Revenue Non-monotonicity in Matching Markets

TL;DR

This paper demonstrates that revenue non-monotonicity of the VCG mechanism occurs even in matching markets, challenging the belief that complementarities are necessary for such non-monotonic behavior in combinatorial auctions.

Contribution

It shows that revenue non-monotonicity of VCG is not due to complementarities and occurs even in simple matching markets.

Findings

VCG revenue can decrease when a buyer's valuation increases.

Non-monotonicity is not solely caused by complementarities.

Revenue non-monotonicity occurs in matching markets, not just complex auctions.

Abstract

The Vickrey-Clarke-Groves (VCG) mechanism is infamously revenue non-monotone in combinatorial auctions. I.e., when a buyer increases their value for a bundle of items, the total auction revenue may decrease. Combinatorial auctions exhibit complementarities which broadly result in complexities in auction theory. This brief note shows that non-monotonicity in multi-item auctions is not a result of complementarities, and in fact, VCG is revenue non-monotone even in matching markets.