多随从诱导策略

本文研究多随从诱导问题.当随从进行Nash不合作对策时,得到了连续诱导策略的一 个存在性充分条件与一种设计方法;当随从进行Nash协商对策时,得到了仿射型和连续型 诱导策略的存在性充分条件与设计方法.     

从方具有多目标的仿射型诱导策略研究

本文讨论当从方具有多个目标，主方对从方的诱地策略设计问题，给出了最优诱导策略和可诱导域的定义，研究了仿射型诱导策略的存在条件及解的结构形式，并探讨了当主方只具有对从方决策的部分观测时的诱导问题。     

多随从非线性诱导策略

利用不变凸性的性质研究静态多随从诱导问题,得到了一类非线性诱导策略的存在性条 件.     

鼓励性策略的存在与构造

本文通过一种凸分析方法,证明了当随从的目标函数是凸函数时,鼓励性策略存在。文中讨论了鼓励性策略的构造。     

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。     

多组对策系统非劣Nash策略的最优均衡解算法

多组对策系统中求解组与组之间的非劣Nash策略至关重要.如何针对一般问题解析求出非劣Nash策略还没有有效的方法.本文阐述了一种利用组与组之间的非劣反应集构造求解非劣Nash策略的迭代算法.为此首先引进多组对策系统组内部合作对策的最优均衡值和最优均衡解的概念,然后通过证明最优均衡解是组内部隐含某一权重向量的合作对策的非劣解,得到求解合作对策的单目标规划问题.进一步说明在组内部该问题的解不仅是非劣解而且对所有局中人都优于不合作时的Nash平衡策略.最后给出了验证该算法有效性的一个实际例子.     

基于粒子群算法的粗糙博弈模型与算法设计

连续博弈中至少存在一个混合策略Nash均衡,但是关于无限策略混合策略Nash均衡的解法,以及局中人的策略集或是效益函数是不确定性博弈均衡问题,国内外相关的研究成果还比较少。运用粒子群算法对目标函数没有严格要求,参数较少,编码简单的优势,创立了一种计算无限策略混合策略的近似算法;并在此基础上提出了粗糙博弈论的概念,以粗糙集和Vague集的理论为基础,发现了一种粗糙博弈论转化为经典博弈论的方法。无限策略混合策略Nash均衡的近似算法和粗糙博弈论的研究为策略集和效益函数不确定时的博弈问题提供了理论依据。算法示例结果表明,基于改进的粒子群算法的无限策略混合策略Nash均衡近似算法和粗糙博弈论的解法是有效可行的。     

不确定非线性系统的鲁棒耗散性与保性能控制

考虑了不确定仿射非线性系统的鲁棒耗散性与保性能控制问题,不确定性范数有界,不满足匹配条件.基于HJI不等式,设计了状态反馈控制器.当扰动存在时,控制器能使系统达到耗散,当扰动为零时,所设计的控制器使系统对于给定的性能函数具有上界,最后研究了不确定线性系统的保性能与耗散性控制情形.     

基于Nash平衡点的网络收益优化策略

研究了非合作用户的网络定价问题．将对策论中主从策略的思想应用到定价策略中，首先分析了在Nash平衡态下使主方收益达到最大时价格所满足的条件；然后结合网络市场的供求关系，将Nash平衡点视为供求平衡点，从而确定了相应的价格；最后以数值例子得出Nash平衡态下用户的速率和网络的收益．结果表明，合理的价控策略能够激发用户合理地使用网络资源，同时给管理者带来最优收入．     

脉动阵列变换的搜索策略及自动化算法*

对于多重循环中,当内层迭代的上下界为外层迭代的仿射函数时,介绍了搜索脉动变换的一个优化策略和相应的自动化算法.     

Pareto-optimal Nash equilibrium: Sufficient conditions and existence in mixed strategies

This paper considers the Nash equilibrium strategy profiles that are Pareto optimal with respect to the rest Nash equilibrium strategy profiles. The sufficient conditions for the existence of such pure strategy profiles are established. These conditions employ the Germeier convolutions of the payoff functions. For the non-cooperative games with compact strategy sets and continuous payoff functions, the existence of the Pareto optimal Nash equilibria in mixed strategies is proved.     

Theoretical and Experimental Investigation of Driver Noncooperative-Game Steering Control Behavior

This paper investigates two noncooperative-game strategies which may be used to represent a human driver's steering control behavior in response to vehicle automated steering intervention.The first strategy,namely the Nash strategy is derived based on the assumption that a Nash equilibrium is reached in a noncooperative game of vehicle path-following control involving a driver and a vehicle automated steering controller.The second one,namely the Stackelberg strategy is derived based on the assumption that a Stackelberg equilibrium is reached in a similar context.A simulation study is performed to study the differences between the two proposed noncooperativegame strategies.An experiment using a fixed-base driving simulator is carried out to measure six test drivers'steering behavior in response to vehicle automated steering intervention.The Nash strategy is then fitted to measured driver steering wheel angles following a model identification procedure.Control weight parameters involved in the Nash strategy are identified.It is found that the proposed Nash strategy with the identified control weights is capable of representing the trend of measured driver steering behavior and vehicle lateral responses.It is also found that the proposed Nash strategy is superior to the classic driver steering control strategy which has widely been used for modeling driver steering control over the past.A discussion on improving automated steering control using the gained knowledge of driver noncooperative-game steering control behavior was made.     

线性时变二次微分对策Nash策略的小波分析法(Ⅱ)——小波逼近解的收敛性

研究小波逼近分析方法的收敛性问题, 对线性时变二次微分对策Nash策略情形, 证明了Nash策略的小波逼近解收敛于精确解, 基于小波逼近的多尺度多分辨特性, 给出了误差估计的阶数.     

Distributed Nash Equilibrium Seeking for General Networked Games With Bounded Disturbances

This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information. First, reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with first-order and second-order players, respectively. In the developed algorithms, the observed disturbance values are included in control signals to eliminate the influence of disturbances, based on which a gradient-like optimization method is implemented for each player. Second, a signum function based distributed algorithm is proposed to attenuate disturbances for games with second-order integrator-type players. To be more specific, a signum function is involved in the proposed seeking strategy to dominate disturbances, based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players’ objective functions. Through Lyapunov stability analysis, it is proven that the players’ actions can approach a small region around the Nash equilibrium by utilizing disturbance observer-based strategies with appropriate control gains. Moreover, exponential (asymptotic) convergence can be achieved when the signum function based control strategy (with an adaptive control gain) is employed. The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform (V-REP) and MATLAB.      

考虑广告投入影响的再制造闭环供应链优化决策博弈模型研究

针对制造/再制造产品的市场竞争与合作问题, 考虑广告投入对产品消费者效用的增长效应及消费者环境偏好的影响, 在构建制造产品和再制造产品的市场需求函数基础上, 应用博弈方法比较分析合作博弈、纳什均衡博弈、Stackelberg主从博弈三种决策模式下制造/再制造产品的最优定价和广告投入策略, 并针对非合作博弈下的效率损失设计了闭环供应链中制造和再制造过程的利益协调机制。数值算例分析表明, 合作博弈决策下供应链总利润最优、制造和再制造产品市场销售价格最高, 而合作博弈和Stackelberg主从博弈都会以牺牲再制造产品利润为代价获得最优利润, 因此再制造部门会偏好纳什均衡博弈, 采取以自身利益最优为目标的竞争策略, 没有动机成为制造部门的跟随者。     

Road Pricing Design Based on Game Theory and Multi-agent Consensus

Consensus theory and noncooperative game theory respectively deal with cooperative and noncooperative interactions among multiple players/agents. They provide a natural framework for road pricing design, since each motorist may myopically optimize his or her own utility as a function of road price and collectively communicate with his or her friends and neighbors on traffic situation at the same time. This paper considers the road pricing design by using game theory and consensus theory. For the case where a system supervisor broadcasts information on the overall system to each agent, we present a variant of standard fictitious play called average strategy fictitious play (ASFP) for large-scale repeated congestion games. Only a weighted running average of all other players' actions is assumed to be available to each player. The ASFP reduces the burden of both information gathering and information processing for each player. Compared to the joint strategy fictitious play (JSFP) studied in the literature, the updating process of utility functions for each player is avoided. We prove that there exists at least one pure strategy Nash equilibrium for the congestion game under investigation, and the players' actions generated by the ASFP with inertia (players' reluctance to change their previous actions) converge to a Nash equilibrium almost surely. For the case without broadcasting, a consensus protocol is introduced for individual agents to estimate the percentage of players choosing each resource, and the convergence property of players' action profile is still ensured. The results are applied to road pricing design to achieve socially local optimal trip timing. Simulation results are provided based on the real traffic data for the Singapore case study.      

N人合作博弈的Nash及演化均衡稳定策略分析

在有限理性的基础上,对N人合作博弈的对称Nash均衡进行了分析,并引入演化博弈理论分析了参与人的演化均衡稳定策略,得到了不同策略选择下的均衡点。进而应用生物复制动态理论对离散时间及连续时间下的复制动态稳定集进行了研究。最后通过实例说明了该方法在博弈均衡选择上的有效性。     

Fully Distributed Nash Equilibrium Seeking for High-Order Players With Actuator Limitations

This paper explores the problem of distributed Nash equilibrium seeking in games, where players have limited knowledge on other players’ actions. In particular, the involved players are considered to be high-order integrators with their control inputs constrained within a pre-specified region. A linear transformation for players’ dynamics is firstly utilized to facilitate the design of bounded control inputs incorporating multiple saturation functions. By introducing consensus protocols with ada...     

Matrix games with missing,interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

In a matrix game, the interactions among players are based on the assumption that each player has accurate information about the payoffs of their interactions and the other players are rationally self‐interested. As a result, the players should definitely take Nash equilibrium strategies. However, in real‐life, when choosing their optimal strategies, sometimes the players have to face missing, imprecise (i.e., interval), ambiguous lottery payoffs of pure strategy profiles and even compound strategy profile, which means that it is hard to determine a Nash equilibrium. To address this issue, in this paper we introduce a new solution concept, called ambiguous Nash equilibrium, which extends the concept of Nash equilibrium to the one that can handle these types of ambiguous payoff. Moreover, we will reveal some properties of matrix games of this kind. In particular, we show that a Nash equilibrium is a special case of ambiguous Nash equilibrium if the players have accurate information of each player's payoff sets. Finally, we give an example to illustrate how our approach deals with real‐life game theory problems.