Mean-Field Analysis and Optimal Control of a Dynamic Rating and Matchmaking System

TL;DR

This paper models large-scale competitive platforms using mean-field theory to analyze rating dynamics, revealing fundamental limits on accuracy, invariance principles, and optimal control strategies for matchmaking and filtering.

Contribution

It introduces a mean-field framework for rating and matchmaking dynamics, deriving a low-dimensional model and identifying optimal control policies and fundamental accuracy limits.

Findings

Skill drift creates an intrinsic accuracy ceiling.

Interaction information content is invariant under certain scaling.

Optimal policies separate filtering and matchmaking decisions.

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.