We study a dynamic matching problem on a two-sided platform with unbalanced patience, in which long-lived supply accumulates over time with a unit waiting cost per period, while short-lived demand departs if not matched promptly. High- or low-quality agents arrive sequentially with one supply agent and one demand agent arriving in each period, and matching payoffs are supermodular. In the centralized benchmark, the optimal policy follows a threshold-based rule that rations high-quality supply, preserving it for future high-quality demand. In the decentralized system, where self-interested agents decide whether to match under an exogenously specified payoff allocation proportion, we characterize a welfare-maximizing Markov perfect equilibrium. Unlike outcomes in the centralized benchmark or in full-backlog markets, the equilibrium exhibits distinct matching patterns in which low-type demand may match with high-type supply even when low-type supply is available. Unlike settings in which both sides have long-lived agents and perfect coordination is impossible, the decentralized system can always be perfectly aligned with the centralized optimum by appropriately adjusting the allocation of matching payoffs across agents on both sides. Finally, when the arrival probabilities for H- and L-type arrivals are identical on both sides, we compare social welfare across systems with different patience levels: full backlog on both sides, one-sided backlog, and no backlog. In the centralized setting, social welfare is weakly ordered across systems. However, in the decentralized setting, the social welfare ranking across the three systems depends on the matching payoff allocation rule and the unit waiting cost, and enabling patience can either increase or decrease social welfare.

翻译：本文研究了一个双边平台上具有不均衡耐心的动态匹配问题，其中长期存在的供给方随时间累积并承担每期单位等待成本，而短期存在的需求方若未能及时匹配则会离开。高质量或低质量的智能体按序到达，每期各有一个供给智能体和一个需求智能体到达，且匹配收益具有超模性。在集中式基准模型中，最优策略遵循基于阈值的规则，对高质量供给进行配给，将其保留给未来的高质量需求。在分散式系统中，自利的智能体在外部指定的收益分配比例下决定是否匹配，我们刻画了一个福利最大化的马尔可夫完美均衡。与集中式基准或完全积压市场的结果不同，该均衡表现出独特的匹配模式：即使存在低质量供给，低类型需求仍可能与高质量供给匹配。与双边均为长期智能体且无法实现完美协调的情境不同，通过适当调整双边智能体间的匹配收益分配，分散式系统总能与集中式最优解完全对齐。最后，当双边H型和L型到达概率相同时，我们比较了不同耐心水平系统间的社会福利：双边完全积压、单边积压和无积压。在集中式设定下，社会福利在不同系统间呈弱序关系。然而在分散式设定中，三个系统的社会福利排序取决于匹配收益分配规则和单位等待成本，且引入耐心既可能提升也可能降低社会福利。