Risk-Free Bidding in Complement-Free Combinatorial Auctions
Vishnu V. Narayan, Gautam Rayaprolu, Adrian Vetta

TL;DR
This paper analyzes risk-free bidding strategies in combinatorial auctions with incomplete information, providing tight profit guarantees for different auction formats and valuation classes, especially for complement-free bidders.
Contribution
It introduces tight worst-case profit guarantees for bid strategies in sequential and simultaneous auctions for complement-free bidders, extending to special cases with identical items.
Findings
Sequential auctions: profit guarantee of (B_1-B_2)^2 when B_2 B_1
Simultaneous auctions: profit guarantee of (B_1-B_2)^2/(2B_1) in first-price case
Second-price auctions: profit guarantee of B_1-B_2
Abstract
We study risk-free bidding strategies in combinatorial auctions with incomplete information. Specifically, what is the maximum profit that a complement-free (subadditive) bidder can guarantee in a multi-item combinatorial auction? Suppose there are bidders and is the value that bidder has for the entire set of items. We study the above problem from the perspective of the first bidder, Bidder~1. In this setting, the worst case profit guarantees arise in a duopsony, that is when , so this problem then corresponds to playing an auction against a budgeted adversary with budget . We present worst-case guarantees for two simple and widely-studied combinatorial auctions, namely, the sequential and simultaneous auctions, for both the first-price and second-price case. In the general case of distinct items, our main results are for the class of {\em fractionally…
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Taxonomy
TopicsAuction Theory and Applications · Consumer Market Behavior and Pricing
