Quick or Cheap? Breaking Points in Dynamic Markets

Abstract

We examine two-sided markets where players arrive stochastically over time and are drawn from a continuum of types. The cost of matching a client and provider varies, 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 in order 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.

Kidney Exchange: An Operations Perspective

“…There are also a few theoretical studies that look at matchings of size 2; Blanchet et al (2020) characterize, as a function of the quality distribution, the optimal amount of waiting in a stochastic model. Mertikopoulos et al (2020) explore trade-offs between quality and number of matches. Ashlagi et al (2020b) find that, in a dynamic version of the classic assignment model (with known qualities), simple "queue-like" policies have almost no allocative efficiency loss.…”

“…On a different matter of repugnance related to kidney transplantation, see, for example, Leider and Roth (2010), and see Elías et al (2019) on public attitudes toward compensation for kidney donors. 78 See Ashlagi et al (2019b), Blanchet et al (2020), Kerimov et al (2020), andMertikopoulos et al (2020) for theoretical papers that consider centralized dynamic matching. 79 In this connection, there is often information about both when currently available donors will no longer be available and when donors who are not currently available will become available.…”