Duality and optimality of auctions for uniform distributions
Giannakopoulos Y, Koutsoupias E (2014)
Publication Type: Conference contribution, Original article
Publication year: 2014
Publisher: Association for Computing Machinery
Pages Range: 259-276
Conference Proceedings Title: Proceedings of the 15th ACM Conference on Economics and Computation (EC)
Event location: USA
ISBN: 9781450325653
Open Access Link: https://arxiv.org/abs/1404.2329
Abstract
We derive exact optimal solutions for the problem of optimizing revenue in single-bidder multi-item auctions for uniform i.i.d. valuations. We give optimal auctions of up to 6 items; previous results were only known for up to three items. To do so, we develop a general duality framework for the general problem of maximizing revenue in many-bidders multi-item additive Bayesian auctions with continuous probability valuation distributions. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the geometric nature of the problem and highlights its connection with the theory of bipartite graph matchings. The duality framework is used not only for proving optimality, but perhaps more importantly, for deriving the optimal auction; as a result, the optimal auction is defined by natural geometric constraints. © 2014 ACM.
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APA:
Giannakopoulos, Y., & Koutsoupias, E. (2014). Duality and optimality of auctions for uniform distributions. In Proceedings of the 15th ACM Conference on Economics and Computation (EC) (pp. 259-276). USA: Association for Computing Machinery.
MLA:
Giannakopoulos, Yiannis, and Elias Koutsoupias. "Duality and optimality of auctions for uniform distributions." Proceedings of the 15th ACM Conference on Economics and Computation, EC 2014, USA Association for Computing Machinery, 2014. 259-276.
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