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.; 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 epsilon(-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 epsilon(-1). Examples illustrate the necessity of some delay to alleviate the tension between short- and long-term value.