# Polyhedral Clinching Auctions for Indivisible Goods

## TL;DR

This paper introduces a polyhedral clinching auction mechanism for indivisible goods that maintains incentive compatibility, individual rationality, and Pareto optimality, with polynomial runtime and strong efficiency guarantees.

## Contribution

It extends the polyhedral clinching auction framework from divisible to indivisible goods, ensuring computational efficiency and improved welfare performance.

## Key findings

- Mechanism runs in polynomial time.
- Achieves over 50% of optimal liquid welfare.
- Surpasses optimal liquid welfare in social welfare.

## 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.