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arXiv · 2304.09033

Linear-quadratic-singular stochastic differential games and applications

Jodi Dianetti
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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.

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Jodi Dianetti. 2023-04-18. Linear-quadratic-singular stochastic differential games and applications. https://arxiv.org/abs/2304.09033

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