Dynamic Matching: Characterizing and Achieving Constant Regret

Abstract

We study how to optimally match agents in a dynamic matching market with heterogeneous match cardinalities and values. A network topology determines the feasible matches in the market. In general, a fundamental trade-off exists between short-term value---which calls for performing matches frequently---and long-term value---which calls, sometimes, for delaying match decisions in order to perform better matches.

We find that in networks that satisfy a general position condition, the tension between short- and long-term value is limited, and a simple periodic clearing policy (nearly) maximizes the total match value simultaneously at all times. Central to our results is the general position gap ε; a proxy for capacity slack in the market. With the exception of trivial cases, no policy can achieve an all-time regret that is smaller, in terms of order, than 1/ε. We achieve this lower bound with a policy, which periodically resolves a natural matching integer linear program, provided that the delay between resolving periods is of the order of 1/ε. Examples illustrate the necessity of some delay to alleviate the tension between short- and long-term value.

Keywords: dynamic matching, queueing, optimal control

JEL Classification: C44, C61, C78