Quick or Cheap? Breaking Points in Dynamic Markets

Abstract

We examine two-sided markets where players arrive stochastically over time. The cost of matching a client and provider is a random variable whose distribution, but not its realization, is known, so a social planner is faced with two contending objectives: a) to reduce players' waiting time before getting matched; and b) to form efficient pairs to reduce matching costs. We show that such markets are characterized by a quick or cheap dilemma: Under a large class of distributional assumptions, there is no `free lunch', i.e., there exists no clearing schedule that is simultaneously optimal along both objectives. We further identify a unique breaking point signifying a stark reduction in matching cost contrasted by an increase in waiting time. Generalizing this model, we identify two regimes: one, where no free lunch exists; the other, where a window of opportunity opens to achieve a free lunch. Remarkably, greedy scheduling is never optimal in this setting.

Keywords: dynamic matching, online markets, market design

JEL Classification: D47, C78, C60, D80