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.

This thesis consists of three self-contained essays that investigate the algebraic structure of matching markets and the stabilization dynamics in decentralized markets. Chapter 2 is based on Wu and Roth (2018). It studies envy-free matchings that naturally arise from workers retiring or companies expanding. We show that the set of envy-free matchings forms a lattice that has a Conway-like join, but not a Conway-like meet. Furthermore, a job hopping process in which companies make offers to their favorite blocking workers, and workers accept their favorite offers, producing a sequence of vacancy chains, is a Tarski operator on this lattice. The fixed points of this Tarski operator correspond to the set of stable matchings; and the steady state matching starting from any given initial state is derived analytically. Chapter 3 is based on Wu (2020). The goal of this chapter, is to provide a systematic approach for analyzing entering classes in the college admissions model. When dealing with a many-to-one matching model, we often convert it into a one-to-one matching problem by assigning each seat of a college to a single student, instead of matching each college to multiple students. The preferences in this new model are significantly correlated and severely restrict the possible changes to entering classes. Through the so-called "rotations" that correspond to the join-irreducible elements in the lattice of stable matchings, we present a unified treatment for several results on entering classes, including the famous "Rural Hospital Theorem". We also show that, the least preferred student in an entering class appears to play a very interesting role. For example, each entering class can be completely characterized by its worst student. Chapter 4 is based on Gu, Roth, and Wu (2020). The motivating question is that, how come some black markets, such as the market for hitmen are well-regulated, but many others like the market for drugs are far from being under our control, even though we try very hard to eliminate them. To understand this, we build a three-dimensional discrete time Markov chain to study how black markets evolve over time, focusing on social repugnance and search frictions. We borrow tools from Markov jump processes, random walks, exponential martingales and optional sampling theory to analyze both the steady state limit and the realizations along the way. In the first part of the chapter, we identify conditions that lead to market survival or extinction. And the second part studies speed of convergence. We show that if a market is going to die eventually, then it dies exponentially fast. This further implies if a market has survived for a long time, then it is likely to survive forever.

Better Living Through Economics consists of twelve case studies that demonstrate how economic research has improved economic and social conditions over the past half century by influencing public policy decisions. Economists were obviously instrumental in revising the consumer price index and in devising auctions for allocating spectrum rights to cell phone providers in the 1990s. But perhaps more surprisingly, economists built the foundation for eliminating the military draft in favor of an all-volunteer army in 1973, for passing the Earned Income Tax Credit in 1975, for deregulating airlines in 1978, for adopting the welfare-to-work reforms during the Clinton administration, and for implementing the Pension Reform Act of 2006 that allowed employers to automatically enroll employees in a 401(k). Other important policy changes resulting from economists’ research include a new approach to monetary policy that resulted in moderated economic fluctuations (at least until 2008!), the reduction of trade impediments that allows countries to better exploit their natural advantages, a revision of antitrust policy to focus on those market characteristics that affect competition, an improved method of placing new physicians in hospital residencies that is more likely to keep married couples in the same city, and the adoption of tradable emissions rights which has improved our environment at minimum cost.

The Handbook of Rational Choice Social Research offers the first comprehensive overview of how the rational choice paradigm can inform empirical research within the social sciences. This landmark collection highlights successful empirical applications across a broad array of disciplines, including sociology, political science, economics, history, and psychology. Taking on issues ranging from financial markets and terrorism to immigration, race relations, and emotions, and a huge variety of other phenomena, rational choice proves a useful tool for theory- driven social research. Each chapter uses a rational choice framework to elaborate on testable hypotheses and then apply this to empirical research, including experimental research, survey studies, ethnographies, and historical investigations. Useful to students and scholars across the social sciences, this handbook will reinvigorate discussions about the utility and versatility of the rational choice approach, its key assumptions, and tools.