Peiran Xiao

We study tournaments with managerial discretion in hiring. A manager selects a coworker from a pool of candidates and then competes against him in a Lazear–Rosen–style tournament with a prize equal to a share of total output. A profit-maximizing principal sets the prize share together with a head start (or handicap)—an advantage (or disadvantage) in the output comparison—granted to the manager. The head start affects output through three channels: (i) encouraging the manager, (ii) discouraging the new hire, and (iii) inducing the manager to hire a stronger candidate. The hiring effect dominates the discouragement effect until the strongest candidate is hired; beyond that point, any further head start discourages the new hire more than it encourages the manager. The optimal contract therefore grants just enough head start to induce the manager to hire the strongest candidate.

We study a mechanism design problem without transfers where a principal seeks to efficiently select a project together with an agent to implement it. Each agent’s private type reflects his ability to implement more ambitious projects. Although the principal and selected agent share identical preferences, unselected agents receive nothing, so conflict arises from competition alone. Screening relies on “overpromising,” where higher reports yield increasingly ambitious projects to raise the costs weaker agents incur when imitating stronger ones. Optimal mechanisms mitigate the resulting inefficiencies through “handicapping,” whereby weaker agents are sometimes selected over stronger ones. Notably, handicapping can locally intensify overpromising, since making nearby higher types more likely to be selected increases the project distortion necessary to deter imitation. Thus, handicapping and overpromising can be local complements despite being global substitutes. We discuss implications for competitive early-stage R&D project selection mechanisms.

I study the optimal allocation of positional goods, where consumers’ concern for relative consumption generates externalities. Applications include luxury goods, priority services, education, and organizational hierarchies. Using a mechanism design approach, I characterize feasible allocations through a majorization condition. Under Myerson regularity, the revenue-maximizing mechanism fully separates participating buyers, with possible exclusion at the bottom. Selling a single level guarantees at least half the maximum revenue. When all buyers are served, restricting the seller to a single level increases consumer surplus under an increasing failure rate (IFR). When the seller is restricted to a single level, expanding coverage also benefits consumers under IFR but may hurt them otherwise. I also characterize the welfare-maximizing mechanism with and without subsidies.

I study the optimal design of ratings to motivate an agent’s investment in quality when transfers are unavailable. The principal designs a rating scheme that maps quality to a (possibly stochastic) signal. The agent privately knows his ability and chooses a quality level. A competitive market then offers the agent a wage equal to his expected quality given the signal. When restricted to deterministic ratings, lower censorship is optimal if the ability density is single-peaked, and pass/fail tests are optimal as well if the density is increasing. When randomization is allowed, lower censorship remains optimal if the ability density is log-concave or increasing, and pass/fail tests remain optimal if the density is increasing. By contrast, every optimal rating scheme involves randomization if the density is decreasing and sufficiently log-convex—roughly speaking, if intermediate ability is scarce relative to high and low ability.

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, such as 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.