Rank-Guaranteed Auctions

TL;DR

The paper tackles revenue guarantees in combinatorial auctions with complex bidder preferences by introducing CASA, a rank-guaranteed, priors-free ascending auction. It proves that, under minimal rationality (non-obviously dominated strategies), CASA achieves a $k$-th guarantee with $k=| ext{M}|+1$, tying revenue to the $(| ext{M}|+1)$-th highest valuations per bundle; this is robust to distributional uncertainty and prior-free. A central emphasis is on menu design, showing a fundamental trade-off between menu sufficiency and approximation efficiency, and presenting simple, polynomial-size menus that preserve the benchmark surplus under canonical preference structures. The framework accommodates robustness to collusion/irrationality and discusses alternative formats, efficiency considerations, and extensions, offering practical guidance for implementing multi-item auctions in markets with combinatorial valuations.

Abstract

We propose a combinatorial ascending auction that is "approximately" optimal, requiring minimal rationality to achieve this level of optimality, and is robust to strategic and distributional uncertainties. Specifically, the auction is rank-guaranteed, meaning that for any menu M and any valuation profile, the ex-post revenue is guaranteed to be at least as high as the highest revenue achievable from feasible allocations, taking the (|M|+ 1)th-highest valuation for each bundle as the price. Our analysis highlights a crucial aspect of combinatorial auction design, namely, the design of menus. We provide simple and approximately optimal menus in various settings.

Theorems & Definitions (19)

• Definition 1
• Lemma 1
• Definition 2
• Theorem 1
• Proposition 1
• Proposition 2
• Theorem 2
• Proposition 3
• Definition 3
• Theorem 3