Optimal Growth of a Two-Sided Platform with Heterogeneous Agents

Abstract

We consider the dynamics of a two-sided platform, where the agent population on both sides experiences growth over time with heterogeneous growth rates. The compatibility between buyers and sellers is captured by a bipartite network. The platform sets commissions to optimize its total profit over $T$ periods, considering the trade-off between short-term profit and growth as well as the spatial imbalances in supply and demand. We design an asymptotically optimal policy with the profit loss upper-bounded by a constant independent of $T$ , in contrast with a myopic policy shown to be arbitrarily bad. To derive the policy, we first develop a benchmark problem that captures the platform’s optimal steady state. We then identify the agent types with the lowest relative population ratio compared to the benchmark in each period, and adjust the service level of these types to be higher than or equal to their service level in the benchmark problem. A higher service level accelerates growth but requires substantial subsidies during the growth phase. Additionally, we provide the conditions under which the subsidy is necessary. We further examine the impact of the growth potential and the compatibility network structure on the platform’s optimal profit, the agents’ payment/income, and the optimal commissions at the optimal steady state. To achieve that, we introduce innovative metrics to quantify the long-run growth potential of each agent type. Using these metrics, we show that a “balanced” compatibility network, where the relative long-run growth potential between sellers and buyers for all submarkets is the same as that for the entire market, allows the platform to achieve maximum profitability. Our study provides insight into how the growth potential and compatibility network structure jointly influence the commission policy in the growth process and the optimal steady state.