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Nonzero-Sum Stochastic Games and Mean-Field Games with Impulse Controls

Author

Listed:
  • Matteo Basei

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720-1777; EDF R&D, 75008 Paris, France)

  • Haoyang Cao

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720-1777; The Alan Turing Institute, British Library, NW1 2DB London, United Kingdom)

  • Xin Guo

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720-1777)

Abstract

We consider a general class of nonzero-sum N -player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a veri?cation approach and provide su?cient conditions for the Nash equilibria (NEs) of the game. We then consider the limiting situation when N goes to in?nity, that is, a suitable mean-?eld game (MFG) with impulse controls. We show that under appropriate technical conditions, there exists a unique NE solution to the MFG, which is an ϵ-NE approximation to the N -player game, with ϵ = O 1 N . As an example, we analyze in detail a class of two-player stochastic games which extends the classical cash management problem to the game setting. In particular, we present numerical analysis for the cases of the single player, the two-player game, and the MFG, showing the impact of competition on the player’s optimal strategy, with sensitivity analysis of the model parameters.

Suggested Citation

  • Matteo Basei & Haoyang Cao & Xin Guo, 2022. "Nonzero-Sum Stochastic Games and Mean-Field Games with Impulse Controls," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 341-366, February.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:1:p:341-366
    DOI: 10.1287/moor.2021.1131
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