The Performance of Deferred-Acceptance Auctions

Abstract

Deferred-acceptance auctions are mechanisms whose allocation rule can be implemented using an adaptive reverse greedy algorithm. Milgrom and Segal recently introduced these auctions and proved that they satisfy remarkable incentive guarantees: in addition to being dominant strategy and incentive compatible, they are weakly group-strategyproof and can be implemented by ascending-clock auctions. Neither forward greedy mechanisms nor the VCG mechanism generally possess any of these additional incentive properties. The goal of this paper is to initiate the study of deferred-acceptance auctions from an approximation standpoint. We study what fraction of the optimal social welfare can be guaranteed by these auctions in two canonical problems, knapsack auctions and combinatorial auctions with single-minded bidders. For knapsack auctions, we prove a separation between deferred-acceptance auctions and arbitrary dominant-strategy incentive-compatible mechanisms. For combinatorial auctions with single-minded bidders, we design novel polynomial-time mechanisms that achieve the best of both worlds: the incentive guarantees of a deferred-acceptance auction, and approximation guarantees close to the best possible.

Deferred-Acceptance Auctions for Multiple Levels of Service

“…Dütting et al [11] showed that, even in the binary setting, if the set of bidders that can be simultaneously accepted is defined by a single knapsack constraint of size m, then no DA auction can achieve an approximation better than O(log m). The following theorem provides a matching positive result: a generalized DA auction that achieves the optimal logarithmic approximation.…”

“…Backward greedy algorithms can be inferior to forward greedy algorithms, and the former need not even produce an inclusion-maximal solution. Driven by this concern, Dütting et al [11] subsequently explored the power and limitations of DA auctions from an approximation algorithms viewpoint (see also related work below). Their main results concern knapsack auctions and combinatorial auctions with single-minded bidders.…”

“…Following up on the work of [33], Dütting et al [11] explored the power and limitations of DA auctions from an approximation algorithms viewpoint. They provided both positive and negative results for knapsack auctions and auctions with single-minded bidders.…”

Bribeproof Mechanisms for Two-Values Domains

“…More generally, the trade-off may also involve the type of incentive compatibility condition that we want. For example, [6] showed that a certain class of weakly group strategyproof mechanisms (studied in [14]) can only achieve an approximate social welfare in binary one-parameter domains.…”

“…Proof. We first prove that the particular tie-breaking rule of the mechanism satisfies the following condition: 6 For any i and j = i the following implication holds…”