Stochastic differential games with singular controls and applications

Dianetti Jodi, Bielefeld University

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 convex in the state and linear in the control. Under natural assumptions, we show the existence of open-loop Nash equilibria, which are characterized through a system of reflected 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.

Area: IS14 - Stochastic Control and Game-theoretic Models in Economics and Finance (Giorgio Ferrari)

Keywords: Singular control, forward-backward stochastic differential equations, Nash equilibrium

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