Peiran Xiao

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 a 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 that discloses the student’s quality to the job market. 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 are optimal if the agent’s ability distribution is concentrated towards the top, while lower censorship is optimal if the ability distribution is concentrated towards the mode. When stochastic ratings are allowed, pass/fail tests remain optimal for quality maximization if the ability density is increasing, while stochastic ratings can increase expected quality if medium ability is sufficiently scarce relative to high and low abilities.

I study the optimal allocation of positional goods in the presence of externalities arising from consumers’ concerns about relative consumption. Applications include luxury goods, priority services, education, and organizational hierarchies. Using a mechanism-design approach, I characterize the set of feasible allocations through a majorization condition. The revenue-maximizing mechanism possibly excludes some buyers and fully separates participants under Myerson’s regularity condition. The seller can guarantee at least half the maximum revenue by offering a single good. Without exclusion, offering more levels of goods decreases (increases) consumer surplus under increasing (decreasing) failure rates. Higher participation raises consumer surplus under increasing failure rates.

We introduce managerial discretion into tournaments by allowing a player to choose another to work with and compete against. The manager determines the new hire’s ability and competes with him in a Lazear-Rosen-style tournament, where the prize is a share of the total output. The profit-maximizing principal sets the share and the head start (or handicap) to the manager—an advantage (or disadvantage) in output comparison. The head start affects output through three channels: (i) encouraging the manager, (ii) discouraging the new hire, and (iii) increasing the new hire’s ability. The hiring effect dominates the discouragement effect until the best candidate is hired; beyond that, any further head start discourages the new hire more than it encourages the manager. Thus, the optimal contract provides just enough head start to ensure the manager hires the best candidate. 

We study a mechanism design problem in which a principal selects a project to implement as well as an agent to implement it but cannot use transfers. Conflict arises endogenously through competition: While the principal and selected agent obtain the same positive payoff, an agent who is not selected obtains zero payoff. We show how this feature creates an endogenous upward bias in project selection, whereby the selected project is consistently inefficiently high relative to the agent's type. Optimal mechanisms combine these distortions with “handicaps” that may select weaker agents over stronger ones. Such handicapping can facilitate efficient project selection for the strongest agents. We discuss implications for the design of competitive early-stage R&D project selection mechanisms.

I study the Amador and Bagwell (2022) model of monopolist regulation without transfers. Using the optimal control method, I provide weaker sufficient conditions for the optimality of price-cap regulation, which accommodate cases where the monopolist in the market always sets the price at the cap. For linear demand, price caps are optimal if the cost density is log-concave or decreasing. For log-convex demand functions with constant curvature (e.g., logarithmic and constant elasticity demand), price caps are optimal if the cost density is log-concave or increasing. Methodologically, I develop a sufficiency theorem for optimal control problems with monotonicity and equality constraints on state variables, which can be applied to delegation problems with or without participation constraints.