Iterative Schemes for Markov Perfect Equilibria
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912505664634880 |
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| author | Höfer, Felix Laurière, Mathieu Soner, H. Mete Yan, Qinxin |
| author_facet | Höfer, Felix Laurière, Mathieu Soner, H. Mete Yan, Qinxin |
| contents | We study Markov perfect equilibria in continuous-time dynamic games with finitely many symmetric players. The corresponding Nash system reduces to the Nash-Lasry-Lions equation for the common value function, also known as the master equation in the mean-field setting. In the finite-state space problems we consider, this equation becomes a nonlinear ordinary differential equation admitting a unique classical solution. Leveraging this uniqueness, we prove the convergence of both Picard and weighted Picard iterations, yielding efficient computational methods. Numerical experiments confirm the effectiveness of algorithms based on this approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Iterative Schemes for Markov Perfect Equilibria Höfer, Felix Laurière, Mathieu Soner, H. Mete Yan, Qinxin Optimization and Control 35Q89, 35D40, 49L25, 60G99 We study Markov perfect equilibria in continuous-time dynamic games with finitely many symmetric players. The corresponding Nash system reduces to the Nash-Lasry-Lions equation for the common value function, also known as the master equation in the mean-field setting. In the finite-state space problems we consider, this equation becomes a nonlinear ordinary differential equation admitting a unique classical solution. Leveraging this uniqueness, we prove the convergence of both Picard and weighted Picard iterations, yielding efficient computational methods. Numerical experiments confirm the effectiveness of algorithms based on this approach. |
| title | Iterative Schemes for Markov Perfect Equilibria |
| topic | Optimization and Control 35Q89, 35D40, 49L25, 60G99 |
| url | https://arxiv.org/abs/2507.20898 |