简单且稳健的质量披露：分位数划分的力量
Simple and Robust Quality Disclosure: The Power of Quantile Partition
AI总结：
本文研究了稳健质量披露问题，通过分位数划分方法，提供了一种在不同市场环境下都能保持稳健的披露策略，并给出了显式公式和理论保证。
摘要：
在线平台上质量信息通常通过简单的、基于百分位数的徽章和等级来传达，这些等级在不同的市场环境中保持稳定。受这一实证证据的启发，我们研究了一个市场中稳健的质量披露，其中平台承诺一种公开披露政策，将卖家的产品质量映射为信号，随后卖家设定下游垄断价格。买家具有异质的私人类型和估值，这些估值与质量成线性关系。我们通过最小最大竞争比率评估披露政策：其最坏情况下的收益相对于贝叶斯最优的披露和定价基准，统一覆盖所有质量分布、类型分布和可接受估值。我们的主要结果为分位数划分披露提供了明确的理论依据。对于K-分位数划分政策，我们完全刻画了稳健最优：稳健最优比率由一维固定点方程确定，最优阈值遵循递归。我们还给出了任何分位数划分的稳健比率的显式公式，作为简单的“max-over-bins”表达式，这解释了为什么稳健最优的划分对上分位数分配更精细的分辨率，并产生紧致保证，如1 + 1/K对于均匀百分位数桶。相比之下，我们展示了有限信号单调（质量阈值）划分的稳健性限制，其无法超越因子2的近似。技术上，我们的分析将稳健质量披露减少到稳健披露设计程序中，通过建立所有可行间接收益函数的紧致函数特征来实现。
英文摘要：
Quality information on online platforms is often conveyed through simple, percentile-based badges and tiers that remain stable across different market environments. Motivated by this empirical evidence, we study robust quality disclosure in a market where a platform commits to a public disclosure policy mapping the seller's product quality into a signal, and the seller subsequently sets a downstream monopoly price. Buyers have heterogeneous private types and valuations that are linear in quality. We evaluate a disclosure policy via a minimax competitive ratio: its worst-case revenue relative to the Bayesian-optimal disclosure-and-pricing benchmark, uniformly over all prior quality distributions, type distributions, and admissible valuations. Our main results provide a sharp theoretical justification for quantile-partition disclosure. For K-quantile partition policies, we fully characterize the robust optimum: the optimal worst-case ratio is pinned down by a one-dimensional fixed-point equation and the optimal thresholds follow a backward recursion. We also give an explicit formula for the robust ratio of any quantile partition as a simple "max-over-bins" expression, which explains why the robust-optimal partition allocates finer resolution to upper quantiles and yields tight guarantees such as 1 + 1/K for uniform percentile buckets. In contrast, we show a robustness limit for finite-signal monotone (quality-threshold) partitions, which cannot beat a factor-2 approximation. Technically, our analysis reduces the robust quality disclosure to a robust disclosure design program by establishing a tight functional characterization of all feasible indirect revenue functions.
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