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

René Aïd, Matteo Basei, Giorgia Callegaro, Luciano Campi and Tiziano Vargiolu

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: 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.

Keywords: stochastic differential game; impulse control; Nash equilibrium; quasi-variational inequality (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2020-02
New Economics Papers: this item is included in nep-cmp, nep-gth and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

Published in Mathematics of Operations Research, February, 2020, 45(1), pp. 205 - 232. ISSN: 0364-765X

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http://eprints.lse.ac.uk/100003/ Open access version. (application/pdf)

Related works:
Journal Article: Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with Applications (2020)
Working Paper: Nonzero-sum stochastic differential games with impulse controls: a verification theorem with applications (2020)
Working Paper: Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with Applications (2019)
Working Paper: Nonzero-sum stochastic differential games with impulse controls: a verification theorem with applications (2018)
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