Peiran Xiao

We study a mechanism design problem in which a principal selects a project to implement and 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. A principal seeking to select the strongest agent thus incentivizes weaker agents to overpromise, so that competition endogenously induces bias. Optimal mechanisms manage this bias by either asking for excessively ambitious projects or by allocating to weaker agents over stronger ones. Our results delineate the relative advantage of each tool and discuss implications for the design of 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 the agent’s quality to a possibly stochastic score. The agent has private information about his ability, which determines the cost of investment, and chooses a quality level. The market observes the score and offers a wage equal to the agent’s expected quality. When restricted to deterministic ratings, the quality-maximizing rating is lower censorship if the ability density is unimodal, and a pass/fail test if the density is increasing. When stochastic ratings are allowed, lower censorship remains optimal if the density is log-concave, and a pass/fail test remains optimal if the density is increasing. Stochastic ratings increase expected quality when the density is decreasing and sufficiently log-convex.

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, where the prize is a share of total output. A profit-maximizing principal sets both the prize share and a head start, or handicap, granted to the manager. The head start affects output through three channels: encouraging the manager, discouraging the new hire, and inducing the manager to hire a stronger candidate. 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. Consequently, the optimal contract provides just enough head start to ensure the manager hires the best candidate.

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.