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

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

“…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.…”

“…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. 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.…”

Moving Information Horizon Approach for Dynamic Game Models

“…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.…”

“…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.…”

“…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. 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.…”