{"ID":2825019,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.22038","arxiv_id":"2512.22038","title":"Mean-Field Analysis and Optimal Control of a Dynamic Rating and Matchmaking System","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2512.22038","url_pdf":"https://arxiv.org/pdf/2512.22038v1","authors":"[\"Wataru Nozawa\"]","published":"2025-12-26T14:19:04Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}