This paper empirically studies a decentralized dynamic peer-to-peer matching market. We use data from a leading ride-sharing platform in China to estimate a continuous-time dynamic model of search and match between drivers and passengers. We assess the efficiency of the decentralized market by how much centralized algorithms may improve welfare. We find that a centralized algorithm can increase the number of matches by making matches less frequently and matching agents more assortatively.

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"Many decentralized markets are able to attain a stable outcome despite the absence of acentral authority. A stable matching, however, need not be efficient if preferences are weak. This raises the question whether a decentralized market with weak preferences can attain Pareto efficiency in the absence of a central matchmaker. I show that when agent tastes are independent, the random stable match in a large-enough market is asymptotically Pareto efficient even with weak preferences. In fact, even moderate-sized markets can attain good efficiency levels. The average fraction of agents who can Pareto improve is below 10% in a market of size n = 79 when one side of the market has weak preferences; when both sides have weak preferences, the inefficiency falls below 10% for n> 158. This implies that approximate Pareto efficiency is attainable in a decentralized market even in the absence of a central matchmaker"--Abstract, p. ii.

We study congestion problems in decentralized, two-sided matching markets. The main focus is on the impact of market thickness on these congestion problems. We find that it is often not optimal to make an offer to the best observed agent when the likelihood of acceptance is very low. We derive the optimal offering strategies for firms depending on market thickness and analyze who benefits when the market becomes thicker. We also investigate which market participants would benefit from a centralized market with assortative matching.

We experimentally study decentralized one-to-one matching markets with transfers. We vary the information available to participants, complete or incomplete, and the surplus structure, supermodular or submodular. Several insights emerge. First, while markets often culminate in efficient matchings, stability is more elusive, reflecting the difficulty of arranging attendant transfers. Second, incomplete information and submodularity present hurdles to efficiency and especially stability; their combination drastically diminishes stability's likelihood. Third, matchings form "from the top down" in complete-information supermodular markets, but exhibit many more and less-obviously ordered offers otherwise. Last, participants' market positions matter far more than their dynamic bargaining styles for outcomes.