Centralized versus Decentralized Pricing Controls for Dynamic Matching Platforms

An important operational decision for online service platforms is how much control they have over pricing decisions. Motivated by recent regulations and increased public scrutiny on platform control, we study the effects of decentralized pricing using a fluid model of dynamic two-sided matching. In the centralized setting, the platform dictates the market price by optimizing a certain objective function. In contrast, under full decentralization, each supplier picks a price, adapted to their private cost, to maximize expected earnings. In turn, based on how much they value the service, customers can accept or reject the proposed matches. Our main contribution is to uncover the structure of stationary market equilibria under various degrees of centralization and analyze the resulting social welfare. We show that there exists a unique equilibrium in centralized and decentralized platforms. In the general case, where the platform can restrict the price menu, we characterize the equilibria through a tractable piecewise polynomial system. We establish that, within "impatient" markets (i.e., agents depart after a single match attempt), centralized platforms with plausible objective functions achieve higher social welfare than the decentralized equilibria. By contrast, the decentralized equilibrium converges to the first-best outcome as market participants' patience level uniformly increases. We demonstrate the robustness of these findings through a numerical study and identify semi-centralized pricing rules that retain some flexibility but recover near-optimal outcomes in most regimes. Overall, our work suggests that decentralized pricing creates friction in the matching process, except if supply and demand arrivals are balanced or if the agents are patient