Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with Applications

• 成果类型: Article
• 署名作者: Aid, Rene; Basei, Matteo; Callegaro, Giorgia; Campi, Luciano; Vargiolu, Tiziano
• 署名单位: Universite PSL; Universite Paris-Dauphine; University of California System; University of California Berkeley; University of Padua; University of London; London School Economics & Political Science
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2019.0989
• 发表日期: 2020
• 页码: 205-232
• 关键词: 2-player

摘要

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.