Publication: A policy iteration algorithm for nonzero-sum stochastic impulse games
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2019-02
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EDP Science
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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.
Description
Research work conducted during the 22nd edition of CEMRACS, Numerical methods for stochastic models: control, uncertainty quantification, mean-field, July 17 - August 25, CIRM, Marseille
Keywords
Stochastic impulse game, Nonzero-sum game, Nash equilibrium, Policy iteration, Howard's algorithm, Quasi-variational inequality
Bibliographic citation
ESAIM: 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. 27-45