复杂系统中的合作涌现与自组织
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摘要
近年来,复杂系统中大量个体的集体行为在社会学、生物学和物理学领域备受关注。在这些集体行为中,合作涌现和自组织斑图的研究尤为瞩目。本论文基于演化博弈和复杂网络理论研究了自私个体间的合作行为和相互竞争物种间的自组织斑图。此外,我们还研究了复杂网络中的意见动力学和信誉评价系统。本论文分为三个部分。
首先,基于生态演化博弈,我们从以下三方面研究了生态复杂系统的自组织斑图和物种多样性：
1、在“石头-剪刀-布”博弈中,当中心小区域引入周期注入不同物种的个体时我们观察到靶波涌现。这种周期注入的物种个体(周期节律)首先在中心形成靶波,随后传播至整个空间。在演化过程中,处于随机初始状态的体系在周期节律的驱动下,逐渐被高度有序的靶波所占据。此时,中心注入局部区域和整个体系全局区域的物种个体所占比率随时间出现周期振荡；根据局部振荡周期和全局振荡周期之间的关系,靶波形成可以有三种不同的模式：两个区域的周期振荡同步,间歇同步以及非同步。
2、如果没有周期注入而是初始状态时三物种的个体规则分布在体系中,我们观察到由物种个体构成的自组织斑图,包括单臂螺旋波、多臂螺旋波、同向-反向螺旋波对。这些斑图的形成与初始的三物种个体分布有关。通过分析,我们发现了产生这些自组织斑图的机制,并与解偏微分方程获得的结果完全吻合。我们还讨论了各种自组织斑图在不同个体迁移率下的稳定性,发现单臂螺旋波比多臂螺旋波稳定,而同向螺旋波比具有相同臂数的同向-反向螺旋波对更稳定。
3、我们还研究了物种间个体相互作用强度对物种多样性和自组织斑图的影响。当个体迁移率很低的时候,作用强度大和小的情况下体系都能够维持物种多样性,特别是作用强度大的时候体系出现占据整个空间的螺旋波；中间大小的作用强度则导致物种多样性被破坏。当个体迁移率大的时候,只有作用强度小的情况体下体系才能维持物种多样性。当考虑非均匀初始条件时,我们观察到作用强度对于体系螺旋波斑图的作用有一个临界值：作用强度小于该临界值时螺旋波占据整个空间,体系保持全局有序；而作用强度大于该临界值时全局有序的螺旋波破碎成许多小螺旋波。
然后,基于空间演化博弈,我们从以下三方面探讨了社会复杂系统的自组织斑图与合作涌现：
1、在“囚徒困境”和“铲雪堆”博弈中,我们研究了自适应迁移对自私个体合作行为的影响。在这种自适应迁移机制中个体在博弈时随便获取近邻的策略信息,以便决定在周围有空位的情况下是否迁移。这种局域信息的获取不需要任何成本。我们发现,自适应迁移能够通过两种方式有效地促进合作：首先,适当的人口密度能够最大程度的促进合作,因为人口密度是与个体的迁移速度相联系的。其次,自适应迁移使得初始状态全部为背叛者的体系中出现合作爆发。
2、对“囚徒困境”博弈中个体的收益进行调节,可以调节个体收益分布的差异性。调节强度越大,不同个体的收益差异性越大。我们研究了这种调节强度对合作的影响,发现适当的调节强度对能够最大程度的促进合作。调节强度太大或者太小,这种促进作用都会减小,甚至变为抑制作用。合作者通过形成合作者团簇抵御背叛者的入侵,而且合作者团簇的规模对合作的维持起着关键作用。收益的调节强度正是通过合作者构成的这种自组织结构发挥作用的。
3、在团队中大多数个体都付出的情况下,个体可以通过团队的努力获得更大的回报。然而,如果团队中大多数个体都不付出的话,少量个体的付出将几乎不能获得回报。我们研究了无标度网络中最大度节点间的连边受到攻击(即删除最大度节点间的连线)时“公共物品”博弈中的合作演化。我们主要关注个体参与单群体博弈和多群体博弈时合作的稳定性。有趣的是,在单群体“公共物品”博弈中适度的删除最大度节点间的连线能够促进合作；而在多群体“公共物品”博弈中删除最大度节点间的连线则抑制合作。我们通过财富分布和近似计算的方法解释了这一现象。这说明社会多样性在合作的演化过程中举足轻重。
最后,我们在复杂网络理论的框架下研究了意见动力学和信誉评价系统：
1、我们研究了有向小世界网络中个体自我认同对意见动力学的影响,发现体系呈现出从具有单一公共意见状态到大量意见共存状态的非平衡相变。在有向小世界网络中,断边重连概率的大小表征了个体间有向长程联系的强弱。当个体间的有向长程联系很弱并且个体不坚持自己观点的时候,体系呈现出连续相变：相反,当个体间的有向长程联系和个体自我认同都很强的时候,体系不发生相变；当有向长程联系和个体自我认同介于两者之间的情况时,体系经历非连续相变。
2、如何对网页、科学家以及网络资源进行排序越来越受到计算机学家和物理学家等众多学者们的持续关注。为了便于物品的排序,在评分系统中用户对物品进行打分,分数是离散的数值。我们提出能够同时评价用户信誉和物品品质的迭代算法。我们的算法无论在虚拟数据中还是在MovieLen和Amazon的真实数据中都能提高物品排序的精度。我们提供了能够比较不同信誉评价系统的新思路。
Collective behaviors of abundant individuals in complex systems, including emer-gence of cooperation and self-organized patterns, have received increasing attention in the area of sociology, biology and physics. This thesis investigates the collective behav-iors among selfish individuals and competing species in the framework of evolutional game and complex network theory. Besides, the transmission of information on com-plex networks, such as opinion spreading and rating systems, is also discussed. There are three parts in this thesis.
First of all, self-organized patterns and biodiversity are investigated in a ecological game, consisting of following three point:
1. In a ecology system with three competing species playing rock-paper-scissors game, target waves emerge with incorporating a periodic current of the three species in a small area located at the center. The periodic current acts as a pacemaker, which able to nucleate target waves spreading across the whole population even in the random initial conditions. As a result, the target wave arises finally owing to periodic oscilla-tions of three species'density in both local area and the whole system. Three route toward target waves are observed:synchronization between the periodic current and oscillations of the density of the three species, intermittent synchronization, and non-synchronization. We show the mechanisms of emergence of self-organized pattern due to the interplay between local and global dynamics in a ecology system where three competing species playing the rock-paper-scissors game.
2. If there are no periodic current, but instead of regular initial conditions with three competing species distributing in ordered, single-armed spiral, multi-armed spi-rals the pair of spirals and anti-spirals are observed. It is found that the single-armed spiral is more stable than the multi-armed spirals, while the multi-armed spirals is more stable than the pair of spiral and anti-spirals with the same number of arms.
3. We also study effects of interaction intensity on the biodiversity and self- organized patterns. When individuals move slowly, large and small interaction in-tensities promote biodiversity so that all species coexist. Large interaction intensities in particular ensure this by evoking ordered spiral waves traveling across the spatial grid. Conversely, medium interaction intensities jeopardize biodiversity and indeed prohibit coexistence of the three species. When mobility of individuals is high, on the other hand, only small interaction intensities are able to sustain biodiversity while large interaction intensities fail. By considering heterogeneous initial distributions of the three species, we observe a critical influence of interaction intensity on spiral wave formation. In particular, globally ordered spiral waves can be observed only for inter-action intensities that are below a critical value. Once above, the spiral waves break up and form disordered spatial structures. This work thus indicates that interaction in-tensity is vital for the sustenance of biodiversity and emergence of pattern formation in ecosystems governed by cyclical interactions.
Secondly, cooperation among selfish individuals and its self-organized structure are studied in the framework of spatial game, containing the following three aspects:
1. We investigate the role of adaptive migration in spatial prisoners'dilemma game and the snowdrift game where selfish individuals apply an alternative migration strategy requiring only local information obtainable through game interactions. It is found that adaptive migration can be effective in promoting cooperation in two ways. First, there exists optimal population density leading to the highest cooperation level. Second, adaptive migration can induce an outbreak of cooperation from an environ-ment dominated by defectors.
2. Based on the prisoners'dilemma game, we introduce a regulation strength of payoff to reduce the heterogeneity of the distribution of all such payoffs. There exists an optimal regulation strength, which leads to the cooperation optimally promoted, and the promotive effect disappears if the heterogeneity is regulated to be either too weak or too strong. We find that cooperators on the spatial grid are not isolated but form compact clusters, and the distribution of these clusters is crucial for the promotion of cooperation.
3. Working together in groups may be beneficial with respect to isolated efforts. Yet this is true only if all group members contribute to the success. If not, group ef-forts may become detrimental on individual prosperity. Here we study the evolution of cooperation in public goods games on scale-free networks that are subject to dele-tion of links connected to the highest degree individuals, e.g., under attack. We focus on situations where either only a single group is considered for payoff evaluation or all groups with which a given player is affiliated. While in single-group public goods games there exist an optimal number of removed links for which cooperation thrives best, the effect is monotonously negative for multi-group public goods games. The findings are explained via wealth distributions and analytical approximations, confirm-ing that socially diverse states are crucial for the successful evolution of cooperation.
Last but not least, opinion dynamics and reputation systems are discussed based on the complex networks theory:
1. The influence of the self-affirmation on opinion dynamics is investigated in a directed small-world social network. The system displays a non-equilibrium phase transition from a consensus state to a disordered state with coexistence of opinions. The density of long-range-directed interactions and the strength of self-affirmation strongly affect opinion dynamics. When the long-range-directed interactions are sparse and individual generally does not insist on its opinion, the system will undergo a continuous phase transition, in the opposite case with strong self-affirmation and dense long-range-directed interactions, the system does not display a phase transition. Between those two extreme cases, a discontinuous phase transition emerges in the system.
2. How to rank web pages, scientists and online resources has recently received increasing attention ranging from computer scientists to physicists. We study the rank-ing problem of rating systems where objects are voted by users with discrete ratings. An algorithm is proposed that can simultaneously evaluate the user reputation and ob-ject quality in an iterative refinement way. Ranking accuracy is considerably improved by our algorithm in both the artificially generated data and the real data from Movie-Lens and Amazon. We provide a new way to evaluate and compare the performances of different reputation systems.
首先,基于生态演化博弈,我们从以下三方面研究了生态复杂系统的自组织斑图和物种多样性：
1、在“石头-剪刀-布”博弈中,当中心小区域引入周期注入不同物种的个体时我们观察到靶波涌现。这种周期注入的物种个体(周期节律)首先在中心形成靶波,随后传播至整个空间。在演化过程中,处于随机初始状态的体系在周期节律的驱动下,逐渐被高度有序的靶波所占据。此时,中心注入局部区域和整个体系全局区域的物种个体所占比率随时间出现周期振荡；根据局部振荡周期和全局振荡周期之间的关系,靶波形成可以有三种不同的模式：两个区域的周期振荡同步,间歇同步以及非同步。
2、如果没有周期注入而是初始状态时三物种的个体规则分布在体系中,我们观察到由物种个体构成的自组织斑图,包括单臂螺旋波、多臂螺旋波、同向-反向螺旋波对。这些斑图的形成与初始的三物种个体分布有关。通过分析,我们发现了产生这些自组织斑图的机制,并与解偏微分方程获得的结果完全吻合。我们还讨论了各种自组织斑图在不同个体迁移率下的稳定性,发现单臂螺旋波比多臂螺旋波稳定,而同向螺旋波比具有相同臂数的同向-反向螺旋波对更稳定。
3、我们还研究了物种间个体相互作用强度对物种多样性和自组织斑图的影响。当个体迁移率很低的时候,作用强度大和小的情况下体系都能够维持物种多样性,特别是作用强度大的时候体系出现占据整个空间的螺旋波；中间大小的作用强度则导致物种多样性被破坏。当个体迁移率大的时候,只有作用强度小的情况体下体系才能维持物种多样性。当考虑非均匀初始条件时,我们观察到作用强度对于体系螺旋波斑图的作用有一个临界值：作用强度小于该临界值时螺旋波占据整个空间,体系保持全局有序；而作用强度大于该临界值时全局有序的螺旋波破碎成许多小螺旋波。
然后,基于空间演化博弈,我们从以下三方面探讨了社会复杂系统的自组织斑图与合作涌现：
1、在“囚徒困境”和“铲雪堆”博弈中,我们研究了自适应迁移对自私个体合作行为的影响。在这种自适应迁移机制中个体在博弈时随便获取近邻的策略信息,以便决定在周围有空位的情况下是否迁移。这种局域信息的获取不需要任何成本。我们发现,自适应迁移能够通过两种方式有效地促进合作：首先,适当的人口密度能够最大程度的促进合作,因为人口密度是与个体的迁移速度相联系的。其次,自适应迁移使得初始状态全部为背叛者的体系中出现合作爆发。
2、对“囚徒困境”博弈中个体的收益进行调节,可以调节个体收益分布的差异性。调节强度越大,不同个体的收益差异性越大。我们研究了这种调节强度对合作的影响,发现适当的调节强度对能够最大程度的促进合作。调节强度太大或者太小,这种促进作用都会减小,甚至变为抑制作用。合作者通过形成合作者团簇抵御背叛者的入侵,而且合作者团簇的规模对合作的维持起着关键作用。收益的调节强度正是通过合作者构成的这种自组织结构发挥作用的。
3、在团队中大多数个体都付出的情况下,个体可以通过团队的努力获得更大的回报。然而,如果团队中大多数个体都不付出的话,少量个体的付出将几乎不能获得回报。我们研究了无标度网络中最大度节点间的连边受到攻击(即删除最大度节点间的连线)时“公共物品”博弈中的合作演化。我们主要关注个体参与单群体博弈和多群体博弈时合作的稳定性。有趣的是,在单群体“公共物品”博弈中适度的删除最大度节点间的连线能够促进合作；而在多群体“公共物品”博弈中删除最大度节点间的连线则抑制合作。我们通过财富分布和近似计算的方法解释了这一现象。这说明社会多样性在合作的演化过程中举足轻重。
最后,我们在复杂网络理论的框架下研究了意见动力学和信誉评价系统：
1、我们研究了有向小世界网络中个体自我认同对意见动力学的影响,发现体系呈现出从具有单一公共意见状态到大量意见共存状态的非平衡相变。在有向小世界网络中,断边重连概率的大小表征了个体间有向长程联系的强弱。当个体间的有向长程联系很弱并且个体不坚持自己观点的时候,体系呈现出连续相变：相反,当个体间的有向长程联系和个体自我认同都很强的时候,体系不发生相变；当有向长程联系和个体自我认同介于两者之间的情况时,体系经历非连续相变。
2、如何对网页、科学家以及网络资源进行排序越来越受到计算机学家和物理学家等众多学者们的持续关注。为了便于物品的排序,在评分系统中用户对物品进行打分,分数是离散的数值。我们提出能够同时评价用户信誉和物品品质的迭代算法。我们的算法无论在虚拟数据中还是在MovieLen和Amazon的真实数据中都能提高物品排序的精度。我们提供了能够比较不同信誉评价系统的新思路。
Collective behaviors of abundant individuals in complex systems, including emer-gence of cooperation and self-organized patterns, have received increasing attention in the area of sociology, biology and physics. This thesis investigates the collective behav-iors among selfish individuals and competing species in the framework of evolutional game and complex network theory. Besides, the transmission of information on com-plex networks, such as opinion spreading and rating systems, is also discussed. There are three parts in this thesis.
First of all, self-organized patterns and biodiversity are investigated in a ecological game, consisting of following three point:
1. In a ecology system with three competing species playing rock-paper-scissors game, target waves emerge with incorporating a periodic current of the three species in a small area located at the center. The periodic current acts as a pacemaker, which able to nucleate target waves spreading across the whole population even in the random initial conditions. As a result, the target wave arises finally owing to periodic oscilla-tions of three species'density in both local area and the whole system. Three route toward target waves are observed:synchronization between the periodic current and oscillations of the density of the three species, intermittent synchronization, and non-synchronization. We show the mechanisms of emergence of self-organized pattern due to the interplay between local and global dynamics in a ecology system where three competing species playing the rock-paper-scissors game.
2. If there are no periodic current, but instead of regular initial conditions with three competing species distributing in ordered, single-armed spiral, multi-armed spi-rals the pair of spirals and anti-spirals are observed. It is found that the single-armed spiral is more stable than the multi-armed spirals, while the multi-armed spirals is more stable than the pair of spiral and anti-spirals with the same number of arms.
3. We also study effects of interaction intensity on the biodiversity and self- organized patterns. When individuals move slowly, large and small interaction in-tensities promote biodiversity so that all species coexist. Large interaction intensities in particular ensure this by evoking ordered spiral waves traveling across the spatial grid. Conversely, medium interaction intensities jeopardize biodiversity and indeed prohibit coexistence of the three species. When mobility of individuals is high, on the other hand, only small interaction intensities are able to sustain biodiversity while large interaction intensities fail. By considering heterogeneous initial distributions of the three species, we observe a critical influence of interaction intensity on spiral wave formation. In particular, globally ordered spiral waves can be observed only for inter-action intensities that are below a critical value. Once above, the spiral waves break up and form disordered spatial structures. This work thus indicates that interaction in-tensity is vital for the sustenance of biodiversity and emergence of pattern formation in ecosystems governed by cyclical interactions.
Secondly, cooperation among selfish individuals and its self-organized structure are studied in the framework of spatial game, containing the following three aspects:
1. We investigate the role of adaptive migration in spatial prisoners'dilemma game and the snowdrift game where selfish individuals apply an alternative migration strategy requiring only local information obtainable through game interactions. It is found that adaptive migration can be effective in promoting cooperation in two ways. First, there exists optimal population density leading to the highest cooperation level. Second, adaptive migration can induce an outbreak of cooperation from an environ-ment dominated by defectors.
2. Based on the prisoners'dilemma game, we introduce a regulation strength of payoff to reduce the heterogeneity of the distribution of all such payoffs. There exists an optimal regulation strength, which leads to the cooperation optimally promoted, and the promotive effect disappears if the heterogeneity is regulated to be either too weak or too strong. We find that cooperators on the spatial grid are not isolated but form compact clusters, and the distribution of these clusters is crucial for the promotion of cooperation.
3. Working together in groups may be beneficial with respect to isolated efforts. Yet this is true only if all group members contribute to the success. If not, group ef-forts may become detrimental on individual prosperity. Here we study the evolution of cooperation in public goods games on scale-free networks that are subject to dele-tion of links connected to the highest degree individuals, e.g., under attack. We focus on situations where either only a single group is considered for payoff evaluation or all groups with which a given player is affiliated. While in single-group public goods games there exist an optimal number of removed links for which cooperation thrives best, the effect is monotonously negative for multi-group public goods games. The findings are explained via wealth distributions and analytical approximations, confirm-ing that socially diverse states are crucial for the successful evolution of cooperation.
Last but not least, opinion dynamics and reputation systems are discussed based on the complex networks theory:
1. The influence of the self-affirmation on opinion dynamics is investigated in a directed small-world social network. The system displays a non-equilibrium phase transition from a consensus state to a disordered state with coexistence of opinions. The density of long-range-directed interactions and the strength of self-affirmation strongly affect opinion dynamics. When the long-range-directed interactions are sparse and individual generally does not insist on its opinion, the system will undergo a continuous phase transition, in the opposite case with strong self-affirmation and dense long-range-directed interactions, the system does not display a phase transition. Between those two extreme cases, a discontinuous phase transition emerges in the system.
2. How to rank web pages, scientists and online resources has recently received increasing attention ranging from computer scientists to physicists. We study the rank-ing problem of rating systems where objects are voted by users with discrete ratings. An algorithm is proposed that can simultaneously evaluate the user reputation and ob-ject quality in an iterative refinement way. Ranking accuracy is considerably improved by our algorithm in both the artificially generated data and the real data from Movie-Lens and Amazon. We provide a new way to evaluate and compare the performances of different reputation systems.
引文
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