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Linear-Quadratic-Singular Stochastic Differential Games and Applications

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  • Dianetti, Jodi

    (Center for Mathematical Economics, Bielefeld University)

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.

Suggested Citation

  • Dianetti, Jodi, 2023. "Linear-Quadratic-Singular Stochastic Differential Games and Applications," Center for Mathematical Economics Working Papers 678, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:678
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    References listed on IDEAS

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