A policy iteration algorithm for nonzero-sum stochastic impulse games
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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2019-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Subjects: | |
| Online Access: | https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196502.pdf |
| _version_ | 1828081211189231616 |
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| author | Aïd René Bernal Francisco Mnif Mohamed Zabaljauregui Diego Zubelli Jorge P. |
| author_facet | Aïd René Bernal Francisco Mnif Mohamed Zabaljauregui Diego Zubelli Jorge P. |
| author_sort | Aïd René |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T03:30:41Z |
| format | Article |
| id | doaj.art-e9fa093cff344fea9e50d563b80fe53d |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T03:30:41Z |
| publishDate | 2019-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-e9fa093cff344fea9e50d563b80fe53d2023-01-02T06:33:57ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592019-01-0165274510.1051/proc/201965027proc196502A policy iteration algorithm for nonzero-sum stochastic impulse gamesAïd RenéBernal FranciscoMnif MohamedZabaljauregui DiegoZubelli Jorge P.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.https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196502.pdfstochastic impulse gamenonzero-sum gamenash equilibriumpolicy iterationhoward’s algorithmquasi-variational inequality |
| spellingShingle | Aïd René Bernal Francisco Mnif Mohamed Zabaljauregui Diego Zubelli Jorge P. A policy iteration algorithm for nonzero-sum stochastic impulse games ESAIM: Proceedings and Surveys stochastic impulse game nonzero-sum game nash equilibrium policy iteration howard’s algorithm quasi-variational inequality |
| title | A policy iteration algorithm for nonzero-sum stochastic impulse games |
| title_full | A policy iteration algorithm for nonzero-sum stochastic impulse games |
| title_fullStr | A policy iteration algorithm for nonzero-sum stochastic impulse games |
| title_full_unstemmed | A policy iteration algorithm for nonzero-sum stochastic impulse games |
| title_short | A policy iteration algorithm for nonzero-sum stochastic impulse games |
| title_sort | policy iteration algorithm for nonzero sum stochastic impulse games |
| topic | stochastic impulse game nonzero-sum game nash equilibrium policy iteration howard’s algorithm quasi-variational inequality |
| url | https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196502.pdf |
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