Budget-Feasible Mechanism Design: Simpler, Better Mechanisms and General Payment Constraints

Authors Rian Neogi, Kanstantsin Pashkovich, Chaitanya Swamy



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Author Details

Rian Neogi
  • Dept. of Combinatorics and Optimization, University of Waterloo, Canada
Kanstantsin Pashkovich
  • Dept. of Combinatorics and Optimization, University of Waterloo, Canada
Chaitanya Swamy
  • Dept. of Combinatorics and Optimization, University of Waterloo, Canada

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Rian Neogi, Kanstantsin Pashkovich, and Chaitanya Swamy. Budget-Feasible Mechanism Design: Simpler, Better Mechanisms and General Payment Constraints. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 84:1-84:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ITCS.2024.84

Abstract

In budget-feasible mechanism design, a buyer wishes to procure a set of items of maximum value from self-interested rational players. We are given an item-set U and a nonnegative valuation function v: 2^U ↦ ℝ_+. Each item e is held by a player who incurs a private cost c_e for supplying item e. The goal is to devise a truthful mechanism such that the total payment made to the players is at most some given budget B, and the value of the set returned is a good approximation to OPT: = max {v(S): c(S) ≤ B, S ⊆ U}. We call such a mechanism a budget-feasible mechanism. More generally, there may be additional side constraints requiring that the set returned lies in some downwards-monotone family ℐ ⊆ 2^U. Budget-feasible mechanisms have been widely studied, but there are still significant gaps in our understanding of these mechanisms, both in terms of what kind of oracle access to the valuation is required to obtain good approximation ratios, and the best approximation ratio that can be achieved. 
We substantially advance the state of the art of budget-feasible mechanisms by devising mechanisms that are simpler, and also better, both in terms of requiring weaker oracle access and the approximation factors they obtain. For XOS valuations, we devise the first polytime O(1)-approximation budget-feasible mechanism using only demand oracles, and also significantly improve the approximation factor. For subadditive valuations, we give the first explicit construction of an O(1)-approximation mechanism, where previously only an existential result was known.
We also introduce a fairly rich class of mechanism-design problems that we dub using the umbrella term generalized budget-feasible mechanism design, which allow one to capture payment constraints that are much-more nuanced than a single constraint on the total payment doled out. We demonstrate the versatility of our ideas by showing that our constructions can be adapted to yield approximation guarantees in such general settings as well.
A prominent insight to emerge from our work is the usefulness of a property called nobossiness, which allows us to nicely decouple the truthfulness + approximation, and budget-feasibility requirements. Some of our constructions can be viewed as reductions showing that an O(1)-approximation budget-feasible mechanism can be obtained provided we have a (randomized) truthful mechanism satisfying nobossiness that returns a (random) feasible set having (expected) value Ω(OPT).

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic mechanism design
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Discrete optimization
Keywords
  • Algorithmic mechanism design
  • Approximation algorithms
  • Budget-feasible mechanisms

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References

  1. Georgios Amanatidis, Georgios Birmpas, and Evangelos Markakis. On budget-feasible mechanism design for symmetric submodular objectives. In Proceedings of 13th WINE, pages 1-15, 2017. Google Scholar
  2. Georgios Amanatidis, Georgios Birmpas, and Evangelos K. Markakis. Coverage, matching, and beyond: New results on budgeted mechanism design. In Proceedings of 12th WINE, pages 414-428, 2016. Google Scholar
  3. Georgios Amanatidis, Georgios Birmpas, and Evangelos K. Markakis. On budget-feasible mechanism design for symmetric submodular objectives. In Proceedings of 13th WINE, pages 1-15, 2017. Google Scholar
  4. Georgios Amanatidis, Pieter Kleer, and Guido Schäfer. Budget-feasible mechanism design for non-monotone submodular objectives: Offline and online. In Proceedings of 20th EC, pages 901-919, 2019. Google Scholar
  5. Nima Anari, Gagan Goel, and Afshin Nikzad. Mechanism design for crowdsourcing: An optimal 1-1/e competitive budget-feasible mechanism for large markets. In Proceedings of 55th FOCS, pages 266-275, 2014. Google Scholar
  6. Ashwinkumar Badanidiyuru, Shahar Dobzinski, and Sigal Oren. Optimization with demand oracles. Algorithmica, 81:2244-2269, 2019. Google Scholar
  7. Eric Balkanski, Pranav Garimidi, Vasilis Gkatzelis, Daniel Schoepflin, and Xizhi Tan. Deterministic budget-feasible clock auctions. In Proceedings of 33rd SODA, pages 2940-2963, 2022. Google Scholar
  8. Eric Balkanski and Jason Hartline. Bayesian budget feasibility with posted pricing. In Proceedings of 25th WWW, pages 189-203, 2016. Google Scholar
  9. MohammadHossein Bateni, Mohammad Taghi Hajiaghayi, and Morteza Zadimoghaddam. Submodular secretary problem and extensions. ACM Trans. Algorithms, 9:32:1-32:23, 2013. Google Scholar
  10. Xiaohui Bei, Ning Chen, Nick Gravin, and Pinyan Lu. Budget feasible mechanism design: from prior-free to bayesian. In Proceedings of 44th STOC, pages 449-458, 2012. Google Scholar
  11. Xiaohui Bei, Ning Chen, Nick Gravin, and Pinyan Lu. Worst-case mechanism design via bayesian analysis. SIAM Journal on Computing, 46(4):1428-1448, 2017. Google Scholar
  12. Robert D Carr, Lisa K Fleischer, Vitus J Leung, and Cynthia A Phillips. Strengthening integrality gaps for capacitated network design and covering problems. In Proceedings of 11th SODA, pages 106-115, 2000. Google Scholar
  13. Deeparnab Chakrabarty and Chaitanya Swamy. Interpolating between k-median and k-center: Approximation algorithms for ordered k-median. In Proceedings of 45th ICALP, pages 29:1-29:14, 2018. Google Scholar
  14. Deeparnab Chakrabarty and Chaitanya Swamy. Approximation algorithms for minimum norm and ordered optimization problems. In Proceedings of 51st STOC, pages 126-137, 2019. Google Scholar
  15. Ning Chen, Nick Gravin, and Pinyan Lu. On the approximability of budget feasible mechanisms. In Proceedings of 22nd SODA, pages 685-699, 2011. Google Scholar
  16. Shahar Dobzinski, Christos Papadimitriou, and Yaron Singer. Mechanisms for complement-free procurement. In Proceedings of 12th EC, pages 273-282, 2011. Google Scholar
  17. Konstantinos Georgiou and Chaitanya Swamy. Black-box reductions for cost-sharing mechanism design. Games and Economic Behavior, 113:17-37, 2019. Google Scholar
  18. Nick Gravin, Yaonan Jin, Pinyan Lu, and Chenhao Zhang. Optimal budget-feasible mechanisms for additive valuations. ACM Trans. Econ. Comput., 8(4), 2020. URL: https://doi.org/10.1145/3417746.
  19. Thibaut Horel, Stratis Ioannidis, and S. Muthukrishnan. Budget feasible mechanisms for experimental design. In Proceedings of 11th LATIN, pages 719-730, 2014. Google Scholar
  20. He Huang, Kai Han, Shuang Cui, and Jing Tang. Randomized pricing with deferred acceptance for revenue maximization with submodular objectives. In Proceedings of 32nd WWW, pages 3530-3540, 2023. URL: https://doi.org/10.1145/3543507.3583477.
  21. Pooya Jalaly and Éva Tardos. Simple and efficient budget feasible mechanisms for monotone submodular valuations. In Proceedings of 14th WINE, pages 246-263, 2018. Google Scholar
  22. Stefano Leonardi, Gianpiero Monaco, Piotr Sankowski, and Qiang Zhang. Budget feasible mechanisms on matroids. Algorithmica, 83(5):1222-1237, 2021. Google Scholar
  23. Roger B. Myerson. Optimal auction design. Math. Oper. Res., 6(1):58-73, 1981. Google Scholar
  24. Yaron Singer. Budget feasible mechanisms. In Proceedings of 51st FOCS, pages 765-774, 2010. Google Scholar
  25. Yaron Singer. How to win friends and influence people, truthfully: influence maximization mechanisms for social networks. In Proceedings of 5th WSDM, pages 733-742, 2012. Google Scholar
  26. Yaron Singer. Budget feasible mechanism design. ACM SIGecom Exchanges, 12(2):24-31, 2013. Google Scholar
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