  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.
