Truthful Multi-Parameter Auctions with Online Supply: an Impossible Combination

TL;DR

This paper proves that designing a deterministic truthful auction mechanism for online supply with multiple parameters and uncertain item arrivals cannot achieve any finite approximation to optimal social welfare, highlighting fundamental limitations.

Contribution

It establishes an impossibility result for deterministic truthful mechanisms in multi-parameter online supply auctions, a previously unexplored setting.

Findings

No deterministic truthful mechanism can approximate the optimal welfare.

The impossibility holds even with unlimited computational power.

The result applies to auctions with two bidders and two item types.

Abstract

We study a basic auction design problem with online supply. There are two unit-demand bidders and two types of items. The first item type will arrive first for sure, and the second item type may or may not arrive. The auctioneer has to decide the allocation of an item immediately after each item arrives, but is allowed to compute payments after knowing how many items arrived. For this problem we show that there is no deterministic truthful and individually rational mechanism that, even with unbounded computational resources, gets any finite approximation factor to the optimal social welfare.