Nash Differential Games

2018 ◽  
pp. 173-189
Author(s):  
Zoran Gajić ◽  
Myo-Taeg Lim ◽  
Dobrila Škatarić ◽  
Wu-Chung Su ◽  
Vojislav Kecman
Keyword(s):  
Differential Games ◽  
Nash 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 An Algorithm for Solving a Class of Multiplayer Feedback-Nash Differential Games

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Jorge Herrera de la Cruz ◽  
Benjamin Ivorra ◽  
Ángel M. Ramos
Keyword(s):  
Differential Games ◽  
Numerical Algorithm ◽  
Nash Equilibria ◽  
Numerical Solutions ◽  
Iteration Step ◽  
Benchmark Problems ◽  
Value Iteration ◽  
Game Equilibrium ◽  
Computationally Expensive ◽  
Nash Differential Games

In this work, we introduce a novel numerical algorithm, called RaBVItG (Radial Basis Value Iteration Game) to approximate feedback-Nash equilibria for deterministic differential games. More precisely, RaBVItG is an algorithm based on value iteration schemes in a meshfree context. It is used to approximate optimal feedback Nash policies for multiplayer, trying to tackle the dimensionality that involves, in general, this type of problems. Moreover, RaBVItG also implements a game iteration structure that computes the game equilibrium at every value iteration step, in order to increase the accuracy of the solutions. Finally, with the purpose of validating our method, we apply this algorithm to a set of benchmark problems and compare the obtained results with the ones returned by another algorithm found in the literature. When comparing the numerical solutions, we observe that our algorithm is less computationally expensive and, in general, reports lower errors.

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