Competitive Auctions for Markets with Positive Externalities

TL;DR

This paper introduces a truthful auction mechanism for digital goods with positive externalities among buyers, addressing the complex multi-parameter valuation problem and establishing new competitive benchmarks.

Contribution

It presents the first truthful competitive mechanism for subadditive valuations in markets with externalities, using a new benchmark and revealing limitations of previous benchmarks.

Findings

Achieves a competitive ratio with respect to the new benchmark $\\mathcal{F}^{(3)}$.

Proves an impossibility result for the benchmark $\mathcal{F}^{(2)}$ in the presence of externalities.

Highlights the trade-off between optimal profit and externalities in auction design.

Abstract

In digital goods auctions, there is an auctioneer who sells an item with unlimited supply to a set of potential buyers, and the objective is to design truthful auction to maximize the total profit of the auctioneer. Motivated from an observation that the values of buyers for the item could be interconnected through social networks, we study digital goods auctions with positive externalities among the buyers. This defines a multi-parameter auction design problem where the private valuation of every buyer is a function of other winning buyers. The main contribution of this paper is a truthful competitive mechanism for subadditive valuations. Our competitive result is with respect to a new solution benchmark $\mathcal{F}^{(3)}$; on the other hand, we show a surprising impossibility result if comparing to the benchmark $\mathcal{F}^{(2)}$, where the latter has been used quite successfully in digital goods auctions without extenalities \cite{Goldberg2006}. Our results from $\mathcal{F}^{(2)}$ to $\mathcal{F}^{(3)}$ could be considered as the loss of optimal profit at the cost of externalities.