Generalized Cournot-Stackelberg-Nash equilibrium

The concept of the Cournot-Stackelberg-Nash equilibrium is proposed in which the leader’s payoff is no less than its payoff in the case of the Cournot-Nash equilibrium and the follower’s payoff is no less than its payoff in the case of the Stackelberg-Nash equilibrium. The generalized equilibrium coincides with the Cournot-Nash and Stackelberg-Nash equilibria for extreme values of a parameter. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 3–9, January–February 2006.     

基于博弈论的降低市场力策略

在电力市场中的一个很重要的研究课题就是如何有效的控制和降低市场力，杜绝各种不同合理现象的发生，博弈论就是一个很有效的方法，本文主要针对基于博弈论的降低市场力的策略进行了探讨，提出了工于博弈论的降低市场力模型，并通过该模型对差价和约进行了分析。     

输电网投资规划的Nash均衡分析(二)——混合策略Nash均衡的分析

在输电设备投资博弈中，有可能会出现纯策略Nash均衡不存在或多个Nash均衡同时存在的情况，这对投资主体的决策造成困难。为此，文中引入了混合策略的概念，并以改进的遗传算法为基础，提出了一种适用于输电投资博弈的均衡分析方法，为投资者的进一步决策提供了依据。研究结果表明，在无法确定纯策略Nash衡点时，混合策略均衡点能以概率的形式预见参与各方的投资行为，并进一步说明了在输电投资博弈中各投资者采取的决略确是相互影响的，任何一方的投资数据有所改动，均会影响博弈的最终结果。     

状态无关主动队列管理算法博弈的Nash均衡

状态无关的主动队列管理算法处理分组时不区分分组所在的流的信息,因此在Internet中,它易于设计和部署。文中通过数学分析和仿真方法研究AQM博弈和Nash均衡存在性。假设业务流是Poisson分布的且用户可自由修改发送速率,因而有结论:Drop Tail、RED不能获得Nash均衡,CHOKe可以获得近似Nash均衡。依据判定条件,推导出一种与状态无关且具有效率的Nash均衡AQM算法。     

基于博弈论的P2P系统分析

P2P系统近几年来在网络上有飞速的发展,然而随着用户对网络和P2P系统的了解,使得P2P系统中大量存在欺骗行为,从而导致效率下降。文中以解决P2P系统中的欺骗为目的,通过引入博弈论思想从宏观和微观两方面对P2P系统进行分析:宏观上通过建立数学模型分析P2P系统效率下降甚至崩溃的原因;微观上,通过合理的论证,提出一种以牙还牙机制对P2P系统的欺骗问题进行解决。     

网络路由研究中的博弈论思想

对调整路由过程中存在的一个非合作非零和的动态博弈模型进行了深入的探讨，使之达到一个均衡，使得任何用户不会单方面改变路由策略从而获得更好的性能。分析了两种交互过程以及当前在自私路由中求解均衡的建模方法，对路由研究中的博弈论思想做了进一步的探讨，从而得到求解均衡的一般方法。     

考虑恢复力与经济性均衡的配电网移动储能优化配置策略

近年来风涝等极端自然灾害频发，灾后配电网生命线负荷的持续供电面临严峻挑战。针对台风灾害下配电网灾损难以准确评估、配电网恢复力与经济性难以兼顾的现状，结合台风历史数据与致灾机理，建立了同时考虑台风与暴雨的数据-机理联合驱动的台风下配电网故障率模型；针对极端灾害数据少、预测精度低的问题，利用φ散度获得灾害持续时间的条件风险价值(CVaR)；将移动储能容量作为决策变量，利用纳什谈判方法构建配电网经济性和恢复力均衡模型，实现了对于恢复力和经济性的综合考虑。通过算例测试验证了所提策略的有效性。     

Linear quadratic Nash game-based tracker for multiparameter singularly perturbed sampled-data systems: digital redesign approach

In this paper, a linear quadratic Nash game-based tracker for multiparameter singularly perturbed sample-data systems is developed. A generalized cross-coupled multiparameter algebraic Riccati equation (GCMARE) with two quadratic cost functions is solved by applying the LQR design methodology for the optimal tracker design. Firstly, the asymptotic expansions of the GCMARE are newly established, and the proposed algorithm is able to effectively solve the GCMARE with the quadratic convergence rate. Then, the low-gain digital controller with a high design performance is realized through the prediction-based digital redesign method. Finally, for further improving the tracking performance, the chaos-evolutionary-programming algorithm (CEPA) is utilized to optimally tune the parameters of the tracker. An example is presented to demonstrate the effectiveness of the proposed methodology.     

Equilibrium joining strategies in the single server queues with negative customers

We consider an M/M/1 queue with negative customers. An arriving negative customer will break the server down and the positive customer being served (if any) is forced to leave the system. Once a breakdown occurs, the server is sent immediately for repair while positive customers are not allowed to join the system during the repair process. When the server is available, positive arrivals decide whether to join or balk the system based on a common reward-cost structure. We consider an observable case that the positive arrivals are informed about the number of customers in the system and an unobservable case without any information. The corresponding Nash equilibrium strategies and the socially optimal joining strategies are explored. We get a socially optimal threshold in the observable case and a mixed joining strategy in the unobservable case. The profit maximization issue is studied, and we derive optimal strategies in two information cases. Finally, numerical examples are provided to show the influence of different parameters on the strategies and social benefit.