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A policy iteration algorithm for non-zero sum stochastic impulse games

Author

Listed:
  • René Aïd

    (FiME Lab - Laboratoire de Finance des Marchés d'Energie - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CREST - EDF R&D - EDF R&D - EDF - EDF, LEDa - Laboratoire d'Economie de Dauphine - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres)

  • Francisco Bernal

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Mohamed Mnif

    (LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis] - ENIT - Ecole Nationale d'Ingénieurs de Tunis - UTM - Université de Tunis El Manar, LEGI - Laboratoire d'Économie et de Gestion Industrielle [Tunis] - Ecole Polytechnique de Tunisie - UCAR - Université de Carthage (Tunisie))

  • Diego Zabaljauregui

    (LSE - Department Mathematics [London] - LSE - London School of Economics and Political Science)

  • Jorge P. Zubelli

    (IMPA - Instituto de Matematica Pura e Aplicada - CNPq)

Abstract

This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods available, to the best of our knowledge. Our method relies on the recently introduced characterisation of the value functions and Nash equilibrium via a system of quasi-variational inequalities. While our algorithm is heuristic and we do not provide a convergence analysis, numerical tests show that it performs convincingly in a wide range of situations, including the only analytically solvable example available in the literature at the time of writing.

Suggested Citation

  • René Aïd & Francisco Bernal & Mohamed Mnif & Diego Zabaljauregui & Jorge P. Zubelli, 2019. "A policy iteration algorithm for non-zero sum stochastic impulse games," Post-Print hal-02294353, HAL.
    • Handle: RePEc:hal:journl:hal-02294353
    DOI: 10.1051/proc/201965027
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    Cited by:

    1. Ren'e Aid & Lamia Ben Ajmia & M'hamed Gaigi & Mohamed Mnif, 2021. "Nonzero-sum stochastic impulse games with an application in competitive retail energy markets," Papers 2112.10213, arXiv.org.

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