Nonzero-sum stochastic differential games with impulse controls: a verification theorem with applications - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematics of Operations Research Année : 2020

Nonzero-sum stochastic differential games with impulse controls: a verification theorem with applications

Résumé

We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of this paper is a verification theorem that provides, under some regularity conditions, a suitable system of quasi-variational inequalities for the payoffs and the strategies of the two players at some Nash equilibrium. As an application, we study an impulse game with a one-dimensional state variable, following a real-valued scaled Brownian motion, and two players with linear and symmetric running payoffs. We fully characterize a family of Nash equilibria and provide explicit expressions for the corresponding equilibrium strategies and payoffs. We also prove some asymptotic results with respect to the intervention costs. Finally, we consider two further nonsymmetric examples where a Nash equilibrium is found numerically.
Fichier non déposé

Dates et versions

hal-03355609 , version 1 (27-09-2021)

Identifiants

  • HAL Id : hal-03355609 , version 1

Citer

René Aïd, Matteo Basei, Giorgia Callegaro, Luciano Campi, Tiziano Vargiolu. Nonzero-sum stochastic differential games with impulse controls: a verification theorem with applications. Mathematics of Operations Research, 2020, 45 (1). ⟨hal-03355609⟩
45 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More