Strong Time-Consistent Subset of the Core in Cooperative Differential Games with Finite Time Horizon

2018 ◽  
Vol 79 (10) ◽  
pp. 1912-1928 ◽  
Author(s):  
O. L. Petrosian ◽  
E. V. Gromova ◽  
S. V. Pogozhev
Keyword(s):  
Differential Games ◽  
Finite Time ◽  
Time Horizon ◽  
The Core ◽  
Finite Time Horizon ◽  
Consistent Subset ◽  
Cooperative Differential Games

scholarly journals Linear Quadratic Nash Differential Games of Stochastic Singular Systems

2014 ◽  
Vol 2 (6) ◽  
pp. 553-560
Author(s):  
Haiying Zhou ◽  
Huainian Zhu ◽  
Chengke Zhang
Keyword(s):  
Differential Games ◽  
Finite Time ◽  
Time Horizon ◽  
Singular Systems ◽  
Existence Condition ◽  
Infinite Time ◽  
Infinite Time Horizon ◽  
Finite Time Horizon ◽  
Stochastic Singular Systems ◽  
Nash Differential Games

AbstractIn this paper, we deal with the Nash differential games of stochastic singular systems governed by Itô-type equation in finite-time horizon and infinite-time horizon, respectively. Firstly, the Nash differential game problem of stochastic singular systems in finite time horizon is formulated. By applying the results of stochastic optimal control problem, the existence condition of the Nash strategy is presented by means of a set of cross-coupled Riccati differential equations. Similarly, under the assumption of the admissibility of the stochastic singular systems, the existence condition of the Nash strategy in infinite-time horizon is presented by means of a set of cross-coupled Riccati algebraic equations. The results show that the strategies of each players interact.

scholarly journals A Constrained Markovian Diffusion Model for Controlling the Pollution Accumulation

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1466
Author(s):  
Beatris Adriana Escobedo-Trujillo ◽  
José Daniel López-Barrientos ◽  
Javier Garrido-Meléndez
Keyword(s):  
Dynamic Programming ◽  
Dirichlet Problem ◽  
Stochastic Control ◽  
Finite Time ◽  
Time Horizon ◽  
Closed Loop ◽  
Programming Techniques ◽  
Pollution Accumulation ◽  
Finite Time Horizon ◽  
The Cost

This work presents a study of a finite-time horizon stochastic control problem with restrictions on both the reward and the cost functions. To this end, it uses standard dynamic programming techniques, and an extension of the classic Lagrange multipliers approach. The coefficients considered here are supposed to be unbounded, and the obtained strategies are of non-stationary closed-loop type. The driving thread of the paper is a sequence of examples on a pollution accumulation model, which is used for the purpose of showing three algorithms for the purpose of replicating the results. There, the reader can find a result on the interchangeability of limits in a Dirichlet problem.

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