(1) 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 affect agents’ bargaining positions. We ask when do such markets clear efficiently and find inefficiencies – mismatch and delay – to be pervasive. Mismatch occurs whenever an agent’s bargaining position is at risk of deteriorating. Delay occurs whenever agents expect their bargaining position to improve. Delay can be extensive and structured with vertically differentiated markets endogenously clearing form the top down.

(2) We conduct an experimental investigation of decentralized bargaining over the terms of trade in matching markets. We study if/when efficient matches will be reached and the terms of trade agreed upon. Multiple theories guide our analysis and we test their predictions against the outcomes of our experiments. We find that inefficiencies are extensive and strongly linked to the changing bargaining positions of players as agreements are reached and others exit the market.