In this study, we propose the polyhedral clinching auction for indivisible goods, which has so far been studied for divisible goods. As in the divisible setting by Goel et al. (2015), our mechanism enjoys incentive compatibility, individual rationality, and Pareto optimality, and works with polymatroidal environments. A notable feature for the indivisible setting is that the whole procedure can be conducted in time polynomial of the number of buyers and goods. Moreover, we show additional efficiency guarantees, recently established by Sato for the divisible setting: The liquid welfare (LW) of our mechanism achieves more than 1/2 of the optimal LW, and that the social welfare is more than the optimal LW.

翻译：在本研究中，我们针对不可分物品提出了多面体扣价拍卖机制，该机制此前仅针对可分物品进行过研究。与Goel等人（2015）针对可分物品的设计类似，我们的机制具备激励相容、个体理性与帕累托最优性，并适用于多拟阵环境。值得注意的是，在不可分物品场景下，整个流程可在买方数量与物品数量的多项式时间内完成。此外，我们还展示了Sato近期针对可分物品场景确立的额外效率保证：机制实现的液体福利（LW）超过最优LW的1/2，且社会福利高于最优LW。