Dynamic Balancing and Matchmaking in Competitive Live-Service Games

Abstract

Competitive live-service games are a rapidly growing segment of the entertainment industry, and their long-run success depends on sustained player engagement. Platforms manage engagement through two operational levers: balancing, which adjusts character strengths through patch updates, and matchmaking, which pairs players for competition. We formulate a dynamic problem of jointly optimizing prospective match fairness and realized outcome parity for a platform that must learn balancing effects from noisy match outcomes, in a setting where the two levers are dynamically coupled and estimation errors propagate nonlinearly through matchmaking. We propose an epoch-based policy that re-estimates character strengths via regularized maximum likelihood at geometrically spaced epoch starts and combines random with loss-aware matchmaking within each epoch. We prove the policy achieves O(ln T) cumulative expected loss over horizon T and establish matching Ω(ln T) lower bounds, confirming rate optimality. Our study reveals distinct, complementary roles: balancing drives the loss order, while matchmaking's random component ensures reliable estimation, and its loss-aware component reduces loss by prioritizing outcome parity. A case study calibrated to Clash Royale's real data and patch history shows that our policy achieves over 35% loss reduction relative to a real-data-implied baseline with high confidence, while using fewer updates, on scales from 10 to nearly one million real players.

Keywords: balancing, matchmaking, live-service games