基于复杂网络的群体Parrondo博弈及悖论效应研究

Parrondo games can produce a paradoxical effect that losing (game A) +losing (game B) = winning (a randomized game A+B). This effect has motivated widespread studies on dynamic mechanisms in counter-intuitive phenomena which exist in physics, biology, economics and other disciplines. At present, Parrondo games have mainly been demonstrated in the individual-player versions, whereas our project aims to establish multi-agent Parrondo games and construct structures of game B applied in arbitrary complex networks. The research focuses on the following parts: Firstly, the influential law that the interactive modes among individuals of the population and the measure indices of networks have on the paradoxical effect are studied. Secondly, on the basis of computer simulations and the theoretical approach of Markov chain, the "agitating" mechanism of game A and the "ratcheting" mechanism of game B are studied. Moreover, the correlations between the "agitating" and "ratcheting" mechanisms are demonstrated. Thirdly, a Parrondo’s paradoxical effect which is produced by the dynamic processes of the evolution of network structure + game B is considered. Then the alternative mechanism that the evolution of network structure instead of the "agitating" mechanism of game A is analyzed. The corresponding conditions and the network characteristics of producing the paradoxical effect are demonstrated. Finally, a new counter-intuitive phenomenon in multi-agent Parrondo games is studied— "the voting paradox", that is, concentration is more conducive to the development of groups than democracy. Furthermore, the emerging phenomenon that "the whole exceeding the sum of its parts" is revealed. Thus, a new game paradigm for the research on the group activities is given.

Parrondo博弈能产生一种“输（A博弈）+输（B博弈）=赢（随机A+B博弈）”的悖论效应，该效应引发了对物理学、生物学和经济学等领域中广泛存在的反直觉现象的动力学机制研究。目前，Parrondo博弈模型主要是个体版，本项目旨在构建群体Parrondo博弈模型和适用于任意复杂网络的B博弈结构，研究群体中个体之间作用方式和网络测度指标对悖论效应的影响规律；利用计算仿真和基于马尔科夫链的理论方法，分析A博弈的“搅动”机制和B博弈的“棘轮”机制，揭示两种机制之间的关联性；研究依靠网络结构演化+B博弈的动力学过程来产生Parrondo悖论效应，分析网络演化对A博弈“搅动”作用的替代机制，揭示产生悖论效应的网络特征和相应条件；研究群体Parrondo博弈中一种新的反直觉现象——集中比民主更利于群体发展的“投票悖论”，揭示由“整体大于部分之和”带来的涌现现象，为研究群体行为提供新的博弈范式。

基于Parrondo博弈，可以产生一种有趣的“输+输=赢”的悖论现象。目前，随着对Parrondo博弈机制及其悖论的深入分析，对Parrondo博弈模型的研究已经扩展到群体博弈和网络博弈。本项目基于复杂网络对群体Parrondo博弈模型进行了悖论效应研究，取得了以下研究成果：.（1）为了从宏观和整体层面理解网络演化的合理性与适应性，本项目采用了一种网络结构演化（A环节）+B博弈（依赖资本）的动力学过程来产生Parrondo悖论效应，主要研究网络结构演化是否可以促进群体的适应性，并分析网络结构演化方式、游戏方式和玩A环节的概率对Parrondo悖论效应的影响。通过仿真分析，发现网络演化能带来福利，有利于提升群体收益。.（2）由于邻居小生境对个体生命状态、博弈输赢收益和竞合行为适应性都存在影响，那么是否也是导致群居或者独居生活方式的原因呢？本项目定义了一种博弈输赢规则和网格演化规则，通过基于离散马尔可夫链的理论分析揭示了“生境棘轮决定生活方式”。.（3）以度-度相关性可调网络为空间载体，对A博弈+B博弈的群体Parrondo博弈进行计算仿真研究，分析当A博弈采用竞争、合作、随机等六种不同的行为方式时，网络度-度相关性对Parrondo悖论效应的影响。通过对B博弈的不对称结构、A博弈的行为方式以及网络拓扑结构的共同作用机制，详细阐述了悖论发生或不发生的微观原因。.（4）对于群体而言，群体决策是一种典型的群体层面的行为。在社会管理中存在一种“投票悖论”的困境，即用最民主的方式可能得到最不科学的结果，针对此现象，本项目构建了考虑群体决策影响的Parrondo博弈模型，研究结果显示在特殊情境下如公共危机管理中，集中决策比民主投票更有效率。.综上，本项目利用Parrondo博弈动力学与网络结构共演化的模式，分析了网络演化、生活方式和竞合行为的合理性，为研究群体行为提供新的博弈范式。