网络演化博弈中的合作与相行为研究

发布时间：2019-01-10 19:42

【摘要】：合作现象不管在人类社会还是在生物界都是一种普遍现象,即使是在自然选择的状况下,在自私的个体之间依然有合作现象。如何理解合作现象的产生成为博弈问题中最基本的问题之一。博弈理论作为一种强有力的工具,他能帮助人们研究存在于社会,生物,经济等领域中的基本性质并找出其中理性的规律。本文主要研究了三种不同的博弈模型。1)我们提出并研究了不满意自适应的两两囚徒困境博弈中的合作行为。我们对比了代理人在两种不同网络结构中博弈演化的情况,一种是全局耦合网络,另外一种是二维正方格子网络。我们发现,在两种网络结构中,合作现象都会出现,且合作者浓度在二维正方格子网络中得到明显增强。在全局耦合网络中,虽然合作者平均收益不可能高于背叛者的收益。但是在二维正方格子中,在相同的博弈参数下,合作者的平均收益要比在全局耦合网络中合作者的平均收益要高。2)我们提出并研究了一个共演化雪堆博弈系统中的合作行为与相变现象。在这个系统中,代理人一开始处于一个随机网络中,近邻相连的代理人进行雪堆博弈。代理人为了获得更高的竞争环境,可以选择模仿近邻在博弈中获得成功的策略,也可以选择断开背叛自己的代理人,并重新在系统中寻找一个代理人相连。模仿近邻策略与代理人之间的重连会导致系统演化至不同的相。3)我们提出了一种不满意自适应的雪堆博弈,在这个系统之中包含两个重要参数,一个是收益参数r,另外一个是重连所需要消耗的费用a。当一个代理人面对对自己不利的局部竞争环境时,可以选择在不需要任何费用的情况下改变自己的策略,也可以选择消耗一定的费用a去重新连接到系统中的其他非近邻代理人。我们发现,当参数r很小时,较大的重连消耗的费用a比较小的a更能促进系统中合作的产生。反之,当参数r比较大时,较大的重连消耗的费用a比较小的a更加抑制了系统中合作的产生。对于给定的r,重连消耗的收益a存在一个临界值,当a小于这个临界值时,系统会进入一个凝结的静止相。在这个静止相中,合作的代理人将相互连接成一个大团体,而背叛的代理人将会被这些合作的代理人所孤立。当a大于这一临界值时,系统会进入一个动态相。在该相中,由合作者与背叛者相互混合于一个大团体中,整个系统处于不断演化的动力学状态中。理论与模拟得出的相变分界线在a-r平面内明显的分离出这两种相结构,从相图中可以看出,对于小r(或者小a),这种互不相连且策略相分离的状态可以在很宽的a(r)范围内存在。
[Abstract]:The phenomenon of cooperation is a common phenomenon in both human society and biology. Even under the condition of natural selection, there is still a phenomenon of cooperation among selfish individuals. How to understand the phenomenon of cooperation has become one of the most basic problems in the game. As a powerful tool, game theory can help people to study the basic properties in the fields of society, biology and economy and find out the law of rationality. In this paper, we mainly study three different game models. 1) We propose and study the cooperative behavior in dissatisfied adaptive pairwise prisoners' dilemma game. We compare the evolution of agents in two different networks, one is global coupling network, the other is two-dimensional square lattice network. It is found that cooperation occurs in both networks and the concentration of collaborators is significantly enhanced in two dimensional square lattice networks. In globally coupled networks, though, the average return of collaborators is unlikely to be higher than that of betrayers. But in a two-dimensional square lattice, under the same game parameters, The average return of the collaborator is higher than that of the cooperator in the global coupled network. 2) We propose and study the cooperative behavior and phase transition in a co-evolution snowdrift game system. In this system, the agents are initially in a random network, and the adjacent agents play snowdrift games. In order to obtain a higher competitive environment, the agent can choose to imitate the strategy of success in the game by the nearest neighbor, or disconnect the agent who betrays himself, and find an agent connection again in the system. Imitating the reconnection between the nearest neighbor strategy and the agent will lead to the evolution of the system to different phases. (3) We propose a dissatisfactory adaptive snowdrift game in which two important parameters are included, one is the income parameter r, the other is the income parameter r. The other is the cost of reconnecting a. When an agent is faced with a local competitive environment that is unfavourable to him, he can choose to change his strategy at no cost. You can also choose to reconnect to other non-nearest neighbor agents in the system at a cost. It is found that when the parameter r is very small, the larger cost of reconnection a can promote the generation of cooperation in the system more than the smaller one. On the other hand, when the parameter r is large, the larger cost a of reconnection is more likely to restrain the production of cooperation in the system than the smaller one. For a given r, there exists a critical value for the income a of reconnection consumption. When a is less than this critical value, the system will enter a condensed stationary phase. In this stillness, agents of cooperation will be connected to each other into a large group, and agents of betrayal will be isolated by these agents of cooperation. When a is larger than this critical value, the system will enter a dynamic phase. In this phase, collaborators and betrayors mingle with each other in a large group, and the whole system is in an evolving dynamic state. The theoretical and simulated phase transition boundaries are clearly separated from the a-r plane. It can be seen from the phase diagram that for small r (or small a),) This state of disconnection and policy separation can exist in a wide range of a (r).
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O225

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