Abstract
Two classes of distributions that are widely used in the analysis of Bayesian auctions are the monotone hazard rate (MHR) and regular distributions. They can both be characterized in terms of the rate of change of the associated virtual value functions: for MHR distributions, the condition is that for values v < v′, ϕ (v′) - ϕ (v) ≥ v′ - v, and for regular distributions, ϕ (v′) - ϕ (v) ≥ 0. Cole and Roughgarden introduced the interpolating class of α-strongly regular distributions (α-SR distributions for short), for which ϕ (v′) - ϕ (v) ≥ α (v′ - v), for 0 ≤ α ≤ 1.
In this article, we investigate five distinct auction settings for which good expected revenue bounds are known when the bidders’ valuations are given by MHR distributions. In every case, we show that these bounds degrade gracefully when extended to α-SR distributions. For four of these settings, the auction mechanism requires knowledge of these distributions (in the remaining setting, the distributions are needed only to ensure good bounds on the expected revenue). In these cases, we also investigate what happens when the distributions are known only approximately via samples, specifically how to modify the mechanisms so that they remain effective and how the expected revenue depends on the number of samples.
- Gagan Aggarwal, Gagan Goel, and Aranyak Mehta. 2009. Efficiency of (revenue-)optimal mechanisms. In Proceedings of the 10th ACM Conference on Electronic Commerce (EC’09). ACM, New York, NY, 235--242. Google ScholarDigital Library
- Simon P. Anderson and Regis Renault. 2003. Efficiency and surplus bounds in Cournot competition. Journal of Economic Theory 113, 2, 253--264.Google ScholarCross Ref
- Pablo Azar, Constantinos Daskalakis, Silvio Micali, and S. Matthew Weinberg. 2013. Optimal and efficient parametric auctions. In Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’13). 596--604. http://dl.acm.org/citation.cfm?id=2627817.2627860. Google ScholarDigital Library
- Sayan Bhattacharya, Gagan Goel, Sreenivas Gollapudi, and Kamesh Munagala. 2012. Budget-constrained auctions with heterogeneous items. Theory of Computing 8, 1, 429--460.Google ScholarCross Ref
- Andrew Caplin and Barry Nalebuff. 1991. Aggregation and imperfect competition: On the existence of equilibrium. Econometrica 25, 1--24.Google ScholarCross Ref
- Andrew Caplin and Barry Nalebuff. 1991. Aggregation and social choice: A mean voter theorem. Econometrica 25, 25--59.Google ScholarCross Ref
- Shuchi Chawla, David L. Malec, and Azarakhsh Malekian. 2011. Bayesian mechanism design for budget-constrained agents. In Proceedings of the 12th ACM Conference on Electronic Commerce (EC’11). ACM, New York, NY, 253--262. Google ScholarDigital Library
- Ludek Cigler, Wolfgang Dvorák, Monika Henzinger, and Martin Starnberger. 2014. Limiting price discrimination when selling products with positive network externalities. In Proceedings of the 10th International Conference on Web and Internet Economics (WINE’14). 44--47.Google ScholarCross Ref
- Richard Cole and Tim Roughgarden. 2014. The sample complexity of revenue maximization. In Proceedings of the 46th Annual ACM Symposium on Theory of Computing (STOC’14). ACM, New York, NY, 243--252. Google ScholarDigital Library
- Constantinos Daskalakis and George Pierrakos. 2011. Simple, optimal and efficient auctions. In Proceedings of the 7th International Workshop on Internet and Network Economics (WINE’11). 109--121. Google ScholarDigital Library
- Peerapong Dhangwatnotai, Tim Roughgarden, and Qiqi Yan. 2015. Revenue maximization with a single sample. Games and Economic Behavior 91, 318--333.Google ScholarCross Ref
- Christian Ewerhart. 2013. Regular type distributions in mechanism design and -concavity. Economic Theory 53, 3, 591--603. http://ezproxy.library.nyu.edu:2048/login?url=http://search.ebscohost.com/login.aspx?direct=true8db=bth8AN=892418218site=ehost-live.Google ScholarCross Ref
- Jason Hartline, Vahab Mirrokni, and Mukund Sundararajan. 2008. Optimal marketing strategies over social networks. In Proceedings of the 17th International Conference on World Wide Web (WWW’08). ACM, New York, NY, 189--198. Google ScholarDigital Library
- J. D. Hartline. 2014. Mechanism Design and Approximation. Book draft.Google Scholar
- J. D. Hartline and A. Karlin. 2007. Profit maximization in mechanism design. In Algorithmic Game Theory, N. Nisan, T. Roughgarden, É. Tardos, and V. V. Vazirani (Eds.). Cambridge University Press, 331--362.Google Scholar
- Jason D. Hartline and Tim Roughgarden. 2009. Simple versus optimal mechanisms. ACM SIGecom Exchanges 8, 1, Article 5, 3 pages. Google ScholarDigital Library
- Robert Kleinberg and Yang Yuan. 2013. On the ratio of revenue to welfare in single-parameter mechanism design. In Proceedings of the 14th ACM Conference on Electronic Commerce (EC’13). ACM, New York, NY, 589--602. Google ScholarDigital Library
- Roger B. Myerson. 1981. Optimal auction design. Mathematics of Operations Research 6, 1, 58--73. Google ScholarDigital Library
- Nikolaus Schweizer and Nora Szech. 2015. The Quantitative View of MYerson Regularity. Discussion Papers, Research Unit: Economics of Change SP II 2015-307. Social Science Research Center Berlin (WZB). http://EconPapers.repec.org/RePEc:zbw:wzbeoc:spii2015307.Google Scholar
Index Terms
- Applications of α-Strongly Regular Distributions to Bayesian Auctions
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