Research

We introduce markup equilibrium—an extension of Walrasian equilibrium in which consumers pay a fixed percentage markup over producer prices. In quasilinear markets, markup equilibria exist despite non-convexities. They are resource-feasible and envy-free, incur no budget deficit, and require little more communication and computation than the ordinary Walrasian equilibrium. The associated markup mechanism is asymptotically incentive-compatible. We also introduce a Bound-Form First Welfare Theorem, which states that for any feasible allocation, the welfare loss compared to the first-best is bounded, using any price vector, by the sum of the resulting (i) budget surplus and (ii) rationing losses suffered by the participants. Using producer prices, this bound implies that any markup equilibrium with a small markup and few unallocated goods is nearly efficient.

I show that the expected $k$th-highest order statistic from a monotone hazard rate distribution is concave in sample size. In independent private value auctions with convex marketing costs, this ensures that the seller’s objective is concave, yielding a finite optimum. Previously circulated as Concavity and convexity of order statistics in sample size.

Auctions are inherently risky: bidders face uncertainty about their prospects of winning and payments, while sellers are unsure about revenue and chances of a successful sale. Auction rules influence the allocation of risk among agents and the behavior of risk-averse bidders, leading to a breakdown of payoff and revenue equivalence and a heightened significance of auction design decisions by sellers. In this paper, we review the literature on risk aversion in auctions, with an emphasis on what can be learned about auction design from theoretical modeling and empirical studies. We survey theoretical results relating to the behavior of risk-averse agents in auctions, the comparison of standard auction formats in the presence of risk aversion and implications for auction design. We discuss standard and more recent approaches to identifying risk preferences in empirical studies and evidence for the significance of risk aversion in auction applications. Finally, we identify areas where existing evidence is relatively scant and ask what questions empirical research might ask given the theory and where further theoretical research may be beneficial given existing empirical results.

This paper studies how small perturbations—misreports, supply shocks, or changes in market participants—affect Walrasian equilibrium prices in finite exchange economies. A sequence of economies is perturbation-proof if the price effect of any bounded perturbation shrinks in proportion to market size. Perturbation-proofness captures both robustness of equilibrium prices to small misspecifications and approximate incentive-compatibility of Walrasian mechanisms. Strong monotonicity is the key driver of this property: it is necessary and sufficient for perturbation-proofness in replica economies and implies it with high probability in i.i.d. random economies. Applying these results to indivisible goods markets shows that sufficient heterogeneity in buyers’ demand yields perturbation-proofness even when individual demand is inelastic. Previously circulated as Strong Monotonicity and Perturbation-Proofness of Exchange Economies.

Many matching markets are suspected to suffer from inefficient levels of congestion. We show this is a real concern in an online labor market and present results of two market-wide experiments designed to reduce congestion.

The first intervention introduced a “soft” cap on the number of applications that could be received for a job opening and the number of days applications were accepted. Despite reducing the number of applications per opening, the intervention did not reduce the hiring probability or reported match quality. A second, more complex intervention that attempted to price externalities directly failed. We find that application fees introduced by the platform reduced hire rates and competition among candidates, suggesting that these fees may have been miscalibrated or higher than socially efficient.

This paper studies how topping up—allowing recipients of in-kind transfers to supplement subsidized consumption in a private market—affects optimal redistribution. Consumers can access a competitive private market, while a social planner offers an alternative nonlinear price schedule. We show that the effect of topping up depends on the correlation between redistributive priority and demand. When the correlation is positive, topping up does not affect the optimal mechanism. When the correlation is negative, topping up weakens screening and reduces redistribution. At the extensive margin, topping up reduces the set of environments in which intervention is optimal. At the intensive margin, topping up weakly reduces both the scope of a free public option and the mass of consumers served, and shifts redistribution away from the consumers with the highest redistributive priority. We characterize the optimal mechanisms and show how topping up changes the comparative statics of optimal redistribution with respect to redistributive priorities.

Wages are often fixed even though tasks vary in difficulty. I study how a firm motivates workers when task assignment is its only incentive instrument. Workers observe task costs and may refuse or quit; the firm commits to compensating unpleasant work with better future assignments. With one worker, the optimal contract assigns tasks above a cutoff that rises with promised utility. With several workers, larger promises earn better tasks on average; workers complete every positive-value task and the least costly negative-value tasks. Pooling tasks among workers adds value, and spare workers expand capacity. Dynamics add value exactly when a static rule assigning all tasks is infeasible. Relative patience governs long-run assignments: negative tasks eventually disappear when workers are more patient, assignments become effectively stationary under equal patience, and difficult tasks recur when the firm is more patient. The model rationalizes task rotation and seniority rules as substitutes for task-contingent pay.

We study a model of trade with repeated interaction between a single buyer and many sellers. The buyer is initially uninformed about her valuations for the various goods and sellers are uninformed about the buyer’s demand. We model this interaction as a multi-armed bandit problem with strategic arms and seek to understand the welfare consequences of various models of buyer behavior. We show that a buyer using a no-regret contextual learning algorithm may be exploited by colluding sellers in an approximate Nash equilibrium for the sellers. However, a buyer with commitment power may extract almost all the gains from trade from the sellers in an approximate dominant-strategy equilibrium for the sellers.