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

Ren\'e A\"id, Matteo Basei, Giorgia Callegaro, Luciano Campi and Tiziano Vargiolu

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Abstract: We consider a general nonzero-sum impulse game with two players. The main mathematical contribution of the paper is a verification theorem which provides, under some regularity conditions, a suitable system of quasi-variational inequalities for the value functions and the optimal strategies of the two players. 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 Nash equilibrium and provide explicit expressions for the optimal strategies and the value functions. We also prove some asymptotic results with respect to the intervention costs. Finally, we consider two further non-symmetric examples where a Nash equilibrium is found numerically.

Date: 2016-04, Revised 2018-11
New Economics Papers: this item is included in nep-ene, nep-gth and nep-pr~
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Citations: View citations in EconPapers (6)

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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 (2020)
Working Paper: Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with Applications (2019)
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