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Buy-Many Mechanisms for Many Unit-Demand Buyers (2204.01962v2)

Published 5 Apr 2022 in cs.GT

Abstract: A recent line of research has established a novel desideratum for designing approximately-revenue-optimal multi-item mechanisms, namely the buy-many constraint. Under this constraint, prices for different allocations made by the mechanism must be subadditive, implying that the price of a bundle cannot exceed the sum of prices of individual items it contains. This natural constraint has enabled several positive results in multi-item mechanism design bypassing well-established impossibility results. Our work addresses the main open question from this literature of extending the buy-many constraint to multiple buyer settings and developing an approximation. We propose a new revenue benchmark for multi-buyer mechanisms via an ex-ante relaxation that captures several different ways of extending the buy-many constraint to the multi-buyer setting. Our main result is that a simple sequential item pricing mechanism with buyer-specific prices can achieve an $O(\log m)$ approximation to this revenue benchmark when all buyers have unit-demand or additive preferences over m items. This is the best possible as it directly matches the previous results for the single-buyer setting where no simple mechanism can obtain a better approximation. From a technical viewpoint we make two novel contributions. First, we develop a supply-constrained version of buy-many approximation for a single buyer. Second, we develop a multi-dimensional online contention resolution scheme for unit-demand buyers that may be of independent interest in mechanism design.

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References (27)
  1. Saeed Alaei. Bayesian combinatorial auctions: Expanding single buyer mechanisms to many buyers. SIAM Journal on Computing, 43(2):930–972, 2014.
  2. The simple economics of approximately optimal auctions. In 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pages 628–637. IEEE, 2013.
  3. A simple and approximately optimal mechanism for an additive buyer. In 2014 IEEE 55th Annual Symposium on Foundations of Computer Science, pages 21–30. IEEE, 2014.
  4. Pricing lotteries. Journal of Economic Theory, 156:144–174, 2015.
  5. Simple mechanisms for subadditive buyers via duality. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pages 170–183, 2017.
  6. Mechanism design for subadditive agents via an ex ante relaxation. In Proceedings of the 2016 ACM Conference on Economics and Computation, pages 579–596, 2016.
  7. Algorithmic pricing via virtual valuations. In Proceedings of the 8th ACM Conference on Electronic Commerce, pages 243–251, 2007.
  8. Multi-parameter mechanism design and sequential posted pricing. In Proceedings of the forty-second ACM symposium on Theory of computing, pages 311–320, 2010.
  9. The power of randomness in bayesian optimal mechanism design. Games and Economic Behavior, 91:297–317, 2015.
  10. Buy-many mechanisms are not much better than item pricing. In Proceedings of the 2019 ACM Conference on Economics and Computation, pages 237–238, 2019.
  11. Menu-size complexity and revenue continuity of buy-many mechanisms. In Proceedings of the 21st ACM Conference on Economics and Computation, pages 475–476, 2020.
  12. Pricing ordered items. arXiv preprint arXiv:2106.04704, 2021.
  13. An o(log log m) prophet inequality for subadditive combinatorial auctions. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pages 306–317, 2020. doi: 10.1109/FOCS46700.2020.00037.
  14. Online contention resolution schemes. In Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, pages 1014–1033. SIAM, 2016.
  15. An end-to-end argument in mechanism design (prior-independent auctions for budgeted agents). In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), pages 404–415. IEEE, 2018.
  16. Optimal auctions vs. anonymous pricing: Beyond linear utility. In Proceedings of the 2019 ACM Conference on Economics and Computation, pages 885–886, 2019.
  17. Simple mechanisms for non-linear agents. arXiv preprint arXiv:2003.00545, 2020.
  18. Revelation gap for pricing from samples. In Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pages 1438–1451, 2021.
  19. Selling multiple correlated goods: Revenue maximization and menu-size complexity. Journal of Economic Theory, 183:991–1029, 2019.
  20. Worst-case efficiency ratio in false-name-proof combinatorial auction mechanisms. In Wiebe van der Hoek, Gal A. Kaminka, Yves Lespérance, Michael Luck, and Sandip Sen, editors, 9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2010), Toronto, Canada, May 10-14, 2010, Volume 1-3, pages 633–640. IFAAMAS, 2010.
  21. Matroid prophet inequalities. In Proceedings of the forty-fourth annual ACM symposium on Theory of computing, pages 123–136, 2012.
  22. Xinye Li and Andrew Chi-Chih Yao. On revenue maximization for selling multiple independently distributed items. Proceedings of the National Academy of Sciences, 110(28):11232–11237, 2013.
  23. Reaping the benefits of bundling under high production costs. In Arindam Banerjee and Kenji Fukumizu, editors, The 24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021, April 13-15, 2021, Virtual Event, volume 130 of Proceedings of Machine Learning Research, pages 1342–1350. PMLR, 2021.
  24. Simple mechanisms for a subadditive buyer and applications to revenue monotonicity. ACM Transactions on Economics and Computation (TEAC), 6(3-4):1–25, 2018.
  25. Qiqi Yan. Mechanism design via correlation gap. In Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms, pages 710–719. SIAM, 2011.
  26. Andrew Chi-Chih Yao. An n-to-1 bidder reduction for multi-item auctions and its applications. In Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 92–109. SIAM, 2014.
  27. The effect of false-name bids in combinatorial auctions: new fraud in internet auctions. Games and Economic Behavior, 46(1):174–188, January 2004.
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