This paper studies a class of games, “all-pay contests,” which capture general asymmetries and sunk investments inherent in scenarios such as lobbying, competition for market power, labor-market tournaments, and R&D races. Players compete for one of several identical prizes by choosing a score. Conditional on winning or losing, it is weakly better to do so with a lower score. This formulation allows for differing production technologies, costs of capital, prior investments, attitudes toward risk, and conditional and unconditional investments, among others. I provide a closed-form formula for players' equilibrium payoffs and analyze player participation. A special case of contests is multiprize, complete-information all-pay auctions.

This paper studies equilibrium behavior in a class of games that models asymmetric competitions with unconditional and conditional investments. Such competitions include lobbying settings, labor-market tournaments, and R&D races, among others. I provide an algorithm that constructs the unique equilibrium in these games and apply it to study competitions in which a fraction of each competitor's investment is sunk and the rest is paid only by the winners. Complete-information all-pay auctions are a special case.

We consider contests with many, possibly heterogeneous, players and prizes, and show that the equilibrium outcomes of such contests are approximated by the outcomes of mechanisms that implement the assortative allocation in an environment with a single agent that has a continuum of possible types. This makes it possible to easily approximate the equilibria of contests whose exact equilibrium characterization is complicated, as well as the equilibria of contests for which there is no existing equilibrium characterization.

We investigate whether a market served by a multiproduct monopolistic seller can be segmented in a way that benefits all consumers and the seller. The seller can offer a different product menu in each market segment, combining second- and third-degree price discrimination. We show that markets for which profit maximization leads to inefficiency can, generically, be segmented into two market segments in a way that increases the surplus of all consumers weakly and of some consumers and the seller strictly. Our constructive proof is based on deriving implications of binding incentive compatibility constraints when profit maximization implies inefficiency.

We provide sufficient conditions for equilibrium existence in first‐price auctions with private values that accommodate non quasi‐linear utilities and value‐distributions that contain atoms and exhibit positive or negative correlation. These conditions show that equilibrium existence often turns on properties of a single statistic of the joint distribution of values, namely, the minimum value in the support of the high‐value distribution (the mHV). We also show that modifying the standard tie‐breaking rule only at the mHV is enough to guarantee equilibrium existence without our sufficient conditions. Our results also apply to Bertrand price competition when each firm's constant marginal cost is private information.

The seller of an asset has the option to buy hard information about the value of the asset from an intermediary. The seller can then disclose this information before selling the asset in a competitive market. We study how the intermediary designs and sells hard information to robustly maximize the intermediary's revenue across all equilibria. Even though the intermediary could use an accurate test that reveals the asset’s value, we show that robust revenue maximization leads to a noisy test with a continuum of possible scores. In addition, the intermediary always charges the seller for disclosing the test score to the market, but not necessarily for running the test. This enables the intermediary to robustly appropriate a significant share of the surplus resulting from the asset sale.

Many countries base college admissions on a centrally administered test. Students invest a great deal of resources to improve their performance on the test, and there is growing concern about the high costs associated with these activities. We consider modifying the test by introducing performance-disclosure policies that pool intervals of performance rankings. Pooling affects the equilibrium allocation of students to colleges, which hurts some students and benefits others, but also affects students’ effort. We investigate how such policies can improve students’ welfare in a Pareto sense, study the Pareto frontier of pooling policies, and identify improvements that are robust to the distribution of college seats. We illustrate the potential applicability of our results with an empirical estimation that uses data on college admissions in Turkey. We find that a policy that pools a large fraction of the lowest-performing students leads to a Pareto improvement in a contest based on the estimated parameters. A laboratory experiment based on the estimated parameters generally supports our theoretical predictions.