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

René Aïd (), Matteo Basei (), Giorgia Callegaro (), Luciano Campi () and Tiziano Vargiolu
Additional contact information
René Aïd: Department of Economics, Paris Dauphine University and Finance For Energy Market Research Centre, 75775 Paris CEDEX 16, France;
Matteo Basei: Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720;
Giorgia Callegaro: Department of Mathematics “Tullio Levi-Civita,” University of Padova, 35122 Padova, Italy;
Luciano Campi: Department of Statistics, London School of Economics and Political Science, London WC2A 2AE, United Kingdom

Mathematics of Operations Research, 2020, vol. 45, issue 1, 205–232

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)
Date: 2020
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Citations: View citations in EconPapers (10)

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https://doi.org/10.1287/moor.2019.0989 (application/pdf)

Related works:
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 (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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