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arxiv: 2512.20001 · v2 · submitted 2025-12-23 · 💰 econ.TH

Allocating Common-Value Goods

Hiroto Sato , Ryo Shirakawa This is my paper

Pith reviewed 2026-05-16 20:45 UTC · model grok-4.3

classification 💰 econ.TH
keywords common-value goodsmechanism designallocation without transfersinformation screeninginduced learningunit-demand agentsoptimal mechanismexclusion
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The pith

The optimal mechanism for allocating common-value goods is defined by two parameters: one for allocation probability and one for induced learning.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

A designer wants to distribute identical goods to as many agents as possible, but each agent holds only partial private information about the shared value and will accept the good only if that value appears high. The mechanism therefore uses every agent's report to help screen others while also determining how much new information the allocation decision itself reveals to the group. The optimum turns out to depend on exactly two numbers: one fixes the chance that any given agent receives the good, and the other fixes how strongly the allocation outcome updates everyone's beliefs about the value. Even though the designer prefers to allocate whenever agents are willing, the best mechanism sometimes excludes agents and withholds the goods even when every agent would accept them. The same two-parameter form continues to work when payments are allowed, though exclusion may then be avoided and payments can be positive and decreasing in allocation probability.

Core claim

The optimal mechanism is summarized by two parameters, one that adjusts the probability of allocation and the other that governs the amount of learning about the common value induced by the allocation decision. This structure screens each agent's private information by drawing on the reports of others while simultaneously shaping what every agent learns from the outcome. Although the designer prefers to allocate the goods, the optimum excludes some agents and may withhold allocation even when all agents would be willing to receive them. The identical structure persists when monetary payments are available, but exclusion need not occur and payments may be strictly positive and decreasing in a

What carries the argument

Two-parameter mechanism in which one parameter sets allocation probability and the other sets the degree of belief updating about the common value that occurs when allocation is realized.

Load-bearing premise

Agents hold only partial private information about the common value and accept the goods only when they infer the value is high enough for screening to work through others' reports.

What would settle it

A calculation or simulation under the model's information structure showing that some mechanism outside the two-parameter family achieves strictly higher designer payoff than any two-parameter candidate.

read the original abstract

We study a simple problem of allocating common-value goods. The designer seeks to allocate the goods to as many unit-demand agents as possible without monetary transfers, while agents, who possess partial private information about the goods, are willing to receive them only when the goods are of high value. Mechanisms screen each agent's private information using the information of other agents, and in doing so shape what agents learn from other agents about the value of the goods. The optimal mechanism can be summarized by two parameters: one adjusts the allocation probability, while the other governs the amount of learning induced by allocation. Although the designer prefers to allocate the goods, the optimal mechanism excludes some agents and, as a result, may withhold allocation even when all agents would be willing to receive them. The optimal mechanism has the same structure even when payments are available, but it may not exclude any agent and may involve strictly positive payments that are decreasing in allocation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper studies allocation of common-value goods to unit-demand agents without transfers. Agents hold partial private information about the common value and accept the good only if it is high-value. Mechanisms screen via other agents' reports while shaping what agents learn about the value. The optimal mechanism is fully characterized by two parameters (one governing allocation probability, one governing learning induced by allocation). Despite the designer's preference for allocation, the optimum excludes some agents and may withhold the good even when all agents are willing to accept. The same two-parameter structure persists when payments are allowed, though exclusion may disappear and payments may be positive and decreasing in allocation.

Significance. If the characterization holds, the paper supplies a clean, low-dimensional description of optimal information design in a common-value allocation setting without transfers. It isolates how exclusion and withholding arise from the interaction of screening and learning, and shows robustness to the introduction of payments. This offers a useful benchmark for mechanism design in environments where willingness is state-dependent and transfers are limited.

major comments (2)
  1. [§4, Theorem 1] §4, Theorem 1: the optimality claim for the two-parameter mechanism rests on the equilibrium conditions derived from the agents' willingness-to-accept constraints; the manuscript must explicitly verify that these conditions are satisfied for the reported parameter values rather than assumed by construction.
  2. [§5.2, Proposition 2] §5.2, Proposition 2: the statement that the mechanism may withhold allocation even when all agents are willing requires an explicit numerical example or parameter region (e.g., a specific distribution of the common value and signal structure) showing that the withholding region is nonempty under the designer's objective.
minor comments (2)
  1. [Notation] Notation: the two free parameters are introduced in the abstract but receive different symbols in the main text; standardize the notation (e.g., α for allocation probability and β for induced learning) throughout.
  2. [Introduction] Introduction, paragraph 3: the description of 'partial private information' should include a short formal definition or example immediately after the informal sentence to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The suggestions help strengthen the presentation of the results. We address each major comment point by point below and will make the indicated revisions.

read point-by-point responses

  1. Referee: [§4, Theorem 1] §4, Theorem 1: the optimality claim for the two-parameter mechanism rests on the equilibrium conditions derived from the agents' willingness-to-accept constraints; the manuscript must explicitly verify that these conditions are satisfied for the reported parameter values rather than assumed by construction.

    Authors: We agree that explicit verification strengthens the argument. While the two-parameter mechanism is constructed to satisfy the willingness-to-accept constraints by design, we will add a short verification step (either in the proof of Theorem 1 or in a new appendix) that directly checks the equilibrium conditions for the reported optimal parameter values. This will confirm that the constraints bind as required and that the mechanism is indeed an equilibrium. revision: yes

  2. Referee: [§5.2, Proposition 2] §5.2, Proposition 2: the statement that the mechanism may withhold allocation even when all agents are willing requires an explicit numerical example or parameter region (e.g., a specific distribution of the common value and signal structure) showing that the withholding region is nonempty under the designer's objective.

    Authors: We thank the referee for this helpful suggestion. To illustrate the result concretely, we will add a specific numerical example to Section 5.2. The example will specify a binary common-value distribution together with a signal structure under which the optimal mechanism withholds the good even though every agent is willing to accept it. This will demonstrate that the withholding region is nonempty for the designer's objective. revision: yes

Circularity Check

0 steps flagged

No circularity in mechanism characterization

full rationale

The paper derives the optimal mechanism's two-parameter structure (allocation probability adjustment and induced learning) directly from the model primitives: unit-demand agents with partial private information about common-value goods, state-dependent willingness to receive, and the designer's goal of maximizing allocations without transfers. The characterization follows from solving the designer's optimization problem that screens via cross-agent information while shaping beliefs. No step reduces a prediction to a fitted input by construction, invokes a self-citation as the sole justification for a uniqueness claim, or renames a known result. The exclusion result despite designer preference for allocation is a standard implication of incentive constraints in common-value settings and does not rely on circular reasoning. The derivation is self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The model rests on standard mechanism-design assumptions plus the specific common-value partial-information setup; no new entities are introduced.

free parameters (2)
  • allocation-probability parameter
    One of the two parameters that summarize the optimal mechanism; adjusts how often agents receive the good.
  • learning-induced-by-allocation parameter
    Second summarizing parameter; controls how much information agents infer from the allocation decision itself.
axioms (3)
  • domain assumption Agents have partial private information about the common value of the goods
    Stated directly in the abstract as the basis for screening and learning.
  • domain assumption Agents accept the good only if they believe its value is high
    Core behavioral assumption enabling the information-screening role of the mechanism.
  • domain assumption No monetary transfers are used
    Explicit constraint of the main problem analyzed.

pith-pipeline@v0.9.0 · 5443 in / 1488 out tokens · 23053 ms · 2026-05-16T20:45:36.705267+00:00 · methodology

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