In this paper, a power allocation problem based on the Cournot game and generalized Nash game is proposed. After integrating dynamic average consensus algorithm and distributed projection neural network through singul...In this paper, a power allocation problem based on the Cournot game and generalized Nash game is proposed. After integrating dynamic average consensus algorithm and distributed projection neural network through singular perturbation systems, a normalized Nash equilibrium seeking algorithm is presented to solve the proposed power allocation problem in a distributed way.Combine Lyapunov stability with the singular perturbation analysis, the convergence of the proposed algorithm is analyzed. A simulation on IEEE 118-bus confirms that the proposed distributed algorithm can adjust the power allocation according to different situations, while keeping the optimal solution within the feasible set.展开更多
When an emergency happens, the scheduling of relief resources to multiple emergency locations is a realistic and intricate problem, especially when the available resources are limited. A non-cooperative games model an...When an emergency happens, the scheduling of relief resources to multiple emergency locations is a realistic and intricate problem, especially when the available resources are limited. A non-cooperative games model and an algorithm for scheduling of relief resources are presented. In the model, the players correspond to the multiple emergency locations, strategies correspond to all resources scheduling and the payoff of each emergency location corresponds to the reciprocal of its scheduling cost. Thus, the optimal results are determined by the Nash equilibrium point of this game. Then the iterative algorithm is introduced to seek the Nash equilibrium point. Simulation and analysis are given to demonstrate the feasibility and availability of the model.展开更多
This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays.Not only the state variable,but also control variables of players involv...This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays.Not only the state variable,but also control variables of players involve discrete and distributed delays.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,the author establishes a necessary maximum principle and a sufficient verification theorem.To explain theoretical results,the author applies them to a dynamic advertising game problem.展开更多
We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations,in which the coefficient contains not only the state process but also its marginal...We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations,in which the coefficient contains not only the state process but also its marginal distribution,and the cost functional is also of mean-field type.It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motions.We establish a necessary condition in the form of maximum principle and a verification theorem,which is a sufficient condition for Nash equilibrium point.We use the theoretical results to deal with a partial information linear-quadratic(LQ)game,and obtain the unique Nash equilibrium point for our LQ game problem by virtue of the unique solvability of mean-field forward-backward doubly stochastic differential equation.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 61673107)the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (Grant No. BM2017002)。
文摘In this paper, a power allocation problem based on the Cournot game and generalized Nash game is proposed. After integrating dynamic average consensus algorithm and distributed projection neural network through singular perturbation systems, a normalized Nash equilibrium seeking algorithm is presented to solve the proposed power allocation problem in a distributed way.Combine Lyapunov stability with the singular perturbation analysis, the convergence of the proposed algorithm is analyzed. A simulation on IEEE 118-bus confirms that the proposed distributed algorithm can adjust the power allocation according to different situations, while keeping the optimal solution within the feasible set.
文摘When an emergency happens, the scheduling of relief resources to multiple emergency locations is a realistic and intricate problem, especially when the available resources are limited. A non-cooperative games model and an algorithm for scheduling of relief resources are presented. In the model, the players correspond to the multiple emergency locations, strategies correspond to all resources scheduling and the payoff of each emergency location corresponds to the reciprocal of its scheduling cost. Thus, the optimal results are determined by the Nash equilibrium point of this game. Then the iterative algorithm is introduced to seek the Nash equilibrium point. Simulation and analysis are given to demonstrate the feasibility and availability of the model.
基金the National Natural Science Foundation of China under Grant No.11701214Shandong Provincial Natural Science FoundationChina under Grant No.ZR2019MA045。
文摘This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays.Not only the state variable,but also control variables of players involve discrete and distributed delays.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,the author establishes a necessary maximum principle and a sufficient verification theorem.To explain theoretical results,the author applies them to a dynamic advertising game problem.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11871309,11671229,71871129,11371226,11301298)the National Key R&D Program of China(Grant No.2018 YFA0703900)+2 种基金the Natural Science Foundation of Shandong Province(No.ZR2019MA013)the Special Funds of Taishan Scholar Project(No.tsqn20161041)the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutions.
文摘We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations,in which the coefficient contains not only the state process but also its marginal distribution,and the cost functional is also of mean-field type.It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motions.We establish a necessary condition in the form of maximum principle and a verification theorem,which is a sufficient condition for Nash equilibrium point.We use the theoretical results to deal with a partial information linear-quadratic(LQ)game,and obtain the unique Nash equilibrium point for our LQ game problem by virtue of the unique solvability of mean-field forward-backward doubly stochastic differential equation.
