Polyhedral Clinching Auctions for Indivisible Goods

Abstract: 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.