No Screening is More Efficient with Multiple Objects

We study efficient mechanism design for allocating multiple heterogeneous objects. The aim is to maximize the residual surplus, the total value generated from an allocation minus the costs of screening. We discover a robust trend indicating that no-screening mechanisms, such as serial dictatorship with exogenous priority order, tend to perform better as the variety of goods increases. We analyze the underlying reasons by characterizing asymptotically efficient mechanisms in a stylized environment. We also apply an automated mechanism design approach to numerically derive efficient mechanisms and validate the trend in general environments. Building on these implications, we propose the register-invite-book system (RIB) as an efficient system for scheduling vaccinations against pandemic diseases.

💡 Research Summary

The paper investigates the design of mechanisms for allocating multiple heterogeneous objects when agents have multi‑dimensional preferences but demand only a single item. The central planner’s objective is to maximize residual surplus, defined as the total value generated by the allocation minus the costly screening (or “ordeal”) effort that agents must expend to signal their preferences. Two canonical mechanisms are contrasted: a no‑screening serial dictatorship (SD) with an exogenously fixed priority order, and the Vickrey‑Clarke‑Groves (VCG) mechanism, which achieves allocative efficiency at the expense of high screening costs.

The authors first introduce a stylized continuous market with a unit mass of agents and a finite set K of object types, each with equal capacity. Each agent’s valuation vector for the K types is drawn i.i.d. from a common distribution (e.g., Weibull). By focusing on the largest order statistic—the agent’s highest valuation among all types—they reduce the multi‑dimensional problem to a single‑dimensional setting. In this reduced environment, they prove that a no‑screening mechanism is efficient if the underlying value distribution satisfies the “new better than used in expectation” (NBUE) property, a condition weaker than the increasing hazard rate (IHR) used in prior work (Hartline and Roughgarden, 2008).

A key theoretical contribution is the analysis of how the number of object types K influences the distribution of the maximum order statistic. As K grows, the tail of the maximum becomes heavier, and the distribution increasingly satisfies NBUE and eventually IHR, regardless of the original marginal distribution. Using extreme‑value theory, they show that in the limit K → ∞ the maximum order statistic converges to one of the three classic extreme‑value families (Gumbel, Fréchet, Weibull). For a broad class of marginal distributions—including all Weibull parameters—the performance ratio of SD to the exact optimal mechanism converges to one. Thus, with many object types, a simple no‑screening rule becomes asymptotically optimal.

To complement the analytical results, the authors employ RegretNet, a deep‑learning based automated mechanism design tool, to numerically compute mechanisms that maximize residual surplus in finite markets. Simulations with 2K agents demanding one of K heterogeneous objects (valuations drawn i.i.d. from Weibull with shape 0.8) reveal that while VCG dominates when K = 1 (the single‑object case), SD overtakes VCG for K ≥ 3, and its performance becomes indistinguishable from the RegretNet‑derived optimal mechanism for K ≥ 6. Additional experiments explore correlation structures: within‑agent correlation (values across objects for the same agent) weakens the advantage of SD, whereas between‑agent correlation (values for the same object across different agents) strengthens it, because screening costs dominate the allocative gains in the latter case.

The paper then translates these findings into a concrete policy proposal for COVID‑19 vaccine appointment scheduling. Many jurisdictions used first‑come‑first‑served (FCFS) systems, which induced substantial wasted effort as individuals scrambled for slots. In contrast, regions that adopted invitation‑based or priority‑based allocation (effectively a serial dictatorship) experienced far less wasted effort and higher overall surplus. Building on this observation, the authors propose the Register‑Invite‑Book (RIB) system: a practical implementation of SD that retains the simplicity of FCFS (a public register and invitation list) while eliminating costly screening. RIB assigns vaccination slots according to an exogenously determined priority (e.g., age, comorbidities), thereby maximizing residual surplus.

The literature review situates the work at the intersection of money‑burning mechanisms, multi‑dimensional mechanism design, and automated mechanism design. While prior studies have characterized optimal mechanisms for single‑dimensional or homogeneous‑good settings, the multi‑dimensional, multi‑object case remains largely intractable. This paper’s contribution is threefold: (1) a rigorous analytical characterization showing that increasing object variety drives the problem toward a single‑dimensional NBUE setting; (2) empirical validation via automated mechanism design that confirms the robustness of the trend across a range of distributions and correlation structures; and (3) a real‑world application demonstrating that simple, no‑screening mechanisms can be both theoretically justified and practically superior in public‑health resource allocation.

In conclusion, the study reveals a counter‑intuitive but robust principle: as the variety of heterogeneous objects expands, mechanisms that avoid costly screening—specifically serial dictatorship with a fixed priority order—become increasingly efficient, eventually approaching optimality. This insight has broad implications for the design of allocation systems in domains ranging from vaccine distribution to school seat assignment, public housing, and any setting where agents must signal preferences over a rich set of distinct goods. Policymakers should therefore consider prioritizing simple, no‑screening allocation rules when faced with high‑dimensional resource environments, as they can achieve near‑optimal social welfare while minimizing the administrative and individual burdens associated with screening.