Dynamic Matching: Characterizing and Achieving Constant Regret

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 tradeoff 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 ${ϵ}^{-1}$. 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 ${ϵ}^{-1}$. Examples illustrate the necessity of some delay to alleviate the tension between short- and long-term value.

This paper was accepted by David Simchi-Levi, revenue management and market analytics.

Funding: This work was supported by the National Science Foundation [Grant CMM-2010940] and the U.S. Department of Defense [Grant STTR A18B-T007].