# Peiran Xiao

I am a sixth-year Ph.D. candidate in Economics at Boston University. My field of research is Microeconomic Theory, with a focus on mechanism design and information economics.

Email: pxiao[at]bu.edu

Address: Department of Economics, Boston University, 270 Bay State Road, Boston, MA 02215

Grads at BU, BC, and Brown are organizing a joint theory workshop!

I study the optimal design of performance or product ratings to motivate agents’ performance or investment in product quality. The principal designs a rating that maps their quality (performance) to possibly stochastic scores. Agents have private information about their abilities (costs of effort/quality) and choose their quality. The market observes the scores and offers a wage equal to the agent’s expected quality [resp. ability].

I first show that an incentive-compatible interim wage function can be induced by a rating (i.e., feasible) if and only if it is a mean-preserving spread of quality [resp. ability] in the quantile space. Thus, I reduce the principal's rating design problem to the design of a feasible interim wage. When restricted to deterministic ratings, the optimal rating design is equivalent to the optimal delegation with participation constraints (Amador and Bagwell, 2022). Using optimal control theory, I provide necessary and sufficient conditions under which lower censorship, especially a simple pass/fail test, is optimal within deterministic ratings. In particular, when the principal elicits maximal effort (quality), lower censorship [resp. pass/fail] is optimal if the density is unimodal [resp. increasing]. I also solve for the optimal deterministic ratings beyond lower censorship for general distributions and preferences. For general ratings, I provide sufficient conditions under which lower censorship remains optimal. In the effort maximization case, a pass/fail test remains optimal if the density is increasing.

### Allocating Positional Goods: A Mechanism Design Approach

“If everyone stands on tiptoe, no one sees better.”

Consumers of positional goods care about their relative positions in the consumption of the goods, so allocating an item to one buyer has externalities on others. Using a mechanism design approach, I characterize the externalities by a feasibility condition. Under Myerson’s regularity, the revenue-maximizing mechanism excludes some low types and fully separates the rest. 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, total pooling (full separation) and no exclusion maximize the consumer surplus if the distribution has an increasing (decreasing) failure rate. Applications include educational arms races, priority services, and luxury goods.

What is the optimal tournament when one player hires the other?

We study the optimal design of a two-player tournament in which one player has discretion over hiring the other. The manager hires an agent of a certain ability and competes with him in a Lazer-Rosen-style tournament. In the tournament, both players produce at heterogeneous marginal costs (abilities), and 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 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 principal with succession concerns may allow hiring sabotage to prevail in equilibrium but will ensure the new hire has a higher ability than the manager.