On Class of Linear Quadratic Non-cooperative Differential Games with Continuous Updating

Kuchkarov, Ildus; Petrosian, Ovanes

doi:10.1007/978-3-030-22629-9_45

Cited by 17 publications

(11 citation statements)

References 9 publications

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“…However, the class of games with continuous updating provides new theoretical results. The class of differential games with continuous updating was introduced in the papers [21], [8], here it is supposed that the updating process evolves continuously in time. In the paper [21], the system of Hamilton-Jacobi-Bellman equations is derived for the Nash equilibrium in a game with continuous updating.…”

Section: Zeyang Wang and Ovanes Petrosianmentioning

confidence: 99%

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On class of non-transferable utility cooperative differential games with continuous updating

Wang¹,

Petrosian²

2020

Journal of Dynamics &Amp; Games

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This paper considers and describes the class of cooperative differential games with the non-transferable utility and continuous updating. It is the first detailed paper about the application of continuous updating approach to the non-transferable utility differential games. The process of how to construct Pareto optimal strategy with continuous updating and Pareto trajectory is described. Another important contribution is that the property of subgame consistency is adopted for the class of games with continuous updating. The resource extraction game model is used as an example. The Pareto optimal strategies and corresponding trajectory are constructed, and the set of Pareto optimal strategies satisfying the subgame consistency property is presented. The results of numerical simulation are demonstrated in the Matlab environment, and the conclusion is drawn.

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Section: Zeyang Wang and Ovanes Petrosianmentioning

confidence: 99%

“…In the paper [21], the system of Hamilton-Jacobi-Bellman equations is derived for the Nash equilibrium in a game with continuous updating. In the paper [8], the class of linear-quadratic differential games with continuous updating is considered, and the explicit form of the Nash equilibrium is obtained.…”

Section: Zeyang Wang and Ovanes Petrosianmentioning

confidence: 99%

On class of non-transferable utility cooperative differential games with continuous updating

Wang¹,

Petrosian²

2020

Journal of Dynamics &Amp; Games

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“…The concept of the looking forward approach was introduced in [13] for differential games, where a new class of games was presented and the foundation for further study of games with dynamic updating or a moving information horizon was laid. To get more information about the approach, one may consider the following papers [13][14][15][16][17][18][19][20]. In the paper [13], the looking forward approach was applied to the cooperative differential game with a finite horizon.…”

Section: Introductionmentioning

confidence: 99%

“…The last papers on the looking forward approach [18,21] were devoted to either studying the looking forward approach for cooperative differential games with nontransferable utility and real-life application of the looking forward approach to economic simulation. The class of differential games with continuous updating was considered in the papers [19,20]; here, it was supposed that the updating process evolves continuously in time. In the paper [19], the system of Hamilton-Jacobi-Bellman equations was derived for the Nash equilibrium in the game with continuous updating.…”

Section: Introductionmentioning

confidence: 99%

“…In the paper [19], the system of Hamilton-Jacobi-Bellman equations was derived for the Nash equilibrium in the game with continuous updating. In the paper [20], the class of linear-quadratic differential games with continuous updating was considered, and the explicit form of the Nash equilibrium was derived. In this paper, we apply the looking forward approach to the class of games with dynamic updating.…”

Section: Introductionmentioning

confidence: 99%

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Moving Information Horizon Approach for Dynamic Game Models

et al. 2019

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In the paper, a new class of dynamic game models with a moving information horizon or dynamic updating is studied. In this class of games, players do not have full information about the game structure (motion equations, payoff functions) on the interval on which the game is defined. It is supposed that the players at each stage of the dynamic game have only truncated information about the game structure defined by the information horizon. Cooperative and noncooperative settings are considered in the paper. Results are illustrated using the oligopoly advertising game model, and comparison between the solution in the initial game model and in the game model with moving information horizon is presented. Simulation results are presented.

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Hamilton-Jacobi-Bellman Equations for Non-cooperative Differential Games with Continuous Updating

Petrosian

Tur

2019

Mathematical Optimization Theory and Operations Research

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On Class of Linear Quadratic Non-cooperative Differential Games with Continuous Updating

Cited by 17 publications

References 9 publications

On class of non-transferable utility cooperative differential games with continuous updating

On class of non-transferable utility cooperative differential games with continuous updating

Moving Information Horizon Approach for Dynamic Game Models

Hamilton-Jacobi-Bellman Equations for Non-cooperative Differential Games with Continuous Updating

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