In this research, we study the problem that a collector acquires items from the owner based on the item qualities the owner declares and an independent appraiser's assessments. The owner is interested in maximizing the probability that the collector acquires the items and is the only one who knows the items' factual quality. The appraiser performs her duties with impartiality, but her assessment may be subject to random noises, so it may not accurately reflect the factual quality of the items. The main challenge lies in devising mechanisms that prompt the owner to reveal accurate information, thereby optimizing the collector's expected reward. We consider the menu size of mechanisms as a measure of their practicability and study its impact on the attainable expected reward. For the single-item setting, we design optimal mechanisms with a monotone increasing menu size. Although the reward gap between the simplest and optimal mechanisms is bounded, we show that simple mechanisms with a small menu size cannot ensure any positive fraction of the optimal reward of mechanisms with a larger menu size. For the multi-item setting, we show that an ordinal mechanism that only takes the owner's ordering of the items as input is not incentive-compatible. We then propose a set of Union mechanisms that combine single-item mechanisms. Moreover, we run experiments to examine these mechanisms' robustness against the independent appraiser's assessment accuracy and the items' acquiring rate.

翻译：本研究探讨了一个问题：收藏家根据物主声明的物品质量以及独立评估师的评估结果，从物主那里获取物品。物主希望最大化收藏家获取物品的概率，并且是唯一知晓物品真实质量的人。评估师公正履行职责，但其评估可能受到随机噪声影响，因此未必能准确反映物品的真实质量。主要挑战在于设计能够促使物主披露真实信息的机制，从而优化收藏家的预期奖励。我们将机制的菜单规模作为其实用性的衡量指标，并研究其对可实现的预期奖励的影响。针对单物品场景，我们设计了具有单调递增菜单规模的最优机制。尽管最简单机制与最优机制之间的奖励差距有界，但研究表明，菜单规模小的简单机制无法保证达到菜单规模大的机制的最优奖励的任意正比例。针对多物品场景，我们证明仅以物主对物品的排序作为输入的序数机制不具备激励相容性。随后，我们提出了一组结合单物品机制的联合机制。此外，我们通过实验检验了这些机制对独立评估师评估精度以及物品获取率的鲁棒性。