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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.22038 |
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| _version_ | 1866912789852848128 |
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| author | Nozawa, Wataru |
| author_facet | Nozawa, Wataru |
| contents | Large-scale competitive platforms are interacting multi-agent systems in which latent skills drift over time and pairwise interactions are shaped by matchmaking. We study a controlled rating dynamics in the mean-field limit and derive a kinetic description for the joint evolution of skills and ratings. In the Gaussian regime, we prove an exact moment closure and obtain a low-dimensional deterministic state dynamics for rating accuracy. This yields three main insights. First, skill drift imposes an intrinsic ceiling on long-run accuracy (the ``Red Queen'' effect). Second, with period-by-period scale control, the information content of interactions satisfies an invariance principle: under signal-matched scaling, the one-step accuracy transition is independent of matchmaking intensity. Third, the optimal platform policy separates: filtering is implemented by a greedy choice of the gain and rating scale, while matchmaking reduces to a static trade-off between match utility and sorting costs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean-Field Analysis and Optimal Control of a Dynamic Rating and Matchmaking System Nozawa, Wataru Optimization and Control Large-scale competitive platforms are interacting multi-agent systems in which latent skills drift over time and pairwise interactions are shaped by matchmaking. We study a controlled rating dynamics in the mean-field limit and derive a kinetic description for the joint evolution of skills and ratings. In the Gaussian regime, we prove an exact moment closure and obtain a low-dimensional deterministic state dynamics for rating accuracy. This yields three main insights. First, skill drift imposes an intrinsic ceiling on long-run accuracy (the ``Red Queen'' effect). Second, with period-by-period scale control, the information content of interactions satisfies an invariance principle: under signal-matched scaling, the one-step accuracy transition is independent of matchmaking intensity. Third, the optimal platform policy separates: filtering is implemented by a greedy choice of the gain and rating scale, while matchmaking reduces to a static trade-off between match utility and sorting costs. |
| title | Mean-Field Analysis and Optimal Control of a Dynamic Rating and Matchmaking System |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2512.22038 |