When to Match: A Cost-Balancing Principle for Dynamic Markets

Abstract

Platforms in ridesharing, food delivery, and online gaming must decide not only whom to match but when: immediate matching cuts waiting, while delay thickens the market and improves match quality. Because demand is hard to forecast, the right waiting window shifts continuously. Fixed-window industry rules are simple but fragile, while forecast-based optimization models are brittle when assumptions fail. This paper develops a matching rule that is as simple as industry practice yet carries a guarantee requiring no forecasts. We study a model in which agents of several types are matched in groups drawing one agent from each type, waiting is costly, and matching costs fall as queues grow. We propose the Cost-Balancing (CB) rule: match as soon as the waiting cost accumulated since the last match reaches a calibrated proportion of the current matching cost. On any finite arrival stream delivering equal numbers of each type, CB calibrated for the worst case incurs at most twice the cost of an optimal clairvoyant policy that knows all future arrivals. No deterministic online rule can guarantee a smaller factor, so CB is worst-case optimal, while greedy and fixed-threshold policies can perform arbitrarily worse than this benchmark. The guarantee extends to matches with fixed heterogeneous consumption requirements. In a game-matching experiment, CB reduces total cost by 3--8\% versus the industry-standard heuristic; in a food-delivery experiment, it reduces average delay by 14.5\% versus the best fixed-rule benchmark. Platforms can manage match timing with Cost-Balancing, a simple, efficient, and robust rule. Its worst-case guarantee provides a safety net even in volatile conditions where fixed rules break down. Responding to realized costs, the rule matches faster during surges and waits longer during lulls, without forecasts or retuning.