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

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 so...

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Bibliographic Details
Published in:	IDEAS Working Paper Series from RePEc
Main Authors:	Aïd, René, Basei, Matteo, Callegaro, Giorgia, Campi, Luciano, Vargiolu, Tiziano
Format:	Paper
Language:	English
Published:	St. Louis Federal Reserve Bank of St. Louis 01.02.2020
Subjects:	Equilibrium
Online Access:	Get full text
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Summary:	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.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
DOI:	10.1287/moor.2019.0989