  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.
