重复囚徒困境的学习和响应模型

囚徒困境问题是博弈论的一个重要范例,对此的研究涉及经济学、社会学、生物学等广泛领域。Axelrod R在文献[1]中从进化的角度研究和探讨了经典囚徒困境的一个扩展--重复囚徒困境。这种博弈要求参与者反复进行囚徒困境的博弈,并且可以记住他们的对抗历史。Axelrod还组织了两次重复囚徒困境的计算机竞赛,最终胜出的都是简单的＂以
牙还牙＂策略[2]。这之后有不少学者试图找到可以击败它的策略,都未能取得显著成功。本文提出了一种学习和响应的理论模型,实际中的许多重复囚徒困境的策略都可以纳入这一模型中。我们分析了实现这一模型的难点和复杂度,同时给出了一种基于树结构的实现方式,并在实验中把它和“以牙还牙”作比较。实验以及分析表明,策略在竞赛中表现的优劣主要取决于如何利用一些启发式规则来权衡学习代价和博弈的总利益,以及在此基础上如何抽取对手的关键信息。     

时间尺度与选择倾向性协同作用下的演化博弈模型

针对合作行为的涌现与维持问题，基于演化博弈理论和网络理论，提出了一种促进合作的演化博弈模型。该模型同时将时间尺度、选择倾向性引入到演化博弈中。在初始化阶段，根据持有策略的时间尺度将个体分为两种类型：一种个体在每个时间步都进行策略更新；另一种个体在每一轮博弈后，以某种概率来决定是否进行策略更新。在策略更新阶段，模型用个体对周围邻居的贡献来表征他的声誉，并假设参与博弈的个体倾向于学习具有较好声誉邻居的策略。仿真实验结果表明，所提出的时间尺度与选择倾向性协同作用下的演化博弈模型中，合作行为能够在群体中维持；惰性个体的存在不利于合作的涌现，但是个体的非理性行为反而能够促进合作。     

Trust-based evolutionary game model assisting AODV routing against selfishness

Self-organizing networks such as wireless ad hoc networks present a number of problems and paradoxes towards trustworthiness and consistency of the network. Lack of cooperation between nodes drastically brings down the throughput of the network. Selfish behavior of the nodes is one of the issues, which deter the trust among them. This paper explores the multiple modes to build trust and proposes an effective, dynamic and distributed framework using evolutionary game theory. Strategic, non-cooperative and evolutionary game theory has been utilized to model the dynamic behavior of selfish nodes in a self-policing ad hoc network. AODV routing assisted by the proposed game model enlightens a cogent scenario, which demonstrates that it can stimulate cooperation among selfish nodes, albeit without negotiations. The proposed model encompasses two distinct modes to learn and predict the behavior of neighbors namely deterministic and random. Deterministic mode is a generic one which helps to analyze the behavior of the network for standard strategic patterns whereas the random strategy profiles are explored using randomized analysis based on genetic algorithm. This paper investigates the simulated results for the two methods and asserts that if nodes use evolved strategies and trust evaluation mechanism, then the model supports in accomplishing the cooperation level to reach the maximum possible.     

二维平面网格上移动成本群体合作行为研究

从移动成本、收益期望与空间博弈的角度,探讨多主体系统的博弈策略演化与系统涌现特征之间的关系。利用空间演化博弈理论,构建了基于个体移动机制的拓扑结构时刻演变的空间演化博弈模型,分析了当主体具有不同的移动成本与收益期望时系统演化的稳定策略,通过分析稳定策略深入探讨系统中合作簇涌现的机理。仿真结果表明,提高移动成本能够最有效地促进系统合作率,同时中等水平的个体收益期望会进一步促进高移动成本的影响效果。     

基于演化博弈的供应网络企业收益与合作行为的关系仿真

利用演化博弈的理论, 探讨了供应网络中处于不同位置的核心企业和非核心企业两个群体间的成员其投入合作的策略根据收益变化而改变的演化过程; 建立了复制动态方程并求得平衡点解, 据此通过复制动态的相位图直观反映了博弈的演化稳定策略; 并通过Netlogo软件对企业行为选择与收益的关系进行了仿真, 其行为选择的演化结果与相位图展示结果具有一致性。研究结论表明, 收益获得及变化是企业合作行为改变以及合作策略选择的重要依据, 企业间演化稳定策略不仅仅局限于参与合作与放弃合作, 长时间观望也是企业可能的策略选择; 最后针对如何提高供应网络企业间合作的稳定性提出了对策建议。     

基于RBF神经网络的攻防博弈模型

为了阐明网络攻防过程中博弈双方如何确定对方的类型,从而选择行动策略,提出了基于RBF神经网络的攻防博弈模型。首先使用两人随机博弈模型来分析网络攻防双方的特点,揭示制约双方选择策略的因素;通过精炼贝叶斯纳什均衡求得博弈双方选择的最优策略;最后,根据可疑者的行动策略和系统的状况,使用RBF神经网络对其类型进行推理。     

Emergence of observable rules in a spatial game system

This study focuses on player’s strategies observed from outside our original spatial game iterated by players, each of which is placed in a lattice site on a two-dimensional square lattice. A particularity of the game lies in the fact that a player’s strategy is not given, but is constructed dynamically in response to the spatial pattern of the player’s actions. This means that the strategy can evolve in time. However, the simulations revealed unexpected results. It was found that all the strategies observed from outside did not evolve, but were fixed in time. This article enumerates all the observed strategies in detail, and examines their characteristics.     

理性背叛的推荐合作激励机制

为了促进协作系统中用户的合作行为,激励机制得到了广泛的使用.然而,现有的激励机制往往存在无条件合作策略占优互惠策略的现象,进而抑制了合作的涌现.为了解决这一问题,本文在推荐激励模型上进一步考虑了用户的理性背叛行为.以演化博弈为框架,研究了理性背叛机制在全局平均学习和当前最优学习两种模式下的策略演化特性.结合实际场景,本文还研究了在非完美推荐下理性背叛机制的鲁棒性问题,并且基于余弦相似度提出了一种策略识别方案.最后,通过大量的数值实验与仿真实验,验证了理性背叛机制的理论特性,也展示了该机制在促进合作方面的有效性能.     

Incentives to Cooperate in Network Formation

We propose a simple mechanism based on taxes and subsidies to enhance high cooperation in evolutionary networks. The interactions among agents are based on the Spatial Prisoners' Dilemma game in which each agent interacts with the same strategy with its local neighbors, collects an aggregate payoff and imitates the strategy of its best neighbor. First we study the mechanism in a regular lattice where it is well-known that the asymptotic fraction of cooperators fluctuates around a constant value for almost all starting proportions and configurations of cooperators. We also explore the mechanism in random and adaptive networks, where adaptability refers to the ability of agents to change their local neighborhood. For theses networks it has been reported that the starting proportion of cooperation has to be sufficiently high in order to obtain highly cooperative levels in the long-run time. The implementation of our mechanism produces successful results in such evolutionary networks, higher levels of cooperation are reached for all initial fractions of cooperation, including the most adverse case of just one cooperator in the network. Additionally, we observe that the network reaches a spatial configuration such that the fraction of cooperators remains in high level even when the mechanism is switched off. As a result the mechanism can work as an ignition engine to achieve highly cooperative level since it can be implemented for a finite period of time.     

观察机制对囚徒困境博弈合作水平的影响

在演化博弈论中,合作有利于增加群体收益.目前,大量的研究工作都在关注合作水平的提高,但忽视了理论与实际的相关性,同时策略更新时间仅限于一个点上的收益.为此,引入完全同步、相对同步、高斯异步、指数异步4种观察机制模型,考虑智能体观察期内所获得的平均收益.随后,采用蒙特卡洛方法进行实验仿真,并分析各观察机制对囚徒困境博弈合作水平的影响.结果表明:在4种模型中都存在观察时间阈值,此时合作水平将达到峰值;最高合作水平在指数异步模型中实现;高斯异步模型中,合作水平与方差成正相关;智能体间的异质性也对合作产生积极影响.这项研究有助于打破传统研究收益的局限,促进合作水平的提高.仿真实验结果为支持社会群体合作提供了一定的理论依据.     

系统直和博弈模型下的合作演化

演化博弈论是生物进化论与博弈论结合产生的理论,已成为研究合作演化行为的有力工具.本文研究了基于系统直和博弈模型下的合作演化行为.首先,利用复制者方程分析了双人双策略及三策略对称博弈的演化动力学过程.然后,以石头剪刀布模型和雪堆模型为基础,采用矩阵直和构建系统直和博弈模型,并将所构造的直和矩阵转化为含参数的系统总支付矩阵.随后,说明了这种方法可推广到n个博弈的情形.最后,利用MATLAB对系统直和博弈模型进行仿真模拟,从系统整体的角度分析合作演化.仿真结果表明,混合之后的系统直和博弈较单一博弈而言,合作策略的占比明显增加,且整个系统稳定性更好.这种合作演化机制呈现了全局互惠.     

Multi-objective design method based on evolution game and its application for suspension

Through research and bionics of biology survival mode, game players with competition, cooperation and self-adaptation capacity are introduced in the multi-objective design. The dynamic behavior and bounded rationality in game processes for players are considered according to Chinese saying “In success, commit oneself to the welfare of the society; in distress, maintain one’s own integrity”. An evolution rule, Poor-Competition-Rich-Cooperation (short for PCRC), is proposed. Then, the corresponding payoff functions of competition and cooperation behavior are established and a multi-objective design method based on evolution game is proposed. The calculation steps are as follows: 1) Taking the design objectives as different game players, and calculating factors of the design variables to objective and fuzzy clustering. The design variables are divided into multiple strategy subsets owned by each game player. 2) According to the evolution rule, each player determines its behavior and payoff function in this game round. 3) In their own strategy subsets, each game player takes their payoff as mono-objective for optimization. It gives the best strategy upon other players. And so the best strategies of all players conform the group strategy in this round. The final equilibrium solution is obtained through multi-round game based on convergence criterion. The validity and reliability of this method are shown by the results of an example of a tri-objective optimization design of passive suspension parameters.     

Scheduling strategy for computational-intensive data flow in generalized cluster environments

A classical problem in the field of distributed computation and parallel processing concerns reasonable allocation of resources among computational-intensive data flows. We introduce the generalized cluster in this paper for processing large-scale scientific computations and to further explore a consecutive cooperation game-based dynamic scheduling strategy. We construct an abstract generalized cluster environment and summarize the types of data flows. We then convert the multi-objective scheduling problem into a multi-objective expectation function-based continuous cooperation game model and discuss its strategy and a solution for its kernel. We also propose a dynamic scheduling mechanism to address the instability of generalized clusters to ensure a reasonable, real-time adjusting allocation scheme by monitoring and compensating appropriately. Finally, we apply our method to a real world application to demonstrate our successful scheduling strategy that achieves superior results for overall cost, cost-performance index, and mean run time when compared with other methods.     

Multi-agent team cooperation: A game theory approach

The main goal of this work is to design a team of agents that can accomplish consensus over a common value for the agents’ output using cooperative game theory approach. A semi-decentralized optimal control strategy that was recently introduced by the authors is utilized that is based on minimization of individual cost using local information. Cooperative game theory is then used to ensure team cooperation by considering a combination of individual cost as a team cost function. Minimization of this cost function results in a set of Pareto-efficient solutions. Among the Pareto-efficient solutions the Nash-bargaining solution is chosen. The Nash-bargaining solution is obtained by maximizing the product of the difference between the costs achieved through the optimal control strategy and the one obtained through the Pareto-efficient solution. The latter solution results in a lower cost for each agent at the expense of requiring full information set. To avoid this drawback some constraints are added to the structure of the controller that is suggested for the entire team using the linear matrix inequality (LMI) formulation of the minimization problem. Consequently, although the controller is designed to minimize a unique team cost function, it only uses the available information set for each agent. A comparison between the average cost that is obtained by using the above two methods is conducted to illustrate the performance capabilities of our proposed solutions.     

Stochastic game logic

Stochastic game logic (SGL) is a new temporal logic for multi-agent systems modeled by turn-based multi-player games with discrete transition probabilities. It combines features of alternating-time temporal logic (ATL), probabilistic computation tree logic and extended temporal logic. SGL contains an ATL-like modality to specify the individual cooperation and reaction facilities of agents in the multi-player game to enforce a certain winning objective. While the standard ATL modality states the existence of a strategy for a certain coalition of agents without restricting the range of strategies for the semantics of inner SGL formulae, we deal with a more general modality. It also requires the existence of a strategy for some coalition, but imposes some kind of strategy binding to inner SGL formulae. This paper presents the syntax and semantics of SGL and discusses its model checking problem for different types of strategies. The model checking problem of SGL turns out to be undecidable when dealing with the full class of history-dependent strategies. We show that the SGL model checking problem for memoryless deterministic strategies as well as the model checking problem of the qualitative fragment of SGL for memoryless randomized strategies is PSPACE-complete, and we establish a close link between natural syntactic fragments of SGL and the polynomial hierarchy. Further, we give a reduction from the SGL model checking problem under memoryless randomized strategies into the Tarski algebra which proves the problem to be in EXPSPACE.     

Spatial strategies in a generalized spatial prisoner’s dilemma

Many strategies, such as tit-for-tat, have been proposed in the iterated prisoner’s dilemma (IPD) in which the prisoner’s dilemma (PD) is carried out repeatedly with two players. A spatial version of the iterated prisoner’s dilemma (SPD) has been studied, where a player at each site plays the IPD game with all the players in the neighborhood. However, the strategies studied in the SPD consider the past actions of a single opponent only. We studied spatial strategies that depend on the configuration of actions taken by all neighbors (as opposed to conventional temporal strategies). Since generosity can be considered as a spatial strategy, we first investigate the generosity required when an action error is involved. We also propose several spatial strategies that outperform many others.This work was presented, in part, at the 9th International Symposium on Artificial Life and Robotics, Oita, Japan, January 28–30, 2004     

Effects of strategy switching and network topology on decision-making in multi-agent systems

To study why the altruistic cooperation can emerge and maintain among self-interested individuals, researchers across several disciplines have made contributions for the solutions of this fascinating problem. Among this, a most-often used framework to describe cooperative dilemma is the evolutionary game theory. In traditional settings, an ideal hypothesis that individuals can feasibly obtain related partners' pay-offs for strategy updating is often adopted. However, considering the impracticality in acquiring accurate pay-offs of referential objects at each round of interaction, we propose switching probability which is independent of pay-offs and denotes the willingness of any individual shifts to another strategy. Here we provide results for the evolutionary dynamics driven by the switching probability in a three-strategy game model, played by the fully connected populations. The findings inform the befitting design of switching probabilities which maximally promote cooperation. We also derive general results that characterise the interaction of the three strategies: coexistence of multiple strategies or domination by some strategy.     

Evolutionary Dynamics of Strategies without Complete Information on Complex Networks

As for the behaviors of multi‐agent system, recent years have witnessed the growing interest in the study of cooperative behaviors by the aid of evolutionary game dynamics on complex networks. Thereinto, the updating rules deciding the evolution of strategies will significantly influence the steady state distribution of the system. The strategy updating rooted in the pursuit of larger benefits, will drive the system to evolve into the coexistence of different states or the domination by some strategies. To relax the often‐used rules required explicit knowledge of the exact payoffs, this paper describes a new approach of updating strategy based on switching probabilities, which is independent on players' payoffs and degrees. And then the equilibrium state of the strategy evolution in the networks is studied. Our work here provides a computationally feasible way of estimating the steady characteristics of the strategy adoption of agents situating on complex networks. The stability analysis elucidates two important features: (i) the takeover of cooperation can be enhanced by the appropriate settings of the switching probabilities between strategies and (ii) larger average degree and power exponent in the employed scale‐free network can make it easier for the coexistence of strategies. The results can help the design of initial strategy distribution of agents located on social networks to promote cooperation.     

有限次重复囚徒博弈中的合作机制研究

模仿现实中人们的决策方式,提出类"触发策略"的策略思想,将原问题由双策略的多阶段博弈转换为多策略的一次性博弈,并建立起扩展的支付矩阵;然后运用进化博弈理论,将随机扰动引入复制子动态,从理论上说明有限次重复囚徒博弈之所以能够涌现合作是复制效应和变异效应共同作用的结果;最后通过建立多主体系统的仿真模型,进一步分析和验证了合作涌现的门限条件和稳定状态。     

一种基于合作博弈论的自动驾驶车道变更模型

提出一个新颖的车道变更模型,采用合作博弈方法激励车辆参与合作.首次将合作博弈理论应用到车道变更领域,设计用于两车变道的纳什讨价还价变道模型,然后扩展为三车的合作博弈变道模型,并求出变道模型的纳什讨价还价解和夏普利值.为了进一步激励车辆参与合作,在收益分配方案中加入支付补偿部分来实现整体收益的可转移性,从而取得模型的解....