Frugal and Truthful Auctions for Vertex Covers, Flows, and Cuts
David Kempe, Mahyar Salek, Cristopher Moore

TL;DR
This paper introduces constant-competitive truthful mechanisms for Vertex Cover, k-flow, and cut auctions, ensuring near-optimal overpayment bounds while maintaining truthfulness in strategic settings.
Contribution
It develops novel, constant-competitive truthful mechanisms for three complex set system auctions, extending prior work with innovative graph transformations and eigenvector-based scaling.
Findings
Mechanism for Vertex Cover uses eigenvector scaling.
Graph pruning for k-flows ensures minimal connectivity.
Graph contraction for cuts standardizes s-t path lengths.
Abstract
We study truthful mechanisms for hiring a team of agents in three classes of set systems: Vertex Cover auctions, k-flow auctions, and cut auctions. For Vertex Cover auctions, the vertices are owned by selfish and rational agents, and the auctioneer wants to purchase a vertex cover from them. For k-flow auctions, the edges are owned by the agents, and the auctioneer wants to purchase k edge-disjoint s-t paths, for given s and t. In the same setting, for cut auctions, the auctioneer wants to purchase an s-t cut. Only the agents know their costs, and the auctioneer needs to select a feasible set and payments based on bids made by the agents. We present constant-competitive truthful mechanisms for all three set systems. That is, the maximum overpayment of the mechanism is within a constant factor of the maximum overpayment of any truthful mechanism, for every set system in the class. The…
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Taxonomy
TopicsAuction Theory and Applications · Consumer Market Behavior and Pricing · Game Theory and Applications
