This paper develops a price-theoretic framework for matching markets with heterogeneous preferences. The model departs from the Gale and Shapley model by assuming that a finite number of agents on one side (colleges) are matched to a continuum of agents on the other side (students). We show that stable matchings correspond to solutions of supply and demand equations, with the selectivity of each college playing a role similar to that of prices. We apply the model to an analysis of how competition induced by school choice gives schools incentives to invest in quality and to asymptotics of school choice mechanisms.

We propose a criterion of approximate incentive compatibility, strategy-proofness in the large (SP-L), and argue that it is a useful second-best to exact strategy-proofness (SP) for market design. Conceptually, SP-L requires that an agent who regards a mechanism’s “prices” as exogenous to her report—be they traditional prices as in an auction mechanism, or price-like statistics in an assignment or matching mechanism—has a dominant strategy to report truthfully. Mathematically, SP-L weakens SP in two ways: (1) truth-telling is required to be approximately optimal (within epsilon in a large enough market) rather than exactly optimal, and (2) incentive compatibility is evaluated ex interim, with respect to all full-support i.i.d. probability distributions of play, rather than ex post with respect to all possible realizations of play. This places SP-L in between the traditional notion of approximate SP, which evaluates incentives to manipulate ex post and as a result is too strong to obtain our main results in support of SP-L, and the traditional notion of approximate Bayes-Nash incentive compatibility, which, like SP-L, evaluates incentives to manipulate ex interim, but which imposes common knowledge and strategic sophistication assumptions that are often viewed as unrealistic.

This paper proposes a perfectly competitive model of a market with adverse selection. Prices are determined by zero-profit conditions, and the set of traded contracts is determined by free entry. Crucially for applications, contract characteristics are endogenously determined, consumers may have multiple dimensions of private information, and an equilibrium always exists. Equilibrium corresponds to the limit of a differentiated products Bertrand game. We apply the model to establish theoretical results on the equilibrium effects of mandates. Mandates can increase efficiency but have unintended consequences. With adverse selection, an insurance mandate reduces the price of low-coverage policies, which necessarily has indirect effects such as increasing adverse selection on the intensive margin and causing some consumers to purchase less coverage.

We propose a new framework for optimal experimentation, which we term the “A/B testing problem.” Our model departs from the existing literature by allowing for fat tails. Our key insight is that the optimal strategy depends on whether most gains accrue from typical innovations or from rare, unpredictable large successes. If the tails of the unobserved distribution of innovation quality are not too fat, the standard approach of using a few high-powered “big” experiments is optimal. However, if the distribution is very fat tailed, a “lean” strategy of trying more ideas, each with possibly smaller sample sizes, is preferred. Our theoretical results, along with an empirical analysis of Microsoft Bing’s EXP platform, suggest that simple changes to business practices could increase innovation productivity.

The endowment effect, the tendency to value possessions more than non-possessions, is a well-known departure from rational choice and has been replicated in numerous settings. We investigate the universality of the endowment effect, its evolutionary significance, and its dependence on environmental factors. We experimentally test for the endowment effect in an isolated and evolutionarily relevant population of hunter-gatherers, the Hadza Bushmen of Northern Tanzania. We find that Hadza living in isolated regions do not display the endowment effect, while Hadza living in a geographic region with increased exposure to modern society and markets do display the endowment effect.