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Simple and Efficient Budget Feasible Mechanisms for Monotone Submodular Valuations

  • Pooya Jalaly Khalilabadi
  • Éva Tardos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11316)

Abstract

We study the problem of a budget limited buyer who wants to buy a set of items, each from a different seller, to maximize her value. The budget feasible mechanism design problem requires the design a mechanism which incentivizes the sellers to truthfully report their cost and maximizes the buyer’s value while guaranteeing that the total payment does not exceed her budget. Such budget feasible mechanisms can model a buyer in a crowdsourcing market interested in recruiting a set of workers (sellers) to accomplish a task for her.

This budget feasible mechanism design problem was introduced by Singer in 2010. We consider the general case where the buyer’s valuation is a monotone submodular function. There are a number of truthful mechanisms known for this problem. We offer two general frameworks for simple mechanisms, and by combining these frameworks, we significantly improve on the best known results, while also simplifying the analysis. For example, we improve the approximation guarantee for the general monotone submodular case from 7.91 to 5; and for the case of large markets (where each individual item has negligible value) from 3 to 2.58. More generally, given an r approximation algorithm for the optimization problem (ignoring incentives), our mechanism is a \(r+1\) approximation mechanism for large markets, an improvement from \(2r^2\). We also provide a mechanism without the large market assumption, where we achieve a \(4r+1\) approximation guarantee. We also show how our results can be used for the problem of a principal hiring in a Crowdsourcing Market to select a set of tasks subject to a total budget.

References

  1. Amanatidis, G., Birmpas, G., Markakis, E.: Coverage, matching, and beyond: new results on budgeted mechanism design. In: Cai, Y., Vetta, A. (eds.) WINE 2016. LNCS, vol. 10123, pp. 414–428. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-54110-4_29CrossRefzbMATHGoogle Scholar
  2. Amanatidis, G., Birmpas, G., Markakis, E.: 2017. On Budget-feasible mechanism design for symmetric submodular objectives. CoRR abs/1704.06901 (2017). http://arxiv.org/abs/1704.06901Google Scholar
  3. Anari, N., Goel, G., Nikzad, A.: Mechanism design for crowdsourcing: an optimal 1–1/e competitive budget-feasible mechanism for large markets. In: 2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS), pp. 266–275. IEEE (2014)Google Scholar
  4. Balkanski, E., Hartline, J.D.: Bayesian budget feasibility with posted pricing. In: Proceedings of the 25th International Conference on World Wide Web, International World Wide Web Conferences Steering Committee, pp. 189–203 (2016)Google Scholar
  5. Bei, X., Chen, N., Gravin, N., Lu, P.: Budget feasible mechanism design: from prior-free to Bayesian. In: Proceedings of the Forty-fourth Annual ACM Symposium on Theory of Computing, pp. 449–458. ACM(2012)Google Scholar
  6. Chen, N., Gravin, N., Lu, P.: On the approximability of budget feasible mechanisms. In: Proceedings of the Twenty-second Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, pp. 685–699 (2011)CrossRefGoogle Scholar
  7. Dobzinski, S., Christos, H.P., Yaron, S.: Mechanisms for complement-free procurement. In: Proceedings of the 12th ACM Conference on Electronic Commerce, pp. 273–282. ACM (2011)Google Scholar
  8. Goel, G., Nikzad, A., Singla, A.: Mechanism design for crowdsourcing markets with heterogeneous tasks. In: Second AAAI Conference on Human Computation and Crowdsourcing (2014)Google Scholar
  9. Jalaly, P., Tardos, É.: 2017. Simple and Efficient Budget Feasible Mechanisms for Monotone Submodular Valuations. CoRR abs/1703.10681 (2017). http://arxiv.org/abs/1703.10681
  10. Khuller, S., Moss, A., Naor, J.S.: The budgeted maximum coverage problem. Inform. Process. Lett. 70(1), 39–45 (1999)MathSciNetCrossRefGoogle Scholar
  11. Singer, Y.: Budget feasible mechanisms. In: 2010 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 765–774. IEEE (2010)Google Scholar
  12. Singla, A., Krause, A.: Incentives for privacy tradeoff in community sensing. In: First AAAI Conference on Human Computation and Crowdsourcing (2013)Google Scholar
  13. Sviridenko, M.: A note on maximizing a submodular set function subject to a knapsack constraint. Oper. Res. Lett. 32(1), 41–43 (2004)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA

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