Abstract
Our work concerns the class of core-selecting mechanisms, as introduced by Ausubel and Milgrom [3]. Such mechanisms have been known to possess good revenue guarantees and some of their variants have been used in practice especially for spectrum and other public sector auctions. Despite their popularity, it has also been demonstrated that these auctions are generally non-truthful. As a result, current research has focused either on identifying core-selecting mechanisms with minimal incentives to deviate from truth-telling, such as the family of Minimum-Revenue Core-Selecting (MRCS) rules, or on proposing truthful mechanisms whose revenue is competitive against core outcomes. Our results contribute to both of these directions. We start with studying the core polytope in more depth and provide new properties and insights, related to the effects of unilateral deviations from a given profile. We then utilize these properties in two ways. First, we propose a truthful mechanism that is \(O(\log {n})\)-competitive against the MRCS benchmark. Our result is the first deterministic core-competitive mechanism for binary single-parameter domains. Second, we study the existence of non-decreasing payment rules, meaning that the payment of each bidder is a non-decreasing function of her bid. This property has been advocated by the core-related literature but it has remained an open question if there exist MRCS non-decreasing mechanisms. We answer the question in the affirmative, by describing a subclass of rules with this property.
A. Tsikiridis—Research was supported by the Hellenic Foundation for Research and Innovation (HFRI) under the HFRI PhD Fellowship grant (Fellowship Number: 289).
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Notes
- 1.
There are several facets in studying revenue monotonicity, as it concerns the effects on revenue when adding new bidders, or increasing the offers of the current bidders.
References
Aggarwal, G., Hartline, J.: Knapsack auctions. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1083–1092 (2006)
Ausubel, L., Baranov, O.: Core-selecting auctions with incomplete information. Int. J. Game Theor. 36(3–4), 393–407 (2019)
Ausubel, L., Milgrom, P.: Ascending auctions with package bidding. Adv. Theor. Econ. 1(1), 1–42 (2002). https://doi.org/10.2202/1534-5963.1019
Ausubel, L., Milgrom, P.: The lovely but lonely vickrey auction. In: Cramton, P., Shoham, Y., Steinberg, R. (eds.) Combinatorial Auctions (2006)
Beck, M., Ott, M.: Revenue monotonicity in core-selecting auctions. Technical Report Stanford University (2010)
Bosshard, V., Wang, Y., Seuken, S.: Non-decreasing payment rules for combinatorial auctions. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence, pp. 105–113 (2018)
Bünz, B., Lubin, B., Seuken,S.: Designing core-selecting payment rules: a computational search approach. In: Proceedings of the 19th ACM Conference on Economics and Computation, p. 109 (2018)
Day, R., Cramton, P.: Quadratic core-selecting payment rules for combinatorial auctions. Oper. Res. 60(3), 588–603 (2012)
Day, R., Milgrom, P.: Core-selecting package auctions. Int. J. Game Theor. 36(3–4), 393–407 (2008)
Day, R., Raghavan, S.: Fair payments for efficient allocations in public sector combinatorial auctions. Manage. Sci. 53(9), 1389–1406 (2007)
Erdil, A., Klemperer, P.: A new payment rule for core-selecting package auctions. J. Eur. Econ. Assoc. 8(2–3), 537–547 (2010)
Goel, G., Khani, M.R., Leme, R.P.: Core-competitive auctions. In: Proceedings of the 16th ACM Conference on Economics and Computation, pp. 149–166 (2015)
Goeree, J., Lien, Y.: On the impossibility of core-selecting auctions. Theor. Econ. 11(1), 41–52 (2016)
Guruswami, V., Hartline, J., Karlin, A., Kempe, D., Kenyon, C., McSherry, F.: On profit-maximizing envy-free pricing. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1164–1173 (2005)
Hartline, J., Immorlica, N., Khani, M.R., Lucier, B., Niazadeh, R.: Fast core pricing for rich advertising auctions. In Proceedings of the 19th ACM Conference on Economics and Computation, pp. 111–112 (2018)
Lamy, L.: Core-selecting package auctions: a comment on revenue-monotonicity. Int. J. Game Theor. 39(3), 503–510 (2010)
Micali, S., Valiant, P.: Collusion-resilient revenue in combinatorial auctions. Technical Report MIT-CSAIL-TR-2007-052, MIT-CSAIL (2007)
Myerson, R.: Optimal auction design. Math. Oper. Res. 6(1), 58–73 (1981)
Ott, M., Beck, M.: Incentives for overbidding in minimum-revenue core-selecting auctions. Tech. rep. Working paper, Stanford University (2013)
Parkes, D., Kalagnanam, J., Eso, M.: Achieving budget-balance with Vickrey-based payment schemes in exchanges. In: Proceedings of the 17th International Joint Conference on Artificial Intelligence, pp. 1161–1168 (2001)
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Markakis, E., Tsikiridis, A. (2019). On Core-Selecting and Core-Competitive Mechanisms for Binary Single-Parameter Auctions. In: Caragiannis, I., Mirrokni, V., Nikolova, E. (eds) Web and Internet Economics. WINE 2019. Lecture Notes in Computer Science(), vol 11920. Springer, Cham. https://doi.org/10.1007/978-3-030-35389-6_20
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