Linear-quadratic-singular stochastic differential games and applications
Abstract
We consider a class of non-cooperative N-player non-zero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is quadratic in the state and linear in the control. We call these games linear-quadratic-singular stochastic differential games. Under natural assumptions, we show the existence of open-loop Nash equilibria, which are characterized through a linear system of forward-backward stochastic differential equations. The proof is based on an approximation via a sequence of games in which players are restricted to play Lipschitz continuous strategies. We then discuss an application of these results to a model of capacity expansion in oligopoly markets.
Cite
@article{arxiv.2304.09033,
title = {Linear-quadratic-singular stochastic differential games and applications},
author = {Jodi Dianetti},
journal= {arXiv preprint arXiv:2304.09033},
year = {2023}
}