This paper studies market clearing in matching markets. The model is non-cooperative, fully decentralized, and in Markov strategies. Workers and firms bargain with each other to determine who will be matched to whom and at what terms of trade. Once a worker- firm pair reach agreement they exit the market. Alternative possible matches provide endogenous outside options. We ask when do such markets clear efficiently and find inefficiencies – mismatch and delay – to be pervasive. Mismatch occurs whenever an agent is at risk of losing a binding endogenous outside option. Delay occurs, instead, when the market evolves in favor of an agent. Delay can be extensive and structured with vertically differentiated markets endogenously clearing form the top down.