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 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 (possibly stochastic) rating scheme that maps quality to a distribution over signals. 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. I reduce the rating design problem to a mechanism design problem with a majorization constraint. When the principal maximizes expected quality, randomization has no value if the ability density is log-concave or increasing: lower censorship is then optimal among all rating schemes, and pass/fail tests are also optimal if the density is increasing. By contrast, every optimal rating scheme involves randomization if the density is decreasing and sufficiently log-convex—roughly, if intermediate ability is scarce relative to high and low ability

A principal designs performance ratings to elicit effort from agents seeking to signal their ability to the job market. Optimal rating design faces a trade-off between informativeness and incentives: to motivate agents, ratings must be informative about effort; yet greater informativeness also helps the market infer ability, weakening the incentives for the lowest-ability agents to exert effort. Consequently, with strictly convex effort costs, optimal rating schemes must involve randomization for agents at the bottom of the ability distribution.

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.