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 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 that discloses the student’s quality to the job market. 

I reduce the principal’s problem to the design of an interim wage as a 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 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. 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 deterministic ratings to remain optimal when stochastic ratings are allowed.

I study the optimal allocation of positional goods with externalities and one-sided transfers. Because consumers care about their relative positions in consumption, 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 satisfies Myerson's regularity. 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 will allow the manager to hire a candidate who is not the best but still better than the manager.

Can echo chambers across social media platforms emerge endogenously? I study a model where rational agents segregate into different platforms because of uncertainty about others’ information accuracy. Agents with different accuracy (high or low) receive binary private signals about a binary state of the world and want to learn the true state. Upon receiving private signals, they choose one of the two platforms to post their signals and observe other users’ signals. Agents remain on the platforms in future periods and continue to observe others’ signals. I show a separating equilibrium exists where agents are segregated by their initial private signals because they believe agents who receive the same signals are more likely to have high accuracy. Compared to pooling on the same platform, segregation can decrease social welfare because agents know other users’ signals will confirm their beliefs and therefore can learn little from these signals.

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.