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.
Nonzero-sum stochastic differential games with impulse controls : a verification theorem with applications / R. Aid, M. Basei, G. Callegaro, L. Campi, T. Vargiolu. - In: MATHEMATICS OF OPERATIONS RESEARCH. - ISSN 0364-765X. - 45:1(2020 Feb), pp. 205-232.
|Titolo:||Nonzero-sum stochastic differential games with impulse controls : a verification theorem with applications|
|Parole Chiave:||Impulse control; Nash equilibrium; Quasi-variational inequality; Stochastic differential game|
|Settore Scientifico Disciplinare:||Settore MAT/06 - Probabilita' e Statistica Matematica|
|Data di pubblicazione:||feb-2020|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1287/moor.2019.0989|
|Appare nelle tipologie:||01 - Articolo su periodico|