Revenue Non-monotonicity in Matching Markets

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.