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.
P. Jalaly Khalilabadi—Work supported in part by NSF grant CCF-1563714, ONR grant N00014-08-1-0031, and a Google Research Grant.
É. Tardos—Work supported in part by NSF grants CCF-1563714, and CCF-1422102, ONR grant N00014-08-1-0031, and a Google Research Grant.
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Notes
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The same authors somewhat improved this bound in Amanatidis et al. (2017) using our analysis from an earlier version of this paper, but the improved bound is at least 5.45.
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By having a \(\theta \)-large market assumption instead, the approximation guarantees for our large market mechanisms increases by a factor of \((1-c\theta )^{-1}\), where \(c \in (0,4)\) is a constant which is different for each mechanism. We omit stating the exact value of c for each mechanism separately.
References
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_29
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/1704.06901
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)
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)
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)
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)
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)
Goel, G., Nikzad, A., Singla, A.: Mechanism design for crowdsourcing markets with heterogeneous tasks. In: Second AAAI Conference on Human Computation and Crowdsourcing (2014)
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
Khuller, S., Moss, A., Naor, J.S.: The budgeted maximum coverage problem. Inform. Process. Lett. 70(1), 39–45 (1999)
Singer, Y.: Budget feasible mechanisms. In: 2010 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 765–774. IEEE (2010)
Singla, A., Krause, A.: Incentives for privacy tradeoff in community sensing. In: First AAAI Conference on Human Computation and Crowdsourcing (2013)
Sviridenko, M.: A note on maximizing a submodular set function subject to a knapsack constraint. Oper. Res. Lett. 32(1), 41–43 (2004)
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Jalaly Khalilabadi, P., Tardos, É. (2018). Simple and Efficient Budget Feasible Mechanisms for Monotone Submodular Valuations. In: Christodoulou, G., Harks, T. (eds) Web and Internet Economics. WINE 2018. Lecture Notes in Computer Science(), vol 11316. Springer, Cham. https://doi.org/10.1007/978-3-030-04612-5_17
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