Linear-quadratic-singular stochastic differential games and applications

Jodi Dianetti ()
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Jodi Dianetti: Bielefeld University

Decisions in Economics and Finance, 2025, vol. 48, issue 1, No 19, 413 pages

Abstract: Abstract We consider a class of non-cooperative N-player nonzero-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.

Keywords: Singular stochastic control; Linear quadratic games; Stochastic maximum principle; Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C72 C73 D24 L13 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10203-023-00422-0

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