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 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.

Over the past few decades, matching models, which use mathematical frameworks to analyze allocation mechanisms for heterogeneous products and individuals, have attracted renewed attention in both theoretical and applied economics. These models have been used in many contexts, from labor markets to organ donations, but recent work has tended to focus on "nontransferable" cases rather than matching models with transfers. In this important book, Pierre-André Chiappori fills a gap in the literature by presenting a clear and elegant overview of matching with transfers and provides a set of tools that enable the analysis of matching patterns in equilibrium, as well as a series of extensions. He then applies these tools to the field of family economics and shows how analysis of matching patterns and of the incentives thus generated can contribute to our understanding of long-term economic trends, including inequality and the demand for higher education.