@inproceedings{ed56175836b64cf9a05f1e64562277e3,
title = "When are welfare guarantees robust?",
abstract = "Computational and economic results suggest that social welfare maximization and combinatorial auction design are much easier when bidders' valuations satisfy the {"}gross substitutes{"} condition. The goal of this paper is to evaluate rigorously the folklore belief that the main take-aways from these results remain valid in settings where the gross substitutes condition holds only approximately. We show that for valuations that pointwise approximate a gross substitutes valuation (in fact even a linear valuation), optimal social welfare cannot be approximated to within a subpolynomial factor and demand oracles cannot be simulated using a subexponential number of value queries. We then provide several positive results by imposing additional structure on the valuations (beyond gross substitutes), using a more stringent notion of approximation, and/or using more powerful oracle access to the valuations. For example, we prove that the performance of the greedy algorithm degrades gracefully for near-linear valuations with approximately decreasing marginal values; that with demand queries, approximate welfare guarantees for XOS valuations degrade gracefully for valuations that are pointwise close to XOS; and that the performance of the Kelso-Crawford auction degrades gracefully for valuations that are close to various subclasses of gross substitutes valuations.",
keywords = "Approximation, Gross substitutes, Linearity, Valuation (set) functions",
author = "Tim Roughgarden and Inbal Talgam-Cohen and Jan Vondr{\'a}k",
note = "Publisher Copyright: {\textcopyright} Tim Roughgarden, Inbal Talgam-Cohen, and Jan Vondr{\'a}k.; 20th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2017 and the 21st International Workshop on Randomization and Computation, RANDOM 2017 ; Conference date: 16-08-2017 Through 18-08-2017",
year = "2017",
month = aug,
day = "1",
doi = "https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2017.22",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
editor = "Rolim, {Jose D. P.} and Klaus Jansen and Williamson, {David P.} and Vempala, {Santosh S.}",
booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 20th International Workshop, APPROX 2017 and 21st International Workshop, RANDOM 2017",
}