The Cost of Simple Bidding in Combinatorial Auctions

TL;DR

This paper demonstrates that in combinatorial auctions, simple bidding strategies are often suboptimal compared to complex bids, which can significantly influence auction outcomes despite their computational complexity.

Contribution

The paper proves that simple bids are never optimal in certain auction instances and highlights the structural reasons and potential impact of complex bidding strategies.

Findings

Complex bids can dominate simple bids in equilibrium.

Optimal complex bids may require exponential bidding on bundles.

Complex bidding significantly affects auction outcomes.

Abstract

We study a class of manipulations in combinatorial auctions where bidders fundamentally misrepresent what goods they are interested in. Prior work has largely assumed that bidders only submit bids on their bundles of interest, which we call simple bidding: strategizing over the bid amounts, but not the bundle identities. However, we show that there exists an entire class of auction instances for which simple bids are never optimal in Bayes-Nash equilibrium, always being strictly dominated by complex bids (where bidders bid on goods they are not interested in). We show this result for the two most widely used auction mechanisms: first price and VCG-nearest. We also explore the structural properties of the winner determination problem that cause this phenomenon, and we use the insights gained to investigate how impactful complex bidding may be. We find that, in the worst case, a bidder's optimal complex bid may require bidding on an exponential number of bundles, even if the bidder is interested only in a single good. Thus, this phenomenon can greatly impact the auction's outcome and should not be ignored by bidders and auction designers alike.