This paper investigates imitation dynamics with continuously distributed delay.In realistic technological,economic,and social environments,individuals are involved in strategic interactions simultaneously while the in...This paper investigates imitation dynamics with continuously distributed delay.In realistic technological,economic,and social environments,individuals are involved in strategic interactions simultaneously while the influences of their decision-making may not be observable instantaneously.It shows that there exists a time delay effect.Different distributions of delay are further considered to efficiently lucubrate the stability of interior equilibrium in the imitation dynamics with continuous distributions of delay in the two-strategy game contexts.Precisely,when the delay follows the uniform distributions and Gamma distributions,the authors present that interior equilibrium can be asymptotically stable.Furthermore,when the probability density of the delay is general density,the authors also determine a sufficient condition for stability derived from the expected delay.Last but not least,the interested but uncomplicated Snowdrift game is utilized to demonstrate our theoretical results.展开更多
This paper is devoted to a new class of differential games with continuous and dynamic updating.The direct application of resource extraction in a case of dynamic and continuous updating is considered.It is proved tha...This paper is devoted to a new class of differential games with continuous and dynamic updating.The direct application of resource extraction in a case of dynamic and continuous updating is considered.It is proved that the optimal control(cooperative strategies)and feedback Nash equilibrium strategies uniformly converge to the corresponding strategies in the game model with continuous updating as the number of updating instants converges to infinity.Similar results are presented for an optimal trajectory(cooperative trajectory),equilibrium trajectory and corresponding payoffs.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11271098Guizhou Provincial Science and Technology Fund under Grant No.[2019]1067the Fundamental Funds for Introduction of Talents of Guizhou University under Grant No.[2017]59。
文摘This paper investigates imitation dynamics with continuously distributed delay.In realistic technological,economic,and social environments,individuals are involved in strategic interactions simultaneously while the influences of their decision-making may not be observable instantaneously.It shows that there exists a time delay effect.Different distributions of delay are further considered to efficiently lucubrate the stability of interior equilibrium in the imitation dynamics with continuous distributions of delay in the two-strategy game contexts.Precisely,when the delay follows the uniform distributions and Gamma distributions,the authors present that interior equilibrium can be asymptotically stable.Furthermore,when the probability density of the delay is general density,the authors also determine a sufficient condition for stability derived from the expected delay.Last but not least,the interested but uncomplicated Snowdrift game is utilized to demonstrate our theoretical results.
基金supported by Postdoctoral International Exchange Program of China,and corresponding author’work is also supported by the National Natural Science Foundation of China(No.72171126).
文摘This paper is devoted to a new class of differential games with continuous and dynamic updating.The direct application of resource extraction in a case of dynamic and continuous updating is considered.It is proved that the optimal control(cooperative strategies)and feedback Nash equilibrium strategies uniformly converge to the corresponding strategies in the game model with continuous updating as the number of updating instants converges to infinity.Similar results are presented for an optimal trajectory(cooperative trajectory),equilibrium trajectory and corresponding payoffs.
