. The present article gives a survey of the most recent results in the realms of super neutron-rich nuclei. Implications of the change in the structure of such nuclei near the nucleon drip lines are discussed. Information about the results obtained by measuring the masses (binding energies) of exotic nuclei, the nucleon-distribution radii (neutron halo) and momentum distributions in them, and their deformations and quantum properties is presented. It is shown that the properties of nuclei lying near the stability boundaries differ strongly from the properties of other nuclei. The problem of the stability of nuclei that is associated with the magic numbers of 20 and 28 is discussed along with the effect of new magic numbers.     

基于遗传算法的重复囚徒困境博弈策略在复杂网络中的演化

利用遗传算法研究重复囚徒困境博弈策略在复杂网络中的演化.研究结果表明：处于复杂网络中有记忆的个体通过基因的复制、重组、变异和选择能够进化出一种自组织的合作机制.这种合作机制既能够在群体中激发合作行为的产生，加强和维护持续的合作行为，同时又能对背叛的个体进行惩罚和报复，因此能够促使复杂网络中进化出具有很高合作率的群体. 关键词： 复杂网络 遗传算法 进化博弈 合作     

The effects of resource limitation and consensual incentives on cooperation

Exploring the evolution of cooperation has been one of the most challenging topics and attracted increasing attention in various realms. Hereby, we institute an analytic model where the relationship between the common benefits and contributions is the typical saturation nonlinearity. We investigate the evolutionary dynamics of cooperation with and without consensual incentives respectively. The population always evolves to full defection when the incentives are absent. Cooperation, however, can be promoted by consensual incentives when the degree of cooperators' preferences for incentives is great. There exists an intermediate amount of resources at which the positive effect of consensual incentives on cooperation is minimized. Furthermore, there is a U-shape relationship between the degree of cooperators' preference for an incentive and the evolution of cooperation. A greater basin of full cooperation can be induced when the cooperators' preference for reward is more pronounced than that for punishment.     

Cautious strategy update promotes cooperation in spatial prisoner’s dilemma game

In the realistic world, individual cautiousness can be often involved or observed when a rational individual makes a decision. However, it remains unclear how such individual cautiousness influences the evolution of cooperative behavior. To this end, we consider a Fermi strategy updating rule, where each individual is assigned a cautiousness index that controls its learning activity, and then study the evolution of cooperation in the spatial prisoner’s dilemma game. Interestingly, it is found that cooperation can be significantly promoted when individuals’ cautiousness is considered. In particular, there exists an optimal range of the degree of cautiousness resulting in the highest cooperation level. The remarkable promotion of cooperation, as well as the emerging phase transition is explained by configurational analysis. The sensitivity of cooperation to initial states with different fractions of cooperators is also discussed. The result illustrates that high densities of cooperators can be established at small initial fractions of cooperators. The detailed mechanism for such phenomenon is explained by analyzing the typical initial configurations.     

The Polarization of the Coupling Strength of Interdependent Networks Stimulates Cooperation

We introduce a mixed network coupling mechanism and study its effects on how cooperation evolves in interdependent networks. This mechanism allows some players (conservative-driven) to establish a fixed-strength coupling, while other players (radical-driven) adjust their coupling strength through the evolution of strategy. By means of numerical simulation, a hump-like relationship between the level of cooperation and conservative participant density is revealed. Interestingly, interspecies interactions stimulate polarization of the coupling strength of radical-driven players, promoting cooperation between two types of players. We thus demonstrate that a simple mixed network coupling mechanism substantially expands the scope of cooperation among structured populations.