تقرير
Feedback Nash Equilibria in Differential Games with Impulse Control
| العنوان: | Feedback Nash Equilibria in Differential Games with Impulse Control |
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| المؤلفون: | Sadana, Utsav, Reddy, Puduru Viswanadha, Zaccour, Georges |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Systems and Control |
| الوصف: | We study a class of deterministic finite-horizon two-player nonzero-sum differential games where players are endowed with different kinds of controls. We assume that Player 1 uses piecewise-continuous controls, while Player 2 uses impulse controls. For this class of games, we seek to derive conditions for the existence of feedback Nash equilibrium strategies for the players. More specifically, we provide a verification theorem for identifying such equilibrium strategies, using the Hamilton-Jacobi-Bellman (HJB) equations for Player 1 and the quasi-variational inequalities (QVIs) for Player 2. Further, we show that the equilibrium number of interventions by Player 2 is upper bounded. Furthermore, we specialize the obtained results to a scalar two-player linear-quadratic differential game. In this game, Player 1's objective is to drive the state variable towards a specific target value, and Player 2 has a similar objective with a different target value. We provide, for the first time, an analytical characterization of the feedback Nash equilibrium in a linear-quadratic differential game with impulse control. We illustrate our results using numerical experiments. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2106.10706 |
| رقم الأكسشن: | edsarx.2106.10706 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |