Equilibrium in a Network Game with Production and Knowledge Externalities

In each node of a network, economy is described by the simple two-period Romer’s model of endogenous growth with production and knowledge externalities. The sum of knowledge levels in the neighbor nodes causes an externality in the production of each node of the network. The game equilibrium in the network is investigated. The agents’ solutions depending on the size of externality are obtained. The uniqueness of inner equilibrium is proved. The role of passive agents in network formation is studied; in particular, the possibilities of adding a passive agent to a regular network, and also of joining of regular networks through nodes with passive agents. It is shown that the sum of knowledge levels in all the nodes decreases under adding of a new link.     

广义Nash平衡点和切换控制在对策论中的应用

通过把平衡点和决策者的动机耦合的方法,提出了广义纳什平衡点这一新概念.决策者的动机通常有两类：一是最大化自己的利益,另一则是最大化对手的利益.如果每一个决策者的动机都是第一类,一个理性的群体就会形成,整个系统最终会达到第一类平衡点（也就是经典的纳什平衡点）.如果每一个决策者的动机都是第二类,一个有智慧的群体就会形成,整个系统最终会达到第二类平衡点.同时,切换控制被用来帮助决策者确定他们的动机.     

Equilibrium Strategy of the Pursuit-Evasion Game in Three-Dimensional Space

The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper, we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer’s three-degree-of-freedom control and the evader’s relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs (HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer’s speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.

     

讨价还价博弈均衡出价策略的算法设计

在商业智能领域,为求解买卖双方讨价还价博弈的均衡出价策略,在逆向归纳法的基础上,开发出两个高效且实用的算法：基于逆向归纳过程,设计出迭代算法;基于逆向归纳结果,设计出递归算法。迭代算法是逆向归纳法的具体实现,而递归算法则并不拘泥于逆向归纳法。在智能电子商务的讨价还价实战中,分设司令部、参谋部、作战部等三个角色模块,给出应用该算法开发智能出价决策支持系统的初步设计思路。     

不完全信息议价博弈的序贯均衡分析与计算实验

本文从理论研究和计算实验两个层次分析和验证了一类带有时间 偏好的单边双类型不完全信息议价博弈模型及其序贯均衡, 运用单阶段偏离法则分别推导和证明了该议价博弈的合并均衡与分离均衡, 并通过策略比较和构造静态出价博弈证明了合并均衡是议价博弈的唯一理性解. 在此基础上, 本文设计不完全信息议价博弈计算实验场景, 基于协同演化计算实验方法验证了议价博弈的序贯均衡解. 最后, 本文探讨了该序贯均衡对于议价双方相应管理策略的实践指导意义.     

Individual Stability of Coalition Structures in Three-Person Games

Automation and Remote Control - Cooperative games with coalition structures are considered, and a principle of coalition structure individual stability with respect to some cooperative solution...     

纯策略纳什均衡的博弈强化学习

将博弈理论与多智能体强化学习结合形成博弈强化学习逐渐受到关注,但是也存在算法的计算复杂度高和无法保证纯策略纳什均衡的问题。Meta equilibrium Q-learning算法通过反应函数将原始博弈转换为元博弈,而元博弈推导出的元均衡是纯策略纳什均衡。该算法在保证纯策略纳什均衡的前提下能够使得每个智能体的回报不低于某特定阈值。同时,基于分形的均衡程度评估模型能够通过计算任意状态的分形维数来判断其稳态,并评估任意状态与均衡状态之间的距离,该模型可以检验元均衡的科学性与合理性,上述算法和模型的相关结论在福利博弈和夺控战中都得到具体验证。     

A Differential Game Model of Oligopoly

Most of the literature on oligopoly deals with profit-maximizing firms engaging in “static” repetitive games. As the number of firms increases, the Nash-equilibrium strategy for each Cournot oligopolist converges to the competitive solution. In a two-person, zero-sum differential game model of duopoly [1] we introduced dynamic elements and explored alternative entrepreneurial goals. The duopolists endeavor to outsell each other subject to a no-loss constraint; the saturation of present markets by past sales and the impact on future goodwill by current advertisement are handled through “state variables.” The differential game formulation [1, 2] offers two advantages: (a) near perfect information leads to frequent existence of pure strategy equilibria and (b) the use of optimal control theory facilitates the characterization of the time structure of an equilibrium. However, the two-person, zero-sum framework is too restrictive while a general theory for solving n-person, non-zero sum differential games has still not been developed [3, 4].     

Numerical Simulation of Non-cooperative and Cooperative Equilibrium Solutions for a Stochastic Government Debt Stabilization Game

Computational Economics - In this article, we consider the impact uncertainty has on policies and realization of targets aimed at the stabilization of government debt. The problem is motivated by...     

模糊协商微分对策及其折中解

对于协商问题，为避免非线性问题带来求解上的困难并且使其能够处理不确定信息，基于T-S模糊微分对策的思想，构造出协商微分对策的模糊线性化模型．进一步探讨了在模糊线性协商微分对策系统下相应于折中解的控制器的设计方法．对一个2∶2对策问题做了仿真，其效果说明了解决问题方法的可行性．     

Coordination of the Equilibrium Controls in Hierarchic Systems by Game Theory Methods

In connection with a wide prevalence of hierarchic structure systems in very different spheres of activity (industrial and economic, animate nature, etc.) and considerable difficulties associated with their analysis, the problem of the unit, the “AND” problem according to the Bertalanffy playful formulation, has become of paramount importance. At the same time the integration into the unit is achieved by means of coordination. It is the coordination (in particular, the coordination principles) that permits the revealing of mechanisms for achieving integration in hierarchic control systems [8].     

具有保留效用的一般网络价格竞争博弈的寡占均衡

本文讨论了具有保留效用的一般网络的多个服务提供商之间的价格竞争博弈问题.给出了用户均衡的定义,并证明了其存在性、唯一性和连续性.由服务提供商所给价格和对应价格的用户均衡,给出了寡占均衡和严格寡占均衡的定义.根据Wardrop原理,给出了给定价格下用户均衡流量分配的特征刻画.本文还讨论了寡占均衡和严格寡占均衡的性质,给出严格寡占均衡价格的特征刻画,并用并行链路网络例证了文章的主要结果.     

Improving Data Utility Through Game Theory in Personalized Differential Privacy

Journal of Computer Science and Technology - Due to dramatically increasing information published in social networks, privacy issues have given rise to public concerns. Although the presence of...     

基于模糊微分对策多机空战组内协同的U解

鉴于协商微分对策多具有强非线性和不确定性特点,为避免非线性问题等带来求解上的困难和能处理不确定信息,基于T-S模糊微分对策的思想,对非线性的基于Utilitarian解(简称U解)的协商微分对策的状态方程和性能分别进行了模糊化和二次型化,构造出面向U解的协商微分对策的模糊线性化模型,研究了协商U解模型中加权系数的确定,并进一步探讨了在模糊线性协商微分对策系统下相应于U解的控制器的设计方法.研究工作和仿真结果可以说明,相对于Nash协商解,协商理论的U解更能反映整体效果,更易于推广.     

基于环境Pareto 支配选择策略的有约束多目标差分进化算法

在处理有约束多目标问题的进化算法中, 目前普遍采用Deb 教授提出的约束占优的直接支配选择策略. 在约束处理中, 优秀不可行解与优秀可行解同样重要, 但在直接支配选择策略中, 不可行解被选择的几率很小. 针对此问题, 设计一种环境Pareto 支配的选择策略, 并基于此提出用于解决有约束多目标问题的差分进化算法. 对经典测试函数进行仿真计算, 结果表明, 与其他算法相比, 所提出的算法具有更高的收敛性和稳定性.

     

超密集网络中基于多基站博弈均衡的分布式无线资源管理算法

移动边缘计算和超密集网络技术在扩大移动设备计算能力和增加网络容量方面有明显的优势.然而,在两者融合的场景下,如何有效降低基站之间的同信道干扰,减少任务传输的时延和能耗是一个重要研究课题.本文设计了一个基于多基站博弈均衡的分布式无线资源管理算法.将小基站之间的无线资源管理问题转化为博弈问题,提出一种基于奖励驱动的策略选择算法.基站通过迭代不断更新其策略的选择概率,最终优化子信道分配和发射功率的调控.仿真结果表明,我们的算法在提高信道利用率和降低任务处理的时延和能耗方面具有优势.     

一种面向多Agent交互的博弈Nash均衡求解方法

现有的图型博弈Nash均衡求解方法基本是在离散化剖面空间中搜索求解,最终只能得到近似Nash均衡。针对现有求解方法存在的不足,把求解图型博弈的Nash均衡看作是连续策略空间中的函数优化问题,定义Agents在策略剖面中的效用偏离度之和为优化目标,其最优解就是博弈的Nash均衡。本文基于对实例的分析指出目标函数下降梯度的计算可归结为一组线性规划,进而提出一种求解图型博弈Nash均衡的新型梯度下降算法。算法分析及实验研究表明,对于多Agent交互模型中的相关问题,本文提出的方法可求解任意图结构图型博弈Nash均衡,对于大规模图型博弈也有较好的求解精度和求解效率。     

Pareto group structure in a multicriteria optimization problem

A multicriteria choice problem is considered. It is proposed to solve this problem by requiring the solution to be invariant under a certain group of transformations. Groups of transformations of a linear space that preserve the Pareto order in this space are investigated. The maximum group of such transformations is calculated up to group isomorphism. The most interesting discrete and continuous subgroups of the Pareto group are considered.     

Numerical Construction of Stackelberg Solutions in a Linear Positional Differential Game Based on the Method of Polyhedra

We consider the problem of constructing approximate Stackelberg solutions in a linear non-zero-sum positional differential game of two players with terminal payoffs and player controls chosen on convex polyhedra. A formalization of player strategies and motions generated by them is based on the formalization and results of the theory of zero-sum positional differential games developed by N.N. Krasovskii and his scientific school. The problem of finding a Stackelberg solution reduces to solving nonstandard optimal control problems. We propose an approach based on operations with convex polyhedra.     

基于微分博弈的移动目标防御最优策略

目前,针对移动目标防御最优策略研究大多采用经典单/多阶段博弈和Markov博弈模型,无法在连续实时网络攻防对抗中进行灵活决策.为实现实时选取最优移动目标防御策略,在研究节点级传染病模型与微分博弈理论的基础上,提出了一种移动目标防御微分博弈模型,对网络空间重要节点构造安全状态演化方程与攻防收益目标函数,并设计开环纳什均衡求解算法以得出最优防御策略.仿真结果表明,该方法可有效对网络攻击进行实时防御,并且可针对网络关键节点制定相应移动目标防御策略.