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

Aïd, René, Basei, Matteo, Callegaro, Giorgia, Campi, Luciano and Vargiolu, Tiziano (2018) Nonzero-sum stochastic differential games with impulse controls: a verification theorem with applications. Mathematics of Operations Research. ISSN 0364-765X (In Press)

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Abstract

We consider a general nonzero-sum impulse game with two players. The main mathemat- ical contribution of the paper is a verification theorem which provides, under some regularity conditions, a suitable system of quasi-variational inequalities for the payoffs and the strate- gies 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 non-symmetric examples where a Nash equilibrium is found numerically.

Item Type: Article
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 31 Jan 2019 14:54
Last Modified: 02 Apr 2019 23:11
URI: http://eprints.lse.ac.uk/id/eprint/100003

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