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 International Journal of Business and Management , 2009, Abstract: Nash games and Stackelberg games play crucial roles in game theory community. In this note, we consider the Nash games and Stackelberg games (leader-follower games) again. Based on game theory model, we point out that an equilibrium of Stackelberg games has not close relation with an equilibrium of Nash games, in which we compare the Stackelberg game with Nash game under the same condition.
 方宇娟,魏韡,梅生伟,刘锋 控制理论与应用 , 2018, DOI: 10.7641/CTA.2018.70669 Abstract: 本文构建了以热电联产机组(combined heat and power unit, CHP)、电力市场和热力市场为参与者的主从博 弈模型, 并基于电力市场中节点边际电价(locational marginal electricity price, LMEP)的概念, 提出了节点边际热价 (locational marginal heat price, LMHP)的概念. 在节点边际电价的求解中, 采用了支路潮流(branch power flow, BPF) 模型, 考虑了配电网中的网络损耗从而可以得到更精确的计算结果. 在节点边际热价的求解中, 考虑了管道热损耗, 并基于管道损耗方程分析了节点边际热价的分布规律. 在此基础上, 采用变步长迭代寻优算法求解热电联产机组、 电力市场、热力市场各自最优出力和最优报价策略. 最后, 通过一个6节点电网–4节点热网的算例对所构建的主从 博弈模型及热电联产机组的竞价策略进行了验证.Based on the concept of locational marginal electricity price (LMEP) in the electricity market, this paper proposes locational marginal heat price (LMHP). Then stackelberg game, whose participants are combined heat and power unit (CHP), electricity market and heat market, is established to solve the optimal bidding strategy of CHP in the combined heat and electricity market. Branch power flow (BPF) model is applied to obtain LMEPs. The power loss is considered in the district electricity network to calculate LMEPs accurately. Meanwhile, the heat loss is regarded in the solution of LMHPs. And the distribution law of LMHPs are analyzed based on the pipe heat loss functions. In this paper, a variablestep iterative optimization algorithm is introduced to solve the optimal generation and optimal bidding strategies for CHP, electricity market and heat market. Finally, a 6-node electrical 4-node heat network is presented in the case study to verify the stackelburg models and optimal bidding prices for CHPs.
 Computer Science , 2009, Abstract: This paper investigates inventory management in a multi channel distribution system consisting of one manufacturer and an arbitrary number of retailers that face stochastic demand. Existence of the pure Nash equilibrium is proved and parameter restriction which implies uniqueness of it is derived. Also the Stackelberg game where the manufacturer plays a roll as a leader is discussed. Under specified parameter restrictions which guarantee profitability, sufficient condition for uniqueness of Stackelberg equilibrium is obtained. In addition comparison with simultaneous move game is made. The result shows that when whole prices are equal to production cost, manufacturer carries more inventory than simultaneous move game. Keywords: Inventory management, Substitution, Nash equilibrium, Stackelberg equilibrium.
 AUCO Czech Economic Review , 2012, Abstract: We deal with n-person normal form games where a subset of players decide to cooperate (signatories) and choose strategies by maximizing the aggregate welfare of the coalition members as in International Environmental Agreements (IEA) context. The non-cooperating (non-signatories) players choose their strategies as a Nash equilibrium. In this paper the partial cooperative equilibrium (PCE) under the Nash-Cournot and the Stackelberg assumptions are considered and presented also in the case of non-signatories multiple decision. Some properties are discussed in both situations, particularly the profit of the players are compared.
 Computer Science , 2014, DOI: 10.1613/jair.3269 Abstract: There has been significant recent interest in game-theoretic approaches to security, with much of the recent research focused on utilizing the leader-follower Stackelberg game model. Among the major applications are the ARMOR program deployed at LAX Airport and the IRIS program in use by the US Federal Air Marshals (FAMS). The foundational assumption for using Stackelberg games is that security forces (leaders), acting first, commit to a randomized strategy; while their adversaries (followers) choose their best response after surveillance of this randomized strategy. Yet, in many situations, a leader may face uncertainty about the follower's surveillance capability. Previous work fails to address how a leader should compute her strategy given such uncertainty. We provide five contributions in the context of a general class of security games. First, we show that the Nash equilibria in security games are interchangeable, thus alleviating the equilibrium selection problem. Second, under a natural restriction on security games, any Stackelberg strategy is also a Nash equilibrium strategy; and furthermore, the solution is unique in a class of security games of which ARMOR is a key exemplar. Third, when faced with a follower that can attack multiple targets, many of these properties no longer hold. Fourth, we show experimentally that in most (but not all) games where the restriction does not hold, the Stackelberg strategy is still a Nash equilibrium strategy, but this is no longer true when the attacker can attack multiple targets. Finally, as a possible direction for future research, we propose an extensive-form game model that makes the defender's uncertainty about the attacker's ability to observe explicit.
 EURASIP Journal on Advances in Signal Processing , 2009, DOI: 10.1155/2009/305978 Abstract: Interactions among selfish users sharing a common transmission channel can be modeled as a noncooperative game using the game theory framework. When selfish users choose their transmission probabilities independently without any coordination mechanism, Nash equilibria usually result in a network collapse. We propose a methodology that transforms the noncooperative game into a Stackelberg game. Stackelberg equilibria of the Stackelberg game can overcome the deficiency of the Nash equilibria of the original game. A particular type of Stackelberg intervention is constructed to show that any positive payoff profile feasible with independent transmission probabilities can be achieved as a Stackelberg equilibrium payoff profile. We discuss criteria to select an operating point of the network and informational requirements for the Stackelberg game. We relax the requirements and examine the effects of relaxation on performance.
 控制与决策 , 2007, Abstract: 针对多用户多优先级网络系统的管理问题,利用对策论中的Nash平衡和激励Stackelberg策略等相关概念,提出了理想状态下的激励价控策略设计.在系统的动态平衡状态下,利用信息量的瞬时变化率及用户与平衡点的偏离,给出了非线性交叉干扰的多激励价控策略,加强了用户与网络管理者的合作性,激励和引导非合作用户选取对系统整体有益的服务请求,以提高网络资源的利用率.
 赵文会,祁宇,范韩璐 控制理论与应用 , 2018, DOI: 10.7641/CTA.2018.70589 Abstract: 针对当前风、光、储、火组成的区域能源网络经济效益不突出, 以及传统火电机组减排的问题, 本文建立了一种 主从博弈模型, 将电网运营商和发电商作为不同地位决策者, 通过优化电网运营商制定的分时上网电价与发电商的调度 控制策略, 对上级电网进行“削峰填谷”, 实现发电商自身的经济效益以及环境效益的最大化. 在模型中, 选择电网运营 商制定的分时上网电价作为主体, 发电商收益作为从体, 主体以降低CO2, SO2的排放量为目标, 从体以提高发电商自身 的收益为目标; 按照风光储系统的运行模式, 其主网所处的峰/平/谷运行时段以及整个网络发/用电供需平衡状况, 综合 考虑火电机组的环境效益和发电系统的经济性, 对分布式能源以及传统火电厂的调度进行优化. 最后, 将构建的主从博 弈模型在IEEE 10机系统算例中进行仿真, 对模型的有效性以及分时上网电价的引导作用能否整个系统实现经济效益和 环境效益的双赢进行验证.In view of the poor economic benefits of regional power grid consisting of wind, photovoltaics, energy storage system, thermal power plant and the emissions of traditional thermal power unit. In this paper, a Stackelberg Game Model that sets the grid operators and generators as decision makers in different positions is established. In the model, the step tariff set by grid operators and the dispatching control strategy of generators are optimized to realize the shaving peaks and filling valleys of superior power grid and to maximize the generators’ economic and environmental benefits. In the model, the prices during various periods set by the grid operators are regarded as a principle party and the earnings of generator are regarded as a subordinate party. The principle party aims to reduce the emission of CO2 and SO2, the subordinate party sets improving its own profits as a target. According to different operation modes of wind-pv-es hybrid system, the running period and supply-demand situation of the whole gird, the dispatching of distributed energy resource and traditional thermal power plant is optimized with consideration of the environmental benefits of thermal power units and the economic performance of the generator. Finally, the Stackelberg Game Model is simulated in the IEEE 10 system to verify the effectiveness of the model and whether the step tariff can allow the whole system to achieve both economic and environmental benefits.
 系统工程理论与实践 , 2006, Abstract: Multi-Cournot competition model and Multi-Stackelberg competition model are studied comparatively.Analysis shows that when the number of oligopoly firms is between 2 and 12,the profit in multi-Cournot competition would be higher than the profit of followers in multi-Stackelberg competition.If oligarch adopts active competition strategy,it would obtain higher profit through multi-Cournot competition,even it loses the chance to be the leader in multi-Stackelberg competition.When the number of oligopoly firms is equal or higher than 13,the profit in multi-Cournot competition would be lower than the profit of followers in multi-Stackelberg competition.If oligarch adopts active competition strategy,it would obtain lower profit through multi-Cournot competition,while loses the chance to be the leader in multi-Stackelberg competition.
 Mathematics , 2013, Abstract: In Stackelberg v/s Stackelberg games a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium problems are plagued by the nonuniqueness of follower equilibria and nonconvexity of leader problems whereby the problem of providing sufficient conditions for existence of global or even local equilibria remains largely open. Indeed available existence statements are restrictive and model specific. In this paper, we present what is possibly the first general existence result for equilibria for this class of games. Importantly, we impose no single-valuedness assumption on the equilibrium of the follower-level game. Specifically, under the assumption that the objectives of the leaders admit a quasi-potential function, a concept we introduce in this paper, the global and local minimizers of a suitably defined optimization problem are shown to be the global and local equilibria of the game. In effect existence of equilibria can be guaranteed by the solvability of an optimization problem, which holds under mild and verifiable conditions. We motivate quasi- potential games through an application in communication networks.
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