We study a dynamic matching procedure where homogeneous agents arrive at random according to a Poisson process and form edges at random yielding a sparse market. Agents leave according to a certain departure distribution and may leave early by forming a pair with a compatible agent. The primary objective is to maximize the number of matched agents. Our main result is to show that a mild condition on the departure distribution suffices to get almost optimal performance of instantaneous matching, despite operating in a thin market. We are thus the first to provide a natural condition under which instantaneous decisions are superior in a market that is both sparse and thin. This result is surprising because similar results in the previous literature are based on market thickness. In addition, instantaneous matching performs well with respect to further objectives such as minimizing waiting times and avoiding the risk of market congestion. We develop new techniques for proving our results going beyond commonly adopted methods for Markov processes.

翻译：我们研究了一种动态匹配过程，其中同质代理根据泊松过程随机到达并随机形成边，从而产生一个稀疏市场。代理根据某种离开分布离开，并可能通过形成相容配对提前离开。主要目标是最大化匹配代理数量。我们的主要结果表明，即使在薄市场中，仅需对离开分布施加一个温和条件，即可使瞬时匹配达到近乎最优的性能。因此，我们是首个在既稀疏又薄的市场中，提出瞬时决策具有优越性的自然条件。这一结果令人惊讶，因为以往文献中的类似结果均依赖于市场厚度。此外，瞬时匹配在最小化等待时间和避免市场拥堵风险等附加目标上表现优异。我们开发了超越马尔可夫过程常用方法的新技术来证明结果。