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Asymptotically Optimal Welfare of Posted Pricing for Multiple Items with MHR Distributions

Authors Alexander Braun, Matthias Buttkus, Thomas Kesselheim

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Author Details

Alexander Braun
  • Institute of Computer Science, Universität Bonn, Germany
Matthias Buttkus
  • Institute of Computer Science, Universität Bonn, Germany
Thomas Kesselheim
  • Institute of Computer Science, Universität Bonn, Germany

Acknowledgements

We thank the anonymous reviewers for helpful comments on improving the presentation of the paper.

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Alexander Braun, Matthias Buttkus, and Thomas Kesselheim. Asymptotically Optimal Welfare of Posted Pricing for Multiple Items with MHR Distributions. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ESA.2021.22

Abstract

We consider the problem of posting prices for unit-demand buyers if all n buyers have identically distributed valuations drawn from a distribution with monotone hazard rate. We show that even with multiple items asymptotically optimal welfare can be guaranteed.
Our main results apply to the case that either a buyer’s value for different items are independent or that they are perfectly correlated. We give mechanisms using dynamic prices that obtain a 1 - Θ (1/(log n))-fraction of the optimal social welfare in expectation. Furthermore, we devise mechanisms that only use static item prices and are 1 - Θ ((log log log n)/(log n))-competitive compared to the optimal social welfare. As we show, both guarantees are asymptotically optimal, even for a single item and exponential distributions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic mechanism design
  • Theory of computation → Online algorithms
Keywords
  • Prophet Inequalities
  • Monotone Hazard Rate
  • Competitive Analysis
  • Posted Prices
  • Combinatorial Auctions
  • Matching

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