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第二十六届中国控制会议

作者： Xu Yashan 1 1.School of Mathematical Sciences,Fudan University,Shanghai 200433,P.R.China

The paper is concerned with stackelberg differential games for two *** on different assumptions on the favor of the players,several notions of stackelberg equilibrium solution in the open-loop form are introduced,which are different from the concept given by ***,etc([3]).Specialization of this model to the case of linear quadratic differential game with indefinite coefficients is *** obtain a sufficient and necessary condition to the existence of an equilibrium by the operator ***,two representation formulas of the equilibrium are presented respectively via a two-point boundary value problem and a Riccati equation.

关键词： stackelberg equilibrium Differential games Linear quadratic Open-loop Non-cooperative

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Linear Quadratic Leader-Follower Stochastic Differential Games:Closed-Loop Solvability

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系统科学与复杂性学报:英文版 2023年第4期36卷 1373-1406页

作者： LI Zixuan SHI Jingtao School of Mathematics Shandong UniversityJinan 250100China

In this paper,a leader-follower stochastic differential game is studied for a linear stochastic differential equation with quadratic cost *** coefficients in the state equation and the weighting matrices in the cost functionals are all ***-loop strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in *** follower first solves a stochastic linear quadratic optimal control problem,and his optimal closed-loop strategy is characterized by a Riccati equation,together with an adapted solution to a linear backward stochastic differential *** the leader turns to solve a stochastic linear quadratic optimal control problem of a forward-backward stochastic differential equation,necessary conditions for the existence of the optimal closed-loop strategy for the leader is given by a Riccati *** examples are also given.

关键词： Backward stochastic differential equation closed-loop solvability leader-follower stochastic differential game linear quadratic control Riccati equation stackelberg equilibrium

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A stackelberg game approach for demand response management of multi-microgrids with overlapping sales areas

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Science China(Information Sciences) 2019年第11期62卷 121-133页

作者： Jun LI Guangqing MA Tao LI Wushun CHEN Yu GU School of Mechatronic Engineering and Automation Shanghai University CASCO Signal Ltd. Key Laboratory of Pure Mathematics and Mathematical Practice School of Mathematical SciencesEast China Normal University

Microgrids are increasingly participating directly in the electricity market as sellers in order to fulfill the power demand in specific regions. In this study, we consider a demand response management model for multi-microgrids and multi-users, with overlapping sales areas. We construct a stackelberg game model of microgrids and users, and then analyze the equilibrium strategies systematically. As such, we prove that there is a unique stackelberg equilibrium solution for the game. In equilibrium, the electricity price strategies of the microgrids and the demand strategies of the users achieve a balance. Furthermore, we propose a numerical algorithm, supported by a simulation, to compute the equilibrium solution and give the proof of convergence.

关键词： electricity market microgrid demand response management overlapping sales areas game theory stackelberg equilibrium

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A stackelberg Differential Game Based Bandwidth Allocation in Satellite Communication Network

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China Communications 2018年第8期15卷 205-214页

作者： Jingtao Su Shengsong Yang Haitao Xu Xianwei Zhou School of Computer and Communication Engineering University of Science and Technology Beijing

In this paper, a stackelberg differential game based approach is proposed to solve the bandwidth allocation problems in satellite communication network. All the satellites are divided into two groups, one has high download requirements, and the other one has low download requirements. Each satellites group has its own controller for bandwidth allocation, and can get payments from the satellites for the allocated resources. The relationships between the controllers and satellites are formed as a stackelberg game. In our model, differential equation is introduced to describe the bandwidth dynamics for the whole satellite communication network. Combine the differential equation and stackelberg game together, we can formulate the bandwidth allocation problems in satellite communication network as a Stackelber differential game. The solutions to the proposed game is solved based the Bellman dynamic equations. Numerical simulations are given to prove the effeteness and correctness of the proposed approach.

关键词： stackelberg equilibrium bandwidth allocation differential game satellite communication networks

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Analysis of the Duopoly Game Based on Endogenous Timing

Analysis of the Duopoly Game Based on Endogenous Timing

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2010 Chinese Control and Decision Conference

作者： Shengli Chen~1,Xiaohua Yang~2,Kang Ping~1 1.School of Management,Xian University of Finance and Economics,Xian 710061 2.School of Management,Wuhan University of Science and Technology,Wuhan 430074

＜正＞We provide a general analysis of duopoly game in endogenous *** Nash equilibrium outcomes are compared with stackelberg equilibrium *** different sets of conditions are provided for yielding respectively simultaneous and sequential plays and these conditions only depend on the monotonicities of the reaction functions and the payoffs functions in rival strategic variables.

关键词： Endogenous timing Reaction function Nash equilibrium stackelberg equilibrium

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