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Linear-quadratic-singular stochastic differential games and applications

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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.

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Notes

  1. We thank the anonymous referee for suggesting the reference (Dixit and Pindyck 1994) and the precise quoting from Stokey (2008).

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Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project-ID 317210226 - SFB 1283.

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  1. Center for Mathematical Economics (IMW), Bielefeld University, Universitätstrasse, 33615, Bielefeld, Germany

    Jodi Dianetti

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Dianetti, J. Linear-quadratic-singular stochastic differential games and applications. Decisions Econ Finan (2023). https://doi.org/10.1007/s10203-023-00422-0

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