Research
Working Papers
Incentivizing Agents through Ratings [New draft coming soon]
I study the optimal design of ratings to motivate agent investment in quality when transfers are unavailable. The principal designs a rating scheme that maps the agent’s quality to a (possibly stochastic) score. The agent has private information about his ability, which determines his cost of investment, and chooses the quality level. The market observes the score and offers a wage equal to the agent’s expected quality. For example, a school incentivizes learning through a grading policy to disclose the student’s quality to the job market.
I reduce the principal’s problem to the design of an interim wage function of quality. When restricted to deterministic ratings, I provide necessary and sufficient conditions for the optimality of simple pass/fail tests and lower censorship. In particular, when the principal’s objective is expected quality, pass/fail tests (lower censorship) are optimal if the agent’s ability is concentrated at the top (around the mode) of the distribution. The results generalize existing results in optimal delegation with voluntary participation, as pass/fail tests (lower censorship) correspond to take-it-or-leave-it offers (threshold delegation). Additionally, I provide sufficient conditions for pass/fail tests and lower censorship to remain optimal without restriction to deterministic ratings. Pass/fail tests remain optimal for quality maximization if the ability distribution is more concentrated at higher values.
Consumers of positional goods care about their relative positions in the consumption of the goods, so allocating an item to one buyer has externalities on others. Using a mechanism design approach, I characterize the externalities by a feasibility condition. I find the revenue-maximizing mechanism excludes some low types and fully separates the rest if and only if the buyer’s type distribution is regular. The seller can guarantee at least half the maximal revenue by offering one level of positional goods, and the approximation can be arbitrarily close if the buyer’s type distribution is sufficiently concave. Moreover, if the distribution has an increasing (decreasing) failure rate, total pooling (full separation) without exclusion maximizes the consumer surplus, and the consumer surplus is decreasing (increasing) in the number of positional good levels. Applications include education, priority services, luxury goods, and organizational design.
We study the optimal design of a two-player tournament in which one player (the manager) has discretion over hiring the other. The manager determines the new hire’s ability and competes with him in a Lazer-Rosen-style tournament, in which the one with higher output wins a fraction of the total output. The principal determines the payout ratio and the head start (or handicap) to the manager—an advantage (or disadvantage) when comparing output. We find the head start has three effects on the output: (i) encouragement effect on the manager, (ii) discouragement effect on the new hire, and (iii) hiring effect through the increased ability of the new hire. The hiring effect dominates the discouragement effect until the best candidate is hired; once the best is hired, any further head start leads the discouragement effect to dominate the encouragement effect. Therefore, the optimal contract offers just enough head start to induce the manager to hire the best candidate. However, in a two-period model where the first-period winner is retained for the future, the optimal contract may allow the manager to hire a suboptimal candidate who must still have a higher ability than the manager.
Work in Progress
Endogenous Segregation across Social Media Platforms
Group Design with Endogenous Networks
Short Notes
I apply (hybrid) Pontryagin’s maximum principles in the optimal control theory to solve delegation problems (in particular, Amador and Bagwell 2013, 2022), as an alternative to (cumulative) Lagrangian methods developed by Amador, Werning, and Angeletos (2006). In delegation problems with voluntary participation (Amador and Bagwell 2022), where the participation constraint leads to a jump in allocation, I study the global problem (instead of the truncated problem) and provide necessary and sufficient conditions that allow the bang-bang allocation (price cap or opt-out) to be optimal.
Subsumed Notes
I reformulate Gershkov and Winter’s (2023) model of priority services as a mechanism design problem under a feasibility condition. Thus, I provide the necessary and sufficient conditions for their Propositions 1, 2, 7, and 8, while allowing for stochastic priority levels. Under the weaker conditions, adding more priority levels can increase both the provider’s revenue and consumer welfare if the cost distribution has a decreasing failure rate but satisfies Myerson’s regularity. Full separation can be implemented by an all-pay auction. I also show that the provider can guarantee at least half the maximal revenue by offering one priority service in addition to a (free) regular service, and the approximation can be arbitrarily close if the distribution is sufficiently concave. The approach can also be applied to Moldovanu, Sela, and Shi's (2007) model of status contests.
I study how a monopoly certifier designs and prices the quality certification to maximize revenue when agents’ quality is endogenous. The certifier designs the quality certification (i.e., Blackwell experiment) and charges agents a flat certification fee. Agents with heterogeneous costs choose their quality (and whether to take the test) and receive a payment equal to the expected quality conditional on the test result by the competitive market. By characterizing the feasibility condition for interim posterior means, I show the certifier can maximize revenue by committing to a noisy test. The interim approach applies to a more general class of problems, revenue maximization being a special case where feasibility is equivalent to Bayesian plausibility.