Optimal Matching Strategies in Two-sided Markets: A Mean Field Approach
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914595473457152 |
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| author | Bayraktar, Erhan Chu, Dantong Li, Bohan Tai, Ho Man |
| author_facet | Bayraktar, Erhan Chu, Dantong Li, Bohan Tai, Ho Man |
| contents | This paper develops a mean field game framework for dynamic two-sided matching markets, extending existing matching theory by integrating micro-macro dynamics in two-sided environments. Unlike traditional matching models focusing on static equilibrium or unilateral optimization, our framework simultaneously captures dynamic interactions and strategic behaviors of both market sides, as well as the equilibrium. We model two types of agents who meet each other via Poisson processes and make simultaneous matching decisions to maximize their respective objective functionals, and find the corresponding equilibrium. Our approach formulates the equilibrium as a fully coupled Hamilton-Jacobi-Bellman and Fokker-Planck system with nonlocal structure coupling two distinct populations. The mathematical analysis addresses significant challenges from the dual-layered coupling structure and nonlocal structure. We also provide insights into individual behaviors shaping aggregate patterns in labor markets through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Matching Strategies in Two-sided Markets: A Mean Field Approach Bayraktar, Erhan Chu, Dantong Li, Bohan Tai, Ho Man Optimization and Control 35Q89, 45K05, 49N80, 91B39, 91B68 This paper develops a mean field game framework for dynamic two-sided matching markets, extending existing matching theory by integrating micro-macro dynamics in two-sided environments. Unlike traditional matching models focusing on static equilibrium or unilateral optimization, our framework simultaneously captures dynamic interactions and strategic behaviors of both market sides, as well as the equilibrium. We model two types of agents who meet each other via Poisson processes and make simultaneous matching decisions to maximize their respective objective functionals, and find the corresponding equilibrium. Our approach formulates the equilibrium as a fully coupled Hamilton-Jacobi-Bellman and Fokker-Planck system with nonlocal structure coupling two distinct populations. The mathematical analysis addresses significant challenges from the dual-layered coupling structure and nonlocal structure. We also provide insights into individual behaviors shaping aggregate patterns in labor markets through numerical experiments. |
| title | Optimal Matching Strategies in Two-sided Markets: A Mean Field Approach |
| topic | Optimization and Control 35Q89, 45K05, 49N80, 91B39, 91B68 |
| url | https://arxiv.org/abs/2509.26531 |