Approximation Schemes for a Unit-Demand Buyer with Independent Items via Symmetries

@article{Kothari2019ApproximationSF,
  title={Approximation Schemes for a Unit-Demand Buyer with Independent Items via Symmetries},
  author={Pravesh Kothari and Divyarthi Mohan and Ariel Schvartzman and Sahil Singla and S. Matthew Weinberg},
  journal={2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2019},
  pages={220-232}
}
We consider a revenue-maximizing seller with n items facing a single buyer. We introduce the notion of symmetric menu complexity of a mechanism, which counts the number of distinct options the buyer may purchase, up to permutations of the items. Our main result is that a mechanism of quasi-polynomial symmetric menu complexity suffices to guarantee a (1 - epsilon )-approximation when the buyer is unit-demand over independent items, even when the value distribution is unbounded, and that this… 
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