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.

Most of the literature on two-sided matching markets without transfers focuses on the case where a central planner (often an algorithm) clears the market, like in the case of school assignments, or medical residents. In contrast, we focus on decentralized matching markets without transfers, where prices are regulated and thus cannot clear the market, as in the case of taxis. In these markets, time waited in line often plays the role of a numéraire. We investigate the properties of equilibrium in these markets (existence, uniqueness, and welfare). We use this analysis to study the problem of surge pricing: given beliefs on random demand and supply, how should a market designer set prices to minimize expected market inefficiency?

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.

Two-sided matching provides a model of search processes such as those between firms and workers in labor markets or between buyers and sellers in auctions. This book gives a comprehensive account of recent results concerning the game-theoretic analysis of two-sided matching. The focus of the book is on the stability of outcomes, on the incentives that different rules of organization give to agents, and on the constraints that these incentives impose on the ways such markets can be organized. The results for this wide range of related models and matching situations help clarify which conclusions depend on particular modeling assumptions and market conditions, and which are robust over a wide range of conditions. 'This book chronicles one of the outstanding success stories of the theory of games, a story in which the authors have played a major role: the theory and practice of matching markets ... The authors are to be warmly congratulated for this fine piece of work, which is quite unique in the game-theoretic literature.' From the Foreword by Robert Aumann

"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.