基于PSO优化博弈的区块链共识算法

针对现有的区块链共识算法存在决策不均衡、适用性过小和产生共识困难等问题,根据纳什均衡理论,将区块链节点视为博弈的参与者,在共识过程中将节点策略选择的纳什均衡作为共识目标,提出基于纳什均衡的共识算法.在纳什均衡求解中利用聚类算法对同类型节点聚类,用基于拥挤距离和引力搜索算法改进的粒子群优化算法求解以类为基本种群的纳什均衡近似解,将均衡解下所对应的结果作为主节点.设计面向组合投资区块链系统求解共识机制的实验,分别从算法的安全性和扩展性验证该算法的有效性.     

纳什均衡解及其QPSO算法求解

纳什均衡是一种博弈的解的概念,可以对非常广泛类型的博弈作出严格的多的预测。具有量子行为的粒子群算法是一种能够较好的解决优化问题的算法,它是在粒子群算法的基础上发展起来的。本文讨论纳什均衡解,并利用QPSO算法来求解纳什均衡解。通过仿真算法及与几种算法的比较结果验证了算法的有效性,证明了算法的全局收敛性。     

考虑非线性奖惩机制的多主体主从博弈模型

本文针对以往电价机制仅由供方主导而缺乏电能供需双向调节功能的缺点问题,构建了一个考虑双边非线性奖惩机制的电力市场多主体主从博弈模型,以实现市场多主体的利益均衡.首先,在零售端提出了一种由供需双方共同参与且具有动态奖惩激励的电价机制.其次,在此基础上构建了一个以零售商为领导者、用户为跟随者的主从博弈模型,同时利用演化博弈描述用户的动态选择过程.然后,证明了该主从博弈模型纳什均衡解的存在性,并设计了分布式算法进行求解.最后,通过算例分析证明了本文所提博弈模型的合理性,并验证了电价机制在引导用户合理用电、保证供需平衡以及实现成本节约等方面的有效性;同时仿真结果表明给出的分布式求解算法具有较快的收敛速度和良好的稳定性能.     

基于非策略Q学习方法的两个个体优化控制

针对线性离散时间系统的非零和博弈问题,提出一种非策略Q学习算法。首先,提出非零和博弈优化问题,并且严格证明根据每个个体性能指标定义的值函数为线性二次型。然后,基于动态规划和Q学习方法,给出非策略Q学习算法,得到非零和博弈的近似最优解,实现系统的全局纳什均衡。此算法不要求系统模型参数已知,完全利用可测数据学习纳什均衡解。最后,算例仿真验证了方法的有效性。     

基于博弈模型的合作式粒子群优化算法

粒子群算法作为一种新兴的进化优化方法,能够大大减轻复杂的大规模优化问题的计算负担. 根据博弈论的思想,在传统粒子群基础上提出了一种基于博弈模型的合作式粒子群优化算法,算法基于重复博弈模型,在重复博弈中利用一个博弈序列,使得每次博弈都能够产生最大效益,并得到了相应博弈过程的纳什均衡. 通过典型基准测试函数对算法的性能进行对比实验,实验结果表明算法是可行的、有效的,对拓展粒子群算法研究具有重要的理论意义与实际意义.     

资源受限移动边缘计算任务拆分卸载调度决策

研究带有计算访问点的多用户移动边缘计算环境中的多任务调度与卸载决策问题。为了降低移动设备端的能耗,并确保用户任务的延时需求,提出一种基于博弈论的任务卸载决策算法。为了求解博弈模型,将卸载博弈模型转换为势博弈模型,进而证明博弈存在纳什均衡解,并设计一种基于有限改进性质的分布式博弈方法寻找该纳什均衡解。实验结果证明,在不同的起始策略组合条件下,该博弈算法可以得到相对于对比算法更接近于理论最优解的系统总体最优代价。     

认知无线电中基于博弈论的频谱分配算法*

利用博弈论分析了认知无线电网络中动态频谱分配问题,构建了基于博弈论的认知无线电频谱分配问题模型,提出了基于潜在博弈论的分布式频谱分配算法,并得到了相应博弈过程的纳什均衡。仿真结果表明,该算法能在较短时间内收敛到稳定状态,潜在函数取值达到最大值、系统总干扰水平降到最小、用户的SIR水平得到明显改善,达到了潜在博弈下信道分配的纳什均衡,实现了提高频谱利用率的目的。     

基于博弈论的隐私保护分布式数据挖掘

隐私保护的分布式数据挖掘问题是数据挖掘领域的一个研究热点,而基于经济视角,利用博弈论的方法对隐私保护分布式数据挖掘进行研究只是处于初始阶段。基于收益最大化,研究了完全信息静态博弈下分布式数据挖掘中参与者(两方或多方)的策略决策问题,得出了如下结论:数据挖掘在满足一定的条件下,参与者(两方或多方)的准诚信攻击策略是一个帕累托最优的纳什均衡策略;在准诚信攻击的假设下,参与者(多方)的非共谋策略并不是一个纳什均衡策略。同时给出了该博弈的混合战略纳什均衡,它对隐私保护分布式数据挖掘中参与者的决策具有一定的理论和指导意义。     

一种基于马尔可夫博弈的能量均衡路由算法

针对无线传感器网络中耗能不均问题,引入马尔可夫博弈理论,构建了无线传感器网络的马尔可夫博弈模型.在能量均衡路由分析的基础上,给出了一种基于马尔可夫博弈的能量均衡路由算法,该算法从无线传感器网络整体耗能出发,兼顾节点之间的合作.定义了能量和信誉值的二元收益函数,给出了节点转发的状态转移概率,根据收益函数进行能量调节,求解出能量和收益之间的均衡系数——纳什均衡,实现了节点能量的均衡消耗,延长了网络的生命周期.使用PRISM概率仿真工具进行仿真,验证了该博弈模型存在纳什均衡点,同时表明该模型能促进节点之间合作,最大化无线传感器网络的生命周期.     

基于非合作博弈的femtocell 双层网络分布式功率控制

研究在频谱共享条件下家庭基站双层网络的分布式功率控制策略.将宏基站所能承受的干扰限度视为家庭基站的可分配资源,家庭基站以竞价形式对其"购买",从而构成宏基站与家庭基站以及家庭基站用户之间的博弈模型.分析了该博弈过程中纳什均衡解的存在性和惟一性,并给出了在非合作模式下指导家庭基站用户进行理性竞争的分布式功率调整算法.最后,通过仿真实验验证了所提出算法的有效性.     

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.     

Distributed Nash Equilibrium Seeking for Aggregative Games via Derivative Feedback

In this paper, we investigate a continuous-time distributed Nash equilibrium seeking algorithm for a class of aggregative games, with application to the re     

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.     

基于改进蚁群算法的纳什均衡求解

在基本蚁群算法寻优机制的基础上,提出一种用于求解有限n人非合作博弈的纳什均衡解的改进蚁群算法。在全局搜索中,引入遗传算法中的交叉和变异操作提高算法的全局搜索能力。在局部搜索中,嵌入动态随机搜索技术使算法加速收敛到最优解,并通过引入控制步长调整随机搜索向量,保证蚁群始终在混合策略空间内。算例测试结果表明,与传统的遗传算法相比,该算法具有更好的计算性能。     

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.      

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。     

Multi-agent graphical games with input constraints: an online learning solution

This paper studies an online iterative algorithm for solving discrete-time multi-agent dynamic graphical games with input constraints. In order to obtain the optimal strategy of each agent, it is necessary to solve a set of coupled Hamilton-Jacobi-Bellman (HJB) equations. It is very difficult to solve HJB equations by the traditional method. The relevant game problem will become more complex if the control input of each agent in the dynamic graphical game is constrained. In this paper, an online iterative algorithm is proposed to find the online solution to dynamic graphical game without the need for drift dynamics of agents. Actually, this algorithm is to find the optimal solution of Bellman equations online. This solution employs a distributed policy iteration process, using only the local information available to each agent. It can be proved that under certain conditions, when each agent updates its own strategy simultaneously, the whole multi-agent system will reach Nash equilibrium. In the process of algorithm implementation, for each agent, two layers of neural networks are used to fit the value function and control strategy, respectively. Finally, a simulation example is given to show the effectiveness of our method.     

A Novel Distributed Optimal Adaptive Control Algorithm for Nonlinear Multi-Agent Differential Graphical Games

In this paper, an online optimal distributed learning algorithm is proposed to solve leader-synchronization problem of nonlinear multi-agent differential graphical games. Each player approximates its optimal control policy using a single-network approximate dynamic programming (ADP) where only one critic neural network (NN) is employed instead of typical actorcritic structure composed of two NNs. The proposed distributed weight tuning laws for critic NNs guarantee stability in the sense of uniform ultimate boundedness (UUB) and convergence of control policies to the Nash equilibrium. In this paper, by introducing novel distributed local operators in weight tuning laws, there is no more requirement for initial stabilizing control policies. Furthermore, the overall closed-loop system stability is guaranteed by Lyapunov stability analysis. Finally, Simulation results show the effectiveness of the proposed algorithm.      

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.     

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.