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

René Aïd, Francisco Bernal, Mohamed Mnif, Diego Zabaljauregui and Jorge P. Zubelli
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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 de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - 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 - Tunis El Manar University [University of Tunis El Manar] [Tunisia] = Université de Tunis El Manar [Tunisie] = جامعة تونس المنار (ar), 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

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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.

Keywords: stochastic impulse game; nonzero-sum game; Nash equilibrium; policy iteration; Howard’s algorithm; quasi-variational inequality (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

Published in ESAIM: Proceedings and Surveys, 2019, 65 (CEMRACS 2017), ⟨10.1051/proc/201965027⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02294353

DOI: 10.1051/proc/201965027

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