Abstract
Ascending price auctions typically involve a single price path with buyers paying their final bid price. Using this traditional definition, no ascending price auction can achieve the Vickrey-Clarke-Groves (VCG) outcome for general private valuations in the combinatorial auction setting. We relax this definition by allowing discounts to buyers from the final price of the auction (or alternatively, calculating the discounts dynamically during the auction) while still maintaining a single price path. Using a notion called universal competitive equilibrium prices, shown to be necessary and sufficient to achieve the VCG outcome using ascending price auctions, we define a broad class of ascending price combinatorial auctions in which truthful bidding by buyers is an ex post Nash equilibrium. Any auction in this class achieves the VCG outcome and ex post efficiency for general valuations. We define two specific auctions in this class by generalizing two known auctions in the literature [11, 24].
Highlights
Ascending price auctions are preferred over their sealed-bid counterparts in practical settings [10, 9, 26]
We provide a relaxation of the traditional definition of ascending price auctions to retain a single price path but allow for final payments to be determined as an adjustment from clearing prices
We introduced a class of efficient ascending price combinatorial auctions
Summary
Ascending price auctions are preferred over their sealed-bid counterparts in practical settings [10, 9, 26]. For a general private valuations model, i.e., with no externalities and free disposal but no other restrictions on valuations (such as requirements that items are substitutes of each other), there is a negative result due to de Vries et al [11] They show that gross substitutes valuations are almost the largest valuation domain for which an ascending price auction can achieve the VCG outcome. Our main contribution is a broad class of ascending price auctions which achieve the VCG outcome for general valuations using a single price path. Auctions based on primal-dual algorithms are believed to have faster convergence properties [11] In both cases, we present the first ascending (multi-item) Vickrey auction for general valuations with a single price path.
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