Selecting a Match: Exploration vs Decision

TL;DR

This paper analyzes optimal decision strategies in dynamic matching markets with finite lifetimes, providing bounds on collective losses and highlighting differences between discrete and continuum models through theoretical analysis and simulations.

Contribution

It introduces a discrete model for dynamic matching with finite lifetimes and derives tight bounds on agents' losses, addressing variance and market imbalances.

Findings

Bounds on collective losses are tight up to constants.

Discrete models exhibit substantial fluctuations, unlike continuum models.

Simulations show convergence behavior differs between models.

Abstract

In a dynamic matching market, such as a marriage or job market, how should agents balance accepting a proposed match with the cost of continuing their search? We consider this problem in a discrete setting, in which agents have cardinal values and finite lifetimes, and proposed matches are random. We seek to quantify how well the agents can do. We provide upper and lower bounds on the collective losses of the agents, with a polynomially small failure probability, where the notion of loss is with respect to a plausible baseline we define. These bounds are tight up to constant factors. We highlight two aspects of this work. First, in our model, agents have a finite time in which to enjoy their matches, namely the minimum of their remaining lifetime and that of their partner; this implies that unmatched agents become less desirable over time, and suggests that their decision rules should change over time. Second, we use a discrete rather than a continuum model for the population. The discreteness causes variance which induces localized imbalances in the two sides of the market. One of the main technical challenges we face is to bound these imbalances. In addition, we present the results of simulations on moderate-sized problems for both the discrete and continuum versions. For these size problems, there are substantial ongoing fluctuations in the discrete setting whereas the continuum version converges reasonably quickly.