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
Irrational-behavior-proof(IBP) conditions are important aspects to keep stable cooperation in dynamic cooperative games. In this paper, we focus on the establishment of IBP conditions.Firstly, the relations of three k...Irrational-behavior-proof(IBP) conditions are important aspects to keep stable cooperation in dynamic cooperative games. In this paper, we focus on the establishment of IBP conditions.Firstly, the relations of three kinds of IBP conditions are described. An example is given to show that they may not hold, which could lead to the fail of cooperation. Then, based on a kind of limit characteristic function, all these conditions are proved to be true along the cooperative trajectory in a transformed cooperative game. It is surprising that these facts depend only upon the individual rationalities of players for the Shapley value and the group rationalities of players for the core. Finally,an illustrative example is given.展开更多
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.
基金supported by National Natural Science Foundation of China(71571108)Projects of International (Regional) Cooperation and Exchanges of NSFC(71611530712,61661136002)+1 种基金China Postdoctoral Science Foundation Funded Project(2016M600525)Qingdao Postdoctoral Application Research Project(2016029)
文摘Irrational-behavior-proof(IBP) conditions are important aspects to keep stable cooperation in dynamic cooperative games. In this paper, we focus on the establishment of IBP conditions.Firstly, the relations of three kinds of IBP conditions are described. An example is given to show that they may not hold, which could lead to the fail of cooperation. Then, based on a kind of limit characteristic function, all these conditions are proved to be true along the cooperative trajectory in a transformed cooperative game. It is surprising that these facts depend only upon the individual rationalities of players for the Shapley value and the group rationalities of players for the core. Finally,an illustrative example is given.
