Quick or cheap? Breaking points in dynamic markets

TL;DR

This paper analyzes two-sided markets with stochastic arrivals, revealing a fundamental trade-off between reducing waiting times and minimizing matching costs, and identifying conditions under which a 'free lunch' is possible.

Contribution

It introduces a model demonstrating the quick-or-cheap dilemma in dynamic markets and characterizes the conditions for the existence of a free lunch in matching efficiency.

Findings

Existence of a quick-or-cheap trade-off in dynamic markets.

Identification of a unique breaking point in matching costs and waiting times.

Greedy scheduling is never optimal in the studied setting.

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.