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On the (In)approximability of Combinatorial Contracts

Authors Tomer Ezra , Michal Feldman , Maya Schlesinger

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Author Details

Tomer Ezra
  • Simons Laufer Mathematical Sciences Institute, Berkeley, CA, USA
Michal Feldman
  • Tel Aviv University, Israel
Maya Schlesinger
  • Tel Aviv University, Israel

Funding

Feldman and Schlesinger received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 866132), by an Amazon Research Award, and by the NSF-BSF (grant number 2020788). Ezra was funded by the National Science Foundation under Grant No. DMS-1928930 and by the Alfred P. Sloan Foundation under grant G-2021-16778, while the author was in residence at the Simons Laufer Mathematical Sciences Institute (formerly MSRI) in Berkeley, California, during the Fall 2023 semester.

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Tomer Ezra, Michal Feldman, and Maya Schlesinger. On the (In)approximability of Combinatorial Contracts. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 44:1-44:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.44

Abstract

We study two recent combinatorial contract design models, which highlight different sources of complexity that may arise in contract design, where a principal delegates the execution of a costly project to others. In both settings, the principal cannot observe the choices of the agent(s), only the project’s outcome (success or failure), and incentivizes the agent(s) using a contract, a payment scheme that specifies the payment to the agent(s) upon a project’s success. We present results that resolve open problems and advance our understanding of the computational complexity of both settings. In the multi-agent setting, the project is delegated to a team of agents, where each agent chooses whether or not to exert effort. A success probability function maps any subset of agents who exert effort to a probability of the project’s success. For the family of submodular success probability functions, Dütting et al. [2023] established a poly-time constant factor approximation to the optimal contract, and left open whether this problem admits a PTAS. We answer this question on the negative, by showing that no poly-time algorithm guarantees a better than 0.7-approximation to the optimal contract. For XOS functions, they give a poly-time constant approximation with value and demand queries. We show that with value queries only, one cannot get any constant approximation. In the multi-action setting, the project is delegated to a single agent, who can take any subset of a given set of actions. Here, a success probability function maps any subset of actions to a probability of the project’s success. Dütting et al. [2021a] showed a poly-time algorithm for computing an optimal contract for gross substitutes success probability functions, and showed that the problem is NP-hard for submodular functions. We further strengthen this hardness result by showing that this problem does not admit any constant factor approximation. Furthermore, for the broader class of XOS functions, we establish the hardness of obtaining a n^{-1/2+ε}-approximation for any ε > 0.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
Keywords
  • algorithmic contract design
  • combinatorial contracts
  • moral hazard

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References

  1. Tal Alon, Paul Dütting, and Inbal Talgam-Cohen. Contracts with private cost per unit-of-effort. In Proceedings of the 22nd ACM Conference on Economics and Computation, pages 52-69, 2021. URL: https://doi.org/10.1145/3465456.3467651.
  2. Moshe Babaioff, Michal Feldman, and Noam Nisan. Combinatorial agency. In Proc. ACM EC 2006, pages 18-28, 2006. URL: https://doi.org/10.1016/J.JET.2012.01.010.
  3. Yahav Bechavod, Chara Podimata, Steven Wu, and Juba Ziani. Information discrepancy in strategic learning. In International Conference on Machine Learning, pages 1691-1715. PMLR, 2022. URL: https://proceedings.mlr.press/v162/bechavod22a.html.
  4. Curtis Bechtel, Shaddin Dughmi, and Neel Patel. Delegated pandora’s box. In Proceedings of the 23rd ACM Conference on Economics and Computation, pages 666-693, 2022. URL: https://doi.org/10.1145/3490486.3538267.
  5. Matteo Castiglioni, Alberto Marchesi, and Nicola Gatti. Designing menus of contracts efficiently: The power of randomization. In Proceedings of the 23rd ACM Conference on Economics and Computation, pages 705-735, 2022. URL: https://doi.org/10.1145/3490486.3538270.
  6. Matteo Castiglioni, Alberto Marchesi, and Nicola Gatti. Multi-agent contract design: How to commission multiple agents with individual outcomes. In Proceedings of the 24th ACM Conference on Economics and Computation, EC '23, pages 412-448. Association for Computing Machinery, 2023. URL: https://doi.org/10.1145/3580507.3597793.
  7. Krishna Dasaratha, Benjamin Golub, and Anant Shah. Equity pay in networked teams. In Proceedings of the 24th ACM Conference on Economics and Computation, EC 2023, London, United Kingdom, July 9-12, 2023, page 512. ACM, 2023. URL: https://doi.org/10.1145/3580507.3597754.
  8. Paul Dütting, Tomer Ezra, Michal Feldman, and Thomas Kesselheim. Combinatorial contracts. In Proc. IEEE FOCS 2021, pages 815-826, 2021. URL: https://doi.org/10.1109/FOCS52979.2021.00084.
  9. Paul Dütting, Tomer Ezra, Michal Feldman, and Thomas Kesselheim. Multi-agent contracts. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, pages 1311-1324, 2023. URL: https://doi.org/10.1145/3564246.3585193.
  10. Paul Dütting, Michal Feldman, and Yoav Gal Tzur. Combinatorial contracts beyond gross substitutes, 2023. URL: https://doi.org/10.48550/ARXIV.2309.10766.
  11. Paul Dütting, Tim Roughgarden, and Inbal Talgam-Cohen. The complexity of contracts. SIAM Journal on Computing, 50(1):211-254, 2021. URL: https://doi.org/10.1137/20M132153X.
  12. Yuval Emek and Michal Feldman. Computing optimal contracts in combinatorial agencies. Theoretical Computer Science, 452:56-74, 2012. URL: https://doi.org/10.1016/J.TCS.2012.05.018.
  13. Uriel Feige. A threshold of ln n for approximating set cover. J. ACM, 45(4):634-652, 1998. URL: https://doi.org/10.1145/285055.285059.
  14. Sanford J. Grossman and Oliver D. Hart. An analysis of the principal-agent problem. Econometrica, 51(1):7-45, 1983. URL: https://doi.org/10.2307/1912246.
  15. Guru Guruganesh, Jon Schneider, and Joshua R Wang. Contracts under moral hazard and adverse selection. In Proceedings of the 22nd ACM Conference on Economics and Computation, pages 563-582, 2021. URL: https://doi.org/10.1145/3465456.3467637.
  16. J. Hastad. Clique is hard to approximate within n^1-ε. In Proceedings of 37th Conference on Foundations of Computer Science, pages 627-636, 1996. URL: https://doi.org/10.1109/SFCS.1996.548522.
  17. Bengt Holmström. Moral hazard and observability. The Bell journal of economics, pages 74-91, 1979. URL: https://doi.org/10.2307/3003320.
  18. Jon Kleinberg and Robert Kleinberg. Delegated search approximates efficient search. In Proceedings of the 2018 ACM Conference on Economics and Computation, pages 287-302, 2018. URL: https://doi.org/10.1145/3219166.3219205.
  19. Jon Kleinberg and Manish Raghavan. How do classifiers induce agents to invest effort strategically? ACM Transactions on Economics and Computation (TEAC), 8(4):1-23, 2020. URL: https://doi.org/10.1145/3417742.
  20. Benny Lehmann, Daniel Lehmann, and Noam Nisan. Combinatorial auctions with decreasing marginal utilities. In Proceedings of the 3rd ACM conference on Electronic Commerce, pages 18-28, 2001. URL: https://doi.org/10.1145/501158.501161.
  21. Yingkai Li, Jason D. Hartline, Liren Shan, and Yifan Wu. Optimization of scoring rules. In Proceedings of the 23rd ACM Conference on Economics and Computation, EC '22, pages 988-989. Association for Computing Machinery, 2022. URL: https://doi.org/10.1145/3490486.3538338.
  22. Noam Nisan and Ilya Segal. The communication requirements of efficient allocations and supporting prices. Journal of Economic Theory, 129(1):192-224, 2006. URL: https://doi.org/10.1016/J.JET.2004.10.007.
  23. Maneesha Papireddygari and Bo Waggoner. Contracts with information acquisition, via scoring rules. In Proceedings of the 23rd ACM Conference on Economics and Computation, EC '22, pages 703-704. Association for Computing Machinery, 2022. URL: https://doi.org/10.1145/3490486.3538261.
  24. Ramiro Deo-Campo Vuong, Shaddin Dughmi, Neel Patel, and Aditya Prasad. On supermodular contracts and dense subgraphs, 2023. URL: https://doi.org/10.48550/ARXIV.2308.07473.
  25. David Zuckerman. Linear degree extractors and the inapproximability of max clique and chromatic number. In Proceedings of the thirty-eighth annual ACM symposium on Theory of computing, pages 681-690, 2006. URL: https://doi.org/10.1145/1132516.1132612.
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