On Truthful Item-Acquiring Mechanisms for Reward Maximization
Liang Shan, Shuo Zhang, Jie Zhang, Zihe Wang
TL;DR
The paper studies truthful item-acquiring mechanisms under information asymmetry between an owner and a collector, with an independent noisy appraiser. It develops single-item mechanisms (SOM, TMM, OM$_1$) and analyzes the menu-size tradeoff, showing SOM is optimal among deterministic IC monotone mechanisms under a consistency condition, with a bounded reward gap to the omniscient benchmark. Extending to multiple items, it proves that ordinal-only input is not IC and introduces Union Mechanisms that compose single-item mechanisms, revealing unbounded approximation gaps relative to the optimum in both single- and multi-item settings. Experimental results under normal and log-normal distributions demonstrate robustness to appraiser accuracy and indicate that multi-item unions can improve both reward and item-acquisition rates. The work advances non-payment mechanism design for eliciting truthful information and lays groundwork for future extensions, including payments and learning-augmented approaches, with applications to markets like used cars and antiques.
Abstract
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.