Aïd, RenéBernal Martínez, Francisco ManuelMnif, MohamedZabaljauregui, DiegoZubelli, Jorge P.2021-03-102021-03-102019-02ESAIM: Proceedings and Surveys, vol. 65, Feb. 2019 (CEMRACS 2017, Numerical methods for stochastic models: control, uncertainty quantification, mean-field, Marseille, France, July 17 - August 25, 2017) Pp. 27-452267-3059https://hdl.handle.net/10016/32094Research work conducted during the 22nd edition of CEMRACS, Numerical methods for stochastic models: control, uncertainty quantification, mean-field, July 17 - August 25, CIRM, MarseilleThis 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.19eng© EDP Sciences, SMAI 2019.This is an Open Access article distributed under the terms of the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Atribución 3.0 EspañaStochastic impulse gameNonzero-sum gameNash equilibriumPolicy iterationHoward's algorithmQuasi-variational inequalityconference paperMatemáticashttps://doi.org/10.1051/proc/201965027open access2745ESAIM: Proceedings and Surveys: CEMRACS 2017, Numerical methods for stochastic models: control, uncertainty quantification, mean-field, Marseille, France, July 17 - August 25, 201765CC/0000031977