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Linear-quadratic-singular stochastic differential games and applications

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  • Jodi Dianetti

    (Bielefeld University)

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.

Suggested Citation

  • Jodi Dianetti, 2025. "Linear-quadratic-singular stochastic differential games and applications," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 48(1), pages 381-413, June.
    • Handle: RePEc:spr:decfin:v:48:y:2025:i:1:d:10.1007_s10203-023-00422-0
    DOI: 10.1007/s10203-023-00422-0
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    Keywords

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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