A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game

In this study,we propose a spatial prisoner＇s dilemma game model with a 2-stage strategy updating rule,and focus on the cooperation behavior of the system.In the first stage,i.e.,the pre-learning stage,a focal player decides whether to update his strategy according to the pre-learning factor β and the payoff difference between himself and the average of his neighbors.If the player makes up his mind to update,he enters into the second stage,i.e.,the learning stage,and adopts a strategy of a randomly selected neighbor according to the standard Fermi updating rule.The simulation results show that the cooperation level has a non-trivial dependence on the pre-learning factor.Generally,the cooperation frequency decreases as the pre-learning factor increases;but a high cooperation level can be obtained in the intermediate region of- 3〈 β 〈-1.We then give some explanations via studying the co-action of pre-learning and learning.Our results may sharpen the understanding of the influence of the strategy updating rule on evolutionary games.

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.

Effects of Dimers on Cooperation in the Spatial Prisoner's Dilemma Game

We investigate the evolutionary prisoner’s dilemma game in structured populations by introducing dimers,which are defined as that two players in each dimer always hold a same strategy.We find that influences of dimerson cooperation depend on the type of dimers and the population structure.For those dimers in which players interactwith each other,the cooperation level increases with the number of dimers though the cooperation improvement leveldepends on the type of network structures.On the other hand,the dimers,in which there are not mutual interactions,will not do any good to the cooperation level in a single community,but interestingly,will improve the cooperationlevel in a population with two communities.We explore the relationship between dimers and self-interactions and findthat the effects of dimers are similar to that of self-interactions.Also,we find that the dimers,which are establishedover two communities in a multi-community network,act as one type of interaction through which information betweencommunities is communicated by the requirement that two players in a dimer hold a same strategy.

Effects of Topological Randomness on Cooperation in a Deterministic Prisoner's Dilemma Game

In this work, we consider an evolutionary prisoner's dilemma game on a homogeneous random network with the richest-following strategy adoption rule. By constructing homogeneous random networks from a regular ring graph, we investigate the effects of topological randomness on cooperation. In contrast to the ordinary view that the presence of small amount of shortcuts in ring graphs favors cooperation, we find the cooperation inhibition by weak topological randomness. The explanations on the observations are

Adaptive interaction driven by the learning effect in the spatial prisoner's dilemma

We propose a computing model in which individuals can automatically adjust their interaction intensity with their mentor according to the learning effect.This model is designed to investigate the cooperative dynamics of the spatial prisoner's dilemma.More specifically,when the cumulative payoff of a learner is more than his reference earning,he will strengthen his interaction with his mentor;otherwise,he will reduce it.The experimental results indicate that this mechanism can improve the emergence of cooperation in a networked population and that the driving coefficient of interaction intensity plays an important role in promoting cooperation.Interestingly,under a certain social dilemma condition,there exists a minimal driving coefficient that leads to optimal cooperation.This occurs due to a positive feedback effect between the individual's satisfaction frequency and the number of effective neighbors.Moreover,we find that the experimental results are in accord with theoretical predictions obtained from an extension of the classical pair-approximation method.Our conclusions obtained by considering relationships with mentors can provide a new perspective for future investigations into the dynamics of evolutionary games within structured populations.

THE OPTIMAL CONTROL FOR PROMOTING THE COOPERATION IN EVOLUTION GAME GENERATED BY PRISONER'S DILEMMA

Natural selection opposes the evolution of cooperation unless specific mechanisms are at work in Prisoner＇s Dilemma. By taking advantage of the modern control theory, the controller design is discussed and the optimal control is designed for promoting cooperation based on the recent advances in mechanisms for the evolution of cooperation. Two con- trol strategies are proposed： compensation control strategy for the cooperator when playing against a defector and reward control strategy for cooperator when playing against a coop- erator. The feasibility and effectiveness of these control strategies for promoting cooperation in different stages are analyzed. The reward for cooperation can＇t prevent defection from being evolutionary stable strategy （ESS）. On the other hand, compensation for the coopera- tor can＇t prevent defection from emerging and sustaining. By considering the effect and the cost, an optimal control scheme with constraint on the admissible control set is put forward. By analyzing the special nonlinear system of replicator dynamics, the exact analytic solution of the optimal control scheme is obtained based on the maximum principle. Finally, the effectiveness of the proposed method is illustrated by examples.

Evolution of Cooperation in Continuous Prisoner's Dilemma Games on Barabasi-Albert Networks with Degree-Dependent Guilt Mechanism

This paper studies the continuous prisoner's dilemma games (CPDG) on Barabasi-Albert (BA) networks.In the model,each agent on a vertex of the networks makes an investment and interacts with all of his neighboring agents.Making an investment is costly,but which benefits its neighboring agents,where benefit and cost depend on the level of investment made.The payoff of each agent is given by the sum of payoffs it receives in its interactions with all its neighbors.Not only payoff,individual's guilty emotion in the games has also been considered.The negative guilty emotion produced in comparing with its neighbors can reduce the utility of individuals directly.We assume that the reduction amount depends on the individual's degree and a baseline level parameter.The group's cooperative level is characterized by the average investment of the population.Each player makes his investment in the next step based on a convex combination of the investment of his best neighbors in the last step,his best history strategies in the latest steps which number is controlled by a memory length parameter,and a uniformly distributed random number.Simulation results show that this degree-dependent guilt mechanism can promote the evolution of cooperation dramatically comparing with degree-independent guilt or no guilt cases.Imitation,memory,uncertainty coefficients and network structure also play determinant roles in the cooperation level of the population.All our results may shed some new light on studying the evolution of cooperation based on network reciprocity mechanisms.

Effects of Inertia on Evolutionary Prisoner's Dilemma Game

Considering the inertia of individuals in real life,we propose a modified Fermi updating rule,where the inertia of players is introduced into evolutionary prisoner's dilemma game(PDG) on square lattices.We mainly focus on how the inertia affects the cooperative behavior of the system.Interestingly,we find that the cooperation level has a nonmonotonic dependence on the inertia:with small inertia,cooperators will soon be invaded by defectors;with large inertia,players are unwilling to change their strategies and the cooperation level remains the same as the initial state;while a moderate inertia can induce the highest cooperation level.Moreover,effects of environmental noise and individual inertia are studied.Our work may be helpful in understanding the emergence and persistence of cooperation in nature and society.

An Improved Fitness Evaluation Mechanism with Memory in Spatial Prisoner's Dilemma Game on Regular Lattices

To deeply understand the emergence of cooperation in natural,social and economical systems,we present an improved fitness evaluation mechanism with memory in spatial prisoner's dilemma game on regular lattices.In our model,the individual fitness is not only determined by the payoff in the current game round,but also by the payoffs in previous round bins.A tunable parameter,termed as the memory strength(μ),which lies between 0 and 1,is introduced into the model to regulate the ratio of payoffs of current and previous game rounds in the individual fitness calculation.When μ = 0,our model is reduced to the standard prisoner's dilemma game;while μ = 1 represents the case in which the payoff is totally determined by the initial strategies and thus it is far from the realistic ones.Extensive numerical simulations indicate that the memory effect can substantially promote the evolution of cooperation.For μ < 1,the stronger the memory effect,the higher the cooperation level,but μ = 1 leads to a pathological state of cooperation,but can partially enhance the cooperation in the very large temptation parameter.The current results are of great significance for us to account for the role of memory effect during the evolution of cooperation among selfish players.

Inference of interactions between players based on asynchronously updated evolutionary game data

The interactions between players of the prisoner's dilemma game are inferred using observed game data.All participants play the game with their counterparts and gain corresponding rewards during each round of the game.The strategies of each player are updated asynchronously during the game.Two inference methods of the interactions between players are derived with naive mean-field(n MF)approximation and maximum log-likelihood estimation(MLE),respectively.Two methods are tested numerically also for fully connected asymmetric Sherrington-Kirkpatrick models,varying the data length,asymmetric degree,payoff,and system noise(coupling strength).We find that the mean square error of reconstruction for the MLE method is inversely proportional to the data length and typically half(benefit from the extra information of update times)of that by n MF.Both methods are robust to the asymmetric degree but work better for large payoffs.Compared with MLE,n MF is more sensitive to the strength of couplings and prefers weak couplings.

Benefit community promotes evolution of cooperation in prisoners’ dilemma game

Exploring the emergence and maintenance of cooperation in social dilemma is valuable and it arises considerable concerns of many researchers. In this paper, we propose a mechanism to promote cooperation, called benefit community,in which cooperators linking together form a common benefit community and all their payoffs obtained from game are divided coequally. The robustness of conclusions is tested for the PDG(prisoners' dilemma game) on square lattice and WS small world network. We find that cooperation can be promoted by this typical mechanism, especially, it can diffuse and prevail more easily and rapidly on the WS small world network than it on the square lattice, even if a big temptation to defect b. Our research provides a feasible direction to resolve the social dilemma.

PREFERENCE AND EVOLUTION IN THE ITERATED PRISONER'S DILEMMA

Game theory is extensively used to study strategy-making and actions of play- ers. The authors proposed an analysis method for study the evolutionary outcome and behaviors of players with preference in iterated prisoner＇s dilemma. In this article, a preference parameter k was introduced in the payoff matrix, wherein the value of k denotes the player＇s degree of egoism and altruism （preference）. Then, a game-theoretic dynamical model was formulated using Birth-and-Death process. The authors studied how preference influences the evolutionary equilibrium and behaviors of players. The authors get the general results： egoism leads to defection, and altruism can make players build trust and maintain cooperation, and so, the hope of the Pareto optimal solution. In the end, the simulation experiments proved the efficiency of the method.

Conditions Where the Ruled Class Unites for the Revolution:Applicability of a Game Theory on Social Dilemmas

Revolutions,typical cases of crucial social transformations,cannot be realized successfully without a large number of activists.Therefore,creating conditions favorable for acquiring enough participants should be an important topic of Marxist social science.In particular,this problem includes the “free-ride,” because the benefits of revolutionaries’ activities are gained not only by the activists but also by all other members.The paper analyzes problems such as this one,applying non-cooperative game theory to social dilemma problems.This leads to some interesting results.In this research,the problem of the workers’ choice between unity or freeride is first defined using numerical examples of the gain structure.It is defined again in a more generalized form using other parameters.In so doing,we express both the cost of participating in the movement and the gains from the concession of the ruling class.Because this analysis focuses on the importance of the number of participants,the concession of the ruling class is framed as a function of the number of participants.The results of this analysis revealed that the economic base and superstructure accurately correspond in some game structures but not in others.In other words,the social dilemma presents either as a case of prisoners’ dilemma or as a chicken game.Furthermore,this paper analyzes the influence of group size,and it was revealed that groups with a large number of members,such as a ruled class,find it particularly difficult to unite.This phenomenon is called the “large group dilemma.” In these ways,this research shows that the aforementioned type of game theory can be used to analyze the difficulties and possibilities of social movements.

Cooperation influenced by the correlation degree of two-layered complex networks in evolutionary prisoner’s dilemma games

An evolutionary prisoner＇s dilemma game is investigated on two-layered complex networks respectively representing interaction and learning networks in one and two dimensions. A parameter q is introduced to denote the correlation degree between the two-layered networks. Using Monte Carlo simulations we studied the effects of the correlation degree on cooperative behaviour and found that the cooperator density nontrivially changes with q for different payoff parameter values depending on the detailed strategy updating and network dimension. An explanation for the obtained results is provided.

Effect of Strategy-Homogeneity on the Prisoner’s Dilemma Game in a Square Lattice

We investigate the effect of strategy-homogeneity on the prisoner’s dilemma game in a square lattice. Strategy-homogeneity means that the population contains at least one connected group in which individuals maintain the same strategy at each iteration and may update according to updating rule at next iteration. The simulation results show that the introduction of strategy-homogeneity increases the cooperation in the evolutionary stable state. For any value of temptation to defect, the density of cooperators in equilibrium state increases firstly and then decreases as the level of strategy-homogeneity increases constantly, and there exists an appropriate level of strategy-homogeneity, maximizing the density of cooperators. The results may be favorable for comprehending cooperative behaviors in societies composed of connected groups with coherent strategy.

考虑配送交通风险的新零售平台、骑手及消费者三方演化博弈分析

新零售行业中配送骑手的交通事故比率不断攀升引起了社会的广泛关注。骑手出于对配送超时和消费者投诉的担心,在配送途中选择超速违章,从而增加交通风险。为避免消费者对配送超时进行投诉,越来越多的平台企业主动建立超时补偿机制,即对配送超时为消费者提供补偿。该补偿机制能否有效减少消费者投诉,进而影响骑手的配送行为,降低其配送中的交通风险,是值得研究的重要问题。构建由新零售平台、骑手及消费者组成的三方演化博弈模型,其中,平台决定是否建立针对消费者的超时补偿机制,骑手在不同风险程度的配送行为之间进行选择,而消费者则决定在超时情况下是否进行投诉。研究发现:平台对于骑手超时的直接惩罚额度是影响骑手的策略中最关键的影响因素。当直接惩罚额度较大时,平台、消费者的任何策略选择都无法改变骑手普遍向高风险配送策略演化的“骑手困境”情况;当直接惩罚额度适中,建立超时补偿机制给平台企业带来的直接效用较大,且平台与消费者普遍对骑手更具有同理心时,三方演化策略均衡可以达到理想状态:平台建立主动补偿机制、骑手低风险配送、消费者对于订单超时选择不投诉。

博弈论视域下体教融合的现实困境、选择逻辑及实施路径

体教融合是促进青少年健康发展的重要途径和历史选择。运用文献资料等方法,梳理出体教融合发展中体育系统和教育系统所处的现实困境,从博弈论的视角分析体教融合合作中“体教双方”的选择逻辑,找到造成体教融合困境的原因,提出解决问题的方法及路径。从博弈论的视域分析,长期以来“体教”融合发展的困境一直未能解决,其成因囿于体育系统和教育系统的利益诉求差异而形成的“非合作博弈(纳什均衡)”。要突破这种困境,需要体教双方从非合作博弈转入合作博弈,从而达到“帕累托最优”解。体教融合的实施路径主要包括:统一思想、调整目标,达成体教融合的最优策略共识;加强顶层设计,形成具有约束力的体教融合合作协议;建构科学的合作利益分配方式,形成体教融合激励相容机制。

大学学科治理中的权力运行:现实困境与机制超越

权力运行是大学学科治理的核心议题,其中,行政权力与学术权力相互混淆、渗透问题被长期关切,然而治理效果有限。以博弈论为基础构建以“局中人-策略-利益”为核心要素的分析框架,尝试新思路求解老问题。研究发现,权力双方通过收益和成本的评估差值而作出自利最大化策略,欠缺对大学学科治理整体利益考量,因而导致利益争夺的局中人困境、决策变更的策略困境、格局失衡的利益困境。为更好突破困境,引导权力良序运行,需要构建基于利益共同体的共生机制破解局中人困境,构建基于小数据矩阵的理性决策机制破解策略困境,强化目标管理通过调适决策的价值理性和工具理性破解利益困境。

价值预期与价值赋予:高校教师劳动关系的匹配博弈模型

在市场化转型时期,高校教师劳动关系的深层逻辑是不同价值间的博弈。价值预期体现为劳动主体在意识层面对价值回报的判断与预估;价值赋予表现为制度对劳动过程的支持程度。基于劳动价值论与制度价值论,对人、劳动价值与制度之间的关系进行深入剖析,以价值赋予与价值预期为横纵坐标,构建基于价值博弈的高校教师劳动关系博弈模型。从模型中发现,高校教师劳动关系有4种基本类型关系:高价值预期与高价值赋予;高价值预期与低价值赋予;低价值预期与高价值赋予;低价值预期与低价值赋予。通过质性访谈检验发现:当人、劳动价值与制度之间的关系相互协调时,以高价值预期与高价值赋予为代表的“双高”类型是劳动关系中的最优博弈类型;反之,则可能出现劳动关系的稳定性缺陷。这由此反映出“人与制度”的伴生性问题。因此,建立高校教师和谐劳动关系需要强化人、劳动价值与制度之间的内在共生逻辑,以及扭转价值失序局面,从而回归价值理性,提升价值赋予与价值预期的适配性。

基于网络演化博弈的信息传播行为分析

演化博弈论将博弈理论与动态演化过程相结合,在演化的过程中追求动态平衡,该方法较好地实现了对在线社交网络信息传播演化趋势的分析。为了进行在线社交网络中的信息传播演化动力学研究,同时分析到达某一均衡状态的原因和方式,首先结合在线社交网络特性构建改进聚集的无标度网络,用户间的交互采用单参数囚徒困境博弈模型,并采用费米规则更新策略。其次,通过数据仿真对影响网络中合作者比例演化的因素进行分析,得到网络聚集性、博弈收益权重会促进网络中的合作行为,而背叛诱惑与噪声因子则对其有抑制作用的结论。最后,结合新浪微博的真实舆论传播数据,对现实网络进行信息传播分析。研究表明,合作者比例是由博弈动力学和网络拓扑结构共同作用的结果,需采取适当的激励机制,以解决在线社交网络中信息传播出现的合作困境。