Derivation of necessary and sufficient conditions for single-stage Stackelberg games via the inducible region concept

The inducible region is defined as the collection of all the possible outcomes. It is typically a subset of the entire decision space. The best the leader can obtain is then the optimal outcome in this inducible region. Necessary and sufficient conditions are derived by first delineating the inducible region, and then obtaining a leader's optimal strategy, if it exists. If not, an ε-strategy always exists, provided that the leader's Stackelberg cost is bounded.     

Three-level Stackelberg decision problems

Three-level Stackelberg decision problems are studied by using the inducible region concept. Through a systematic derivation, it is identified that the leader's control has dual purposes, which in general are not separable. A special class of problems is then considered, where explicit results are obtained.     

基于Stackelberg博弈的协作网络功率分配策略

针对协作网络中的功率分配问题,提出基于Stackelberg博弈的分配策略。首先建立博弈模型,源节点根据中继节点分配的功率给出价格;中继节点根据自身资源情况、信道状态、位置信息以及源节点提出的价格,进行协作传输功率的分配,从而构建用户效用函数;接着证明了该效用函数满足凹函数的条件,且存在均衡点,因此参与决策的用户可以通过求解协作功率和价格的Stackelberg均衡解(SE)最大化自己的效用;最后,通过仿真实验验证了均衡点的存在,并对源节点位置不同情况下节点的价格、功率和效用进行了分析,实验中离中继更近的源节点的协作功率和效用分别是距离较远用户的1.29倍和1.37倍。理论分析与实验结果证明了策略的有效性,而且该策略能适用于协作网络及其他分布式网络。     

Team-optimal closed-loop Stackelberg strategies for systems with slow and fast modest†

This paper discusses team-optimal closed-loop Stackelberg strategies for systems with slow and fast modes. It is established that the cost functions of the players in the pure slow and the full-order games have the same value in the limit as the small singular perturbation parameters tends to zero. It is shown that if the leader bases the design of his approximate strategy on the slow subsystem, while the follower bases his design on the full-order system, then the resulting solution is ill-posed. Moreover, if the fast information is incorporated in the approximate strategy of the leader, then it is shown that the singular perturbation technique of constructing approximate strategies by composing the slow and fast strategies is ill-posed and cannot be used in this problem. A new design methodology to construct approximate Stackelberg strategies by solving reduced-order problems, which have the same information structure as the full-order one, is presented. It is shown that the conditions for existenco and uniqueness of the solution of the full-order problem can be established through those conditions of the reduced-order problems. Finally, it is proved that the approximate strategies, besides being team near-optimal, possess the asymptotic Stackelberg property.     

Mixed Stackelberg strategies in continuous-kernel games

It is shown that continuous-kernel nonzero-sum games with compact strategy spaces could admit both pure and mixed Stackelberg equilibrium solutions, if the cost function of each player is either nonquadratic or nonconvex in his own decision variable. In such a case, the mixed Stackelberg strategy will yield a lower average cost for the leader than the pure Stackelberg strategy. It is also verified that, if the cost functions of the players are quadratic and strictly convex, then only pure Stackelberg strategies can exist.     

Closed-loop strategies in continuous dynamic game with multi-level of hierarchy

The derivation is given of the closed-loop Stackelberg strategy for a class of continuous three-player non-zero-sum differential games using the idea of the team optimal Stackelberg strategy. The game systems are described by linear state dynamics and quadratic objective functions. First, a definition of the three-player hierarchical equilibrium is given, then a general theorem which was developed by Basar (1981) is examined and applied to the game under consideration to deduce some sufficient conditions for the solution of the game to exist. A simple example is given.     

基于Stackelberg博弈论的Multi—Homing负载均衡研究

阐述了Stackelberg博弈的基本理论和模型,并将其应用于多主接入网络的负栽均衡问题中,给出了一种基于Stackelberg博弈理论的多主接入网络带宽分配模型.考虑网络和用户之间的供需平衡,采用线性和非线性价格方案,给出了更加合理的带宽分配策略.仿真结果证明了算法是有效的,Stackelberg博弈模型能够合理有效地利用带宽资源,实现了负载均衡.     

Equilibrium properties of the nash and stackelberg strategies

The Nash and Stackelberg strategies of a nonzero sum game have the common property that they are both noncooperative equilibrium solutions for which no player can achieve an improvement in his performance if he attempts to deviate from his strategy (cheat). In this note we show that the Nash solution is desirable only if it is not dominated by any of the Stackelberg solutions. Otherwise a Stackelberg strategy is always more favorable to both players and, as the Nash solution, it can be enforced once an agreement between the players, specifying the leader and the follower, is reached.     

Solution of N-person Stackelberg games with nearly cooperating leaders

A class of linear-quadratic Stackelberg games with many leaders and many followers is considered. For this game, a proportionality relation is assumed between some of the weighting matrices in the leaders’ cost functions. With this assumption, it is shown that the matrix characterizing the set of necessary conditions to be satisfied by an open-loop Stackelberg strategy has a special spectrum. This property is then used to solve the two-point boundary-value problem (TPBVP) associated with the game by an eigenvector method.     

Stackelberg Strategies for Atomic Congestion Games

We investigate the effectiveness of Stackelberg strategies for atomic congestion games with unsplittable demands. In our setting, only a fraction of the players are selfish, while the rest are willing to follow a predetermined strategy. A Stackelberg strategy assigns the coordinated players to appropriately selected strategies trying to minimize the performance degradation due to the selfish players. We consider two orthogonal cases, namely congestion games with affine latency functions and arbitrary strategies, and congestion games on parallel links with arbitrary non-decreasing latency functions. We restrict our attention to pure Nash equilibria and derive strong upper and lower bounds on the pure Price of Anarchy (PoA) under different Stackelberg strategies.     

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.     

网络通信量控制的主从模型

讨论了网络的通信量控制问题,将激励Stackelberg策略的概念引入到具有用户和网络两层子系统的网络模型中,针对弹性通信量问题,提出了一个线性策略和一个非线性策略,并将此方法扩展到非弹性通信量情形,数值例子及仿真结果说明了此方法的适用性。     

基于Stackelberg安全博弈的动态防御策略选取方法

网络攻防对抗的本质是攻防双方非对等主体之间的博弈过程。针对现有网络防御策略研究中攻防博弈双方主体地位对等的先验假设缺陷,将博弈论非对等局中人思想引入网络防御策略生成模型构建过程,提出一种基于Stackelberg安全博弈的动态防御策略生成方法,通过建立网络模型,利用Stackelberg安全博弈强均衡策略算法生成网络的最优防御策略,既充分考虑攻防行为中双方关系彼此影响,又能确保防御策略生成的准确性。实验结果表明所提模型和方法的可行性和有效性。所提模型和方法能够加强系统的安全性。     

Feedback Stackelberg strategy for M-level hierarchical games

A multilevel feedback Stackelberg strategy is formulated for systems withMplayers arranged in a linear hierarchy of decision making. For a linear-quadratic discrete-time game, sufficient conditions are given for existence and uniqueness of solution.     

无线传感器网络中基于对策论的功率控制

运用对策论中的Stackelberg策略,提出了基于TDMA-CDMA的分簇结构无线传感器网络（WSN）的反向链路功率控制的新算法。根据TDMA机制和CDMA机制相结合的分簇结构无线传感器网络的基本特点,以网络中的簇为单位,建立了一个该簇簇头采用Stackelberg策略控制节点发射功率以达到最大化能量有效性并兼顾网络寿命的数学模型。仿真结果表明Stackelberg策略能起到控制功率及激励网络优化的作用。     

A time-consistent open-loop Stackelberg equilibrium of shelf-space allocation

We propose a differential game to study retailer's allocation strategy of shelf-space shares between the manufacturers of two competing brands. Each manufacturer can influence the allocation decision by her advertising spending to improve her brand's goodwill which in turn affects the demand for her product. The game is played à la Stackelberg with the manufacturers as leaders and the retailer as follower. Stackelberg open-loop equilibrium is characterized and shown to be time-consistent.     

A Stackelberg strategy for continuous-time mixed ${\rm H}_2/{\rm H}_\infty$ control problem with time delay

This paper is concerned with the mixed H2/H∞ control with linear continuous time system and time delay. To deal with this, we presents a Stackelberg strategy by treating the control input and the disturbance as leader and follower, respectively. The leader’s control strategy minimizes the cost function which is in H2 norm and the follower’s control strategy maximizes the cost function which is in H∞ norm. The main technique of this paper is deal with the noncausal relationship of the variables caused by time delay in the control input by introducing two costates to capture the future information and one state to capture the past information. Through theory analyzing, the Stackelberg strategy exists uniquely. Moreover, with the assistance of the extended state space expression, the explicit expression of the strategy is obtained.     

On Linear-Quadratic Stackelberg Games With Time Preference Rates

This note deals with linear-quadratic Stackelberg differential games including time preference rates with an open-loop information structure. The properties of the characteristic matrix associated with the necessary conditions for a Stackelberg strategy are pointed out. It is shown that such a matrix exhibits a special symmetry property of its eigenvalues. Sufficient conditions to guarantee a predefined degree of stability are given based on the distribution of the eigenvalues in the complex plane.     

A Stackelberg solution of dynamic games

The paper proposes a formulation of ε-Stackelberg and Stackelberg strategies for a large class of dynamic closed-loop games, discusses the interpretation of the leader's strategy as the formalization of the intuitive notion of incentives or threats, and considers limitations of the Stackelberg solution concept which, within the dynamic context, are applicable only in situations where the realization of a leader's strategy is ensured by a binding contract. The solution method is based on the idea of discontinuous strategies assuming that the leader punishes the follower by minimizing his payoff if the latter does not comply with the policy selected for him by the leader.     

OEM业务的Stackelberg博弈策略与算法

随着经济全球化的发展和经济的区域化分工,OEM合作已成为一种重要的企业间生产方式。通过分析OEM业务中委托方和被委托方的决策行为及双方关系,建立OEM业务的Stackelberg博弈策略模型,并研究求解算法。首先,分析OEM业务中的委托方和被委托方各自的决策行为;进而以此为基础,建立OEM业务的Stackelberg博弈策略模型。最后,利用双层规划的对偶理论,给出求解OEM业务最优策略的一种多项式时间算法。