802.11网络中基于博弈理论的可变带宽信道分配研究

802.11网络中节点的理性和自私性导致可变带宽信道分配的低公平性、低负载均衡性及低社会效率问题.基于非合作博弈理论将可变带宽信道分配问题建模成策略型博弈模型.首先,给出问题的纳什均衡分配策略,证明了纳什均衡点的存在;然后,针对纳什均衡策略社会效率低的问题,提出一种基于支付的激励机制,使可变带宽信道分配过程收敛到占优决策均衡状态,从而系统整体吞吐量性能达到全局最优;并分析了上述两种策略的公平性和负载均衡问题;最后,给出达到纳什均衡和全局最优状态的可变带宽信道分配算法.仿真结果表明,纳什均衡策略能够获得好的公平性,而全局最优策略的负载均衡和社会效率性能要优于纳什均衡策略.     

博弈论在感知无线电决策机的应用研究

为了使决策机进行策略分析,得到最优的策略,对感知循环、博弈理论以及基于博弈的感知无线电决策机进行了分析.对感知无线电博弈模型中的游戏者、行为、收益等做了相应定义,并针对Neel的决策模型的局限进行了研究.对于多游戏者、多行为、以及多均衡等问题,Neel模型不能很好解决.通过博弈案例的求解分析了多纳什均衡解情况,说明只依靠博弈理论无法得到最优策略,并提出了解决问题的思路.     

Ad Hoc网络中基于重复博弈的攻击预测模型

大多数入侵检测系统预测攻击行为能力较弱,不能实时主动地响应攻击。针对该问题,提出一种基于重复博弈的攻击预测模型。通过建立入侵者和入侵检测系统之间的阶段博弈模型,给出阶段博弈的纳什均衡,并求出重复博弈情况下的子博弈精炼纳什均衡。使用QRE模型预测攻击者和防御者在博弈阶段1~t中选择各种策略的概率,利用Gambit分析得出预测结果。基于GloMoSim的仿真结果表明,相比纳什均衡模型,QRE均衡模型的预测效果更好。     

基于博弈论的动态频谱分配技术研究

提出了一种改进的动态频谱分配博弈模型,对现有的频谱定价函数进行改进,在授权用户对单位频谱价格满意的条件下,频谱价格与授权用户提供带宽数量和次用户的频谱需求数量有关。此外,在次用户的效用函数中,考虑了频谱置换参数,并分析了置换参数和信道质量对次用户动态博弈以及次用户达到纳什均衡的影响。最后,分别用静态博弈和动态博弈分析了次用户之间的竞争频谱行为,并通过仿真验证,次用户的策略最终可以收敛到纳什均衡。     

非合作博弈均衡在确定性Ad hoc网络中的应用

首先介绍了非合作博弈均衡(纳什均衡),并将纳什均衡的基本原理应用到Ad hoc网络中节点间的数据传输中,对采用纳什均衡的几种常用的策略也做了介绍,并着重对其中的TFT策略进行了讨论.并用"Small World"这一概念替代传统的"最短路径"概念,同时对Small-World做了介绍.随后针对Ad hoc网络的某些拓扑结构,将"纳什均衡"策略和目前其他一些激励机制进行了比较和讨论.认为在目前的Ad hoc网络中,非合作博弈均衡(纳什均衡)是比较理想,比较简单的一种分组传输策略.     

基于不完全信息动态博弈的入侵容忍技术

为了使入侵容忍系统和可疑者进行最优的策略选择,提出了基于不完全信息动态博弈的入侵容忍技术.根据博弈双方的特点,引入两人随机博弈模型进行分析,并通过精炼贝叶斯纳什均衡来确定双方选择最优的策略.同时为了能够确定可疑者类型,采用熵权和灰色关联分析的方法来进行推理.结合实例使用各种行为特征值来计算灰色关联度,从而在博弈过程中判断可疑者是黑客的概率,验证了该方法的可行性和客观性,从而更好地帮助入侵容忍系统进行策略选择.     

基于完全信息博弈的"沙漠掘金"游戏策略

为寻求益智类游戏"沙漠掘金"在多人参与下的游戏策略,针对具体的游戏规则进行了深入的分析,分别提出了基于完全信息静态博弈与完全信息动态博弈的游戏策略.首先,通过简化游戏规则将其转变为一个非合作博弈问题.其次,考虑单人游戏中的最优化问题,分析单人游戏的策略并在此基础上采用博弈论的方法对多人游戏的情况进行求解.最后,针对第一关,满足完全信息静态博弈的情况,模拟玩家行动,得出博弈支付矩阵,通过混合策略纳什均衡的方法计算最优策略;针对第二关,满足完全信息动态博弈的情况,构建博弈树并通过逆向递归求解得出最佳的游戏攻略,并分析了多人竞争策略.     

基于完全信息博弈的"沙漠掘金"游戏策略

为寻求益智类游戏"沙漠掘金"在多人参与下的游戏策略,针对具体的游戏规则进行了深入的分析,分别提出了基于完全信息静态博弈与完全信息动态博弈的游戏策略.首先,通过简化游戏规则将其转变为一个非合作博弈问题.其次,考虑单人游戏中的最优化问题,分析单人游戏的策略并在此基础上采用博弈论的方法对多人游戏的情况进行求解.最后,针对第一关,满足完全信息静态博弈的情况,模拟玩家行动,得出博弈支付矩阵,通过混合策略纳什均衡的方法计算最优策略;针对第二关,满足完全信息动态博弈的情况,构建博弈树并通过逆向递归求解得出最佳的游戏攻略,并分析了多人竞争策略.     

异构无线网络用户网络关联优化:一种基于群体博弈的方法

针对异构无线网络(Heterogeneous Wireless Networks,HWNs)负载平衡问题,提出了一种基于群体博弈的用户网络关联方案.首先将HWNs系统用户网络关联问题抽象成一个群体博弈模型,根据用户在网络中得到的收益函数,证明该群体博弈满足势博弈的条件.利用复制动态作为演化动态工具,证明演化的结果最终会收敛到纳什均衡,这个特性确保了每个用户关联到一个效用最优的网络.然后证明纳什均衡点能最大化整个HWNs系统的吞吐量,保证了纳什均衡的有效性.最后,基于复制动态原理提出了用户网络关联算法.仿真实验模拟了用户网络选择过程,得到了均衡点,验证了理论分析的结果.     

无线自组网中节点协作的纳什均衡研究

根据自私节点的特性,提出节点协作的博弈模型。针对单阶段博弈及采取礼尚往来策略、冷酷策略、单步触发策略的重复博弈,分析并比较实现节点协作的纳什均衡条件。结果表明,单阶段博弈中自私节点的纳什均衡类似于囚徒困境,重复博弈采用礼尚往来策略时,实现最佳纳什均衡的临界值最小,相比其他策略更易实现协作。     

Equilibrium Trajectories in Dynamical Bimatrix Games with Average Integral Payoff Functionals

This paper considers models of evolutionary non-zero-sum games on the infinite time interval. Methods of differential game theory are used for the analysis of game interactions between two groups of participants. We assume that participants in these groups are controlled by signals for the behavior change. The payoffs of coalitions are defined as average integral functionals on the infinite horizon. We pose the design problem of a dynamical Nash equilibrium for the evolutionary game under consideration. The ideas and approaches of non-zero-sum differential games are employed for the determination of the Nash equilibrium solutions. The results derived in this paper involve the dynamic constructions and methods of evolutionary games. Much attention is focused on the formation of the dynamical Nash equilibrium with players strategies that maximize the corresponding payoff functions and have the guaranteed properties according to the minimax approach. An application of the minimax approach for constructing optimal control strategies generates dynamical Nash equilibrium trajectories yielding better results in comparison to static solutions and evolutionary models with the replicator dynamics. Finally, we make a comparison of the dynamical Nash equilibrium trajectories for evolutionary games with the average integral payoff functionals and the trajectories for evolutionary games with the global terminal payoff functionals on the infinite horizon.     

Multi-agent discrete-time graphical games and reinforcement learning solutions

This paper introduces a new class of multi-agent discrete-time dynamic games, known in the literature as dynamic graphical games. For that reason a local performance index is defined for each agent that depends only on the local information available to each agent. Nash equilibrium policies and best-response policies are given in terms of the solutions to the discrete-time coupled Hamilton–Jacobi equations. Since in these games the interactions between the agents are prescribed by a communication graph structure we have to introduce a new notion of Nash equilibrium. It is proved that this notion holds if all agents are in Nash equilibrium and the graph is strongly connected. A novel reinforcement learning value iteration algorithm is given to solve the dynamic graphical games in an online manner along with its proof of convergence. The policies of the agents form a Nash equilibrium when all the agents in the neighborhood update their policies, and a best response outcome when the agents in the neighborhood are kept constant. The paper brings together discrete Hamiltonian mechanics, distributed multi-agent control, optimal control theory, and game theory to formulate and solve these multi-agent dynamic graphical games. A simulation example shows the effectiveness of the proposed approach in a leader-synchronization case along with optimality guarantees.     

A game-theoretic and dynamical-systems analysis of selection methods in coevolution

We use evolutionary game theory (EGT) to investigate the dynamics and equilibria of selection methods in coevolutionary algorithms. The canonical selection method used in EGT is equivalent to the standard "fitness-proportional" selection method used in evolutionary algorithms. All attractors of the EGT dynamic are Nash equilibria; we focus on simple symmetric variable-sum games that have polymorphic Nash-equilibrium attractors. Against the dynamics of proportional selection, we contrast the behaviors of truncation selection, (/spl mu/,/spl lambda/),(/spl mu/+/spl lambda/), linear ranking, Boltzmann, and tournament selection. Except for Boltzmann selection, each of the methods we test unconditionally fail to achieve polymorphic Nash equilibrium. Instead, we find point attractors that lack game-theoretic justification, cyclic dynamics, or chaos. Boltzmann selection converges onto polymorphic Nash equilibrium only when selection pressure is sufficiently low; otherwise, we obtain attracting limit-cycles or chaos. Coevolutionary algorithms are often used to search for solutions (e.g., Nash equilibria) of games of strategy; our results show that many selection methods are inappropriate for finding polymorphic Nash solutions to variable-sum games. Another application of coevolution is to model other systems; our results emphasize the degree to which the model's behavior is sensitive to implementation details regarding selection-details that we might not otherwise believe to be critical.     

Nash equilibria in risk-sensitive dynamic games

Dynamic games in which each player has an exponential cost criterion are referred to as risk-sensitive dynamic games. In this note, Nash equilibria are considered for such games. Feedback risk-sensitive Nash equilibrium solutions are derived for two-person discrete time linear-quadratic nonzero-sum games, both under complete state observation and shared partial observation     

The Nash Equilibrium Point of Dynamic Games Using Evolutionary Algorithms in Linear Dynamics and Quadratic System

In this paper, examining some games, we show that classical techniques are not always effective for games with not many stages and players and it can’t be claimed that these techniques of solution always obtain the optimal and actual Nash equilibrium point. For solving these problems, two evolutionary algorithms are then presented based on the population to solve general dynamic games. The first algorithm is based on the genetic algorithm and we use genetic algorithms to model the players' learning process in several models and evaluate them in terms of their convergence to the Nash Equilibrium. in the second algorithm, a Particle Swarm Intelligence Optimization (PSO) technique is presented to accelerate solutions’ convergence. It is claimed that both techniques can find the actual Nash equilibrium point of the game keeping the problem’s generality and without imposing any limitation on it and without being caught by the local Nash equilibrium point. The results clearly show the benefits of the proposed approach in terms of both the quality of solutions and efficiency.     

Complex dynamics and synchronization of a duopoly game with bounded rationality

A dynamic Cournot game characterized by players with bounded rationality is modeled by two non-linear difference equations. The stability of the equilibria of the discrete dynamical system is analyzed. As some parameters of the model are varied, the stability of Nash equilibrium is lost and the complex chaotic behavior occurs. Synchronization of two dynamic Cournot duopoly games are considered. In the case of identical players, such dynamical system becomes symmetric, and this implies that synchronized dynamics can be obtained by a simpler one-dimensional model whose dynamics summarizes the common behavior of the two identical players.     

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。     

基于微分对策的供应链合作广告决策研究

针对供应链系统中制造商和零售商的合作广告计划问题，利用微分对策构建动态模型．分别研究制造商和零售商在合作和非合作条件下的广告策略．运用动态规划原理。分别得出静态反馈Nash均衡和反馈Stackelberg均衡，将两种均衡策略加以比较，结果显示合作广告计划是供应链系统中的一种协调和激励机制，可以提高两个渠道成员以及整个供应链系统的利润。     

On the Structure of Weakly Acyclic Games

The class of weakly acyclic games, which includes potential games and dominance-solvable games, captures many practical application domains. In a weakly acyclic game, from any starting state, there is a sequence of better-response moves that leads to a pure Nash equilibrium; informally, these are games in which natural distributed dynamics, such as better-response dynamics, cannot enter inescapable oscillations. We establish a novel link between such games and the existence of pure Nash equilibria in subgames. Specifically, we show that the existence of a unique pure Nash equilibrium in every subgame implies the weak acyclicity of a game. In contrast, the possible existence of multiple pure Nash equilibria in every subgame is insufficient for weak acyclicity in general; here, we also systematically identify the special cases (in terms of the number of players and strategies) for which this is sufficient to guarantee weak acyclicity.     

Sampled fictitious play for approximate dynamic programming

Sampled fictitious play (SFP) is a recently proposed iterative learning mechanism for computing Nash equilibria of non-cooperative games. For games of identical interests, every limit point of the sequence of mixed strategies induced by the empirical frequencies of best response actions that players in SFP play is a Nash equilibrium. Because discrete optimization problems can be viewed as games of identical interests wherein Nash equilibria define a type of local optimum, SFP has recently been employed as a heuristic optimization algorithm with promising empirical performance. However, there have been no guarantees of convergence to a globally optimal Nash equilibrium established for any of the problem classes considered to date. In this paper, we introduce a variant of SFP and show that it converges almost surely to optimal policies in model-free, finite-horizon stochastic dynamic programs. The key idea is to view the dynamic programming states as players, whose common interest is to maximize the total multi-period expected reward starting in a fixed initial state. We also offer empirical results suggesting that our SFP variant is effective in practice for small to moderate sized model-free problems.