This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals ...This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.展开更多
We propose a computing model in which individuals can automatically adjust their interaction intensity with their mentor according to the learning effect.This model is designed to investigate the cooperative dynamics ...We propose a computing model in which individuals can automatically adjust their interaction intensity with their mentor according to the learning effect.This model is designed to investigate the cooperative dynamics of the spatial prisoner's dilemma.More specifically,when the cumulative payoff of a learner is more than his reference earning,he will strengthen his interaction with his mentor;otherwise,he will reduce it.The experimental results indicate that this mechanism can improve the emergence of cooperation in a networked population and that the driving coefficient of interaction intensity plays an important role in promoting cooperation.Interestingly,under a certain social dilemma condition,there exists a minimal driving coefficient that leads to optimal cooperation.This occurs due to a positive feedback effect between the individual's satisfaction frequency and the number of effective neighbors.Moreover,we find that the experimental results are in accord with theoretical predictions obtained from an extension of the classical pair-approximation method.Our conclusions obtained by considering relationships with mentors can provide a new perspective for future investigations into the dynamics of evolutionary games within structured populations.展开更多
The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainl...The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.展开更多
Dear Editor,In this letter, a finite-time convergent analysis of continuous action iterated dilemma(CAID) is proposed. In traditional evolutionary game theory, the strategy of the player is binary(cooperation or defec...Dear Editor,In this letter, a finite-time convergent analysis of continuous action iterated dilemma(CAID) is proposed. In traditional evolutionary game theory, the strategy of the player is binary(cooperation or defection), which limits the number of strategies a player can choose from.展开更多
Dear Editor,The distributed generalized-Nash-equilibrium(GNE)seeking in noncooperative games with nonconvexity is the topic of this letter.Inspired by the sequential quadratic programming(SQP)method,a multi-timescale ...Dear Editor,The distributed generalized-Nash-equilibrium(GNE)seeking in noncooperative games with nonconvexity is the topic of this letter.Inspired by the sequential quadratic programming(SQP)method,a multi-timescale multi-agent system(MAS)is developed,and its convergence to a critical point of the game is proven.To illustrate the qualities and efficacy of the theoretical findings,a numerical example is elaborated.展开更多
基金supported by the National Key Research and Development Program of China(2022YFA1006103,2023YFA1009203)the National Natural Science Foundation of China(61925306,61821004,11831010,61977043,12001320)+2 种基金the Natural Science Foundation of Shandong Province(ZR2019ZD42,ZR2020ZD24)the Taishan Scholars Young Program of Shandong(TSQN202211032)the Young Scholars Program of Shandong University。
文摘This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.
基金Project supported by the National Natural Science Foundation of China(Grant No.61963013).
文摘We propose a computing model in which individuals can automatically adjust their interaction intensity with their mentor according to the learning effect.This model is designed to investigate the cooperative dynamics of the spatial prisoner's dilemma.More specifically,when the cumulative payoff of a learner is more than his reference earning,he will strengthen his interaction with his mentor;otherwise,he will reduce it.The experimental results indicate that this mechanism can improve the emergence of cooperation in a networked population and that the driving coefficient of interaction intensity plays an important role in promoting cooperation.Interestingly,under a certain social dilemma condition,there exists a minimal driving coefficient that leads to optimal cooperation.This occurs due to a positive feedback effect between the individual's satisfaction frequency and the number of effective neighbors.Moreover,we find that the experimental results are in accord with theoretical predictions obtained from an extension of the classical pair-approximation method.Our conclusions obtained by considering relationships with mentors can provide a new perspective for future investigations into the dynamics of evolutionary games within structured populations.
基金supported in part by the Strategic Priority Research Program of Chinese Academy of Sciences(XDA27030100)National Natural Science Foundation of China(72293575, 11832001)。
文摘The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.
基金supported in part by the National Science Fund for Distinguished Young Scholarship of China (62025602)the National Natural Science Foundation of China (11931915, U22B2036)+2 种基金Fok Ying-Tong Education Foundationm China (171105)Technological lmnovation Team of Shaanxi Province (2020TD013)the Tencent Foundation and XPLORER PRIZE。
文摘Dear Editor,In this letter, a finite-time convergent analysis of continuous action iterated dilemma(CAID) is proposed. In traditional evolutionary game theory, the strategy of the player is binary(cooperation or defection), which limits the number of strategies a player can choose from.
基金partially supported by the National Natural Science Foundation of China(62173308)the Natural Science Foundation of Zhejiang Province of China(LR20F030001)+3 种基金the Jinhua Science and Technology Project(2022-1-042)University of Macao(MYRG2022-00108-FST,MYRG-CRG202200010-ICMS)the Science and Technology Development Fund,Macao S.A.R(0036/2021/AGJ)Chinese Guangdong’s S&T project(2022A0505020028)。
文摘Dear Editor,The distributed generalized-Nash-equilibrium(GNE)seeking in noncooperative games with nonconvexity is the topic of this letter.Inspired by the sequential quadratic programming(SQP)method,a multi-timescale multi-agent system(MAS)is developed,and its convergence to a critical point of the game is proven.To illustrate the qualities and efficacy of the theoretical findings,a numerical example is elaborated.
