Giannakopoulos Y, Koutsoupias E (2018)
Publication Type: Journal article
Publication year: 2018
Book Volume: 47
Pages Range: 121-165
Journal Issue: 1
URI: http://arxiv.org/abs/1404.2329
DOI: 10.1137/16M1072218
Open Access Link: http://arxiv.org/abs/1404.2329
We develop a general duality-theory framework for revenue maximization in additive Bayesian auctions. 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. We demonstrate the power of the framework by applying it to a multiple-good monopoly setting where the buyer has uniformly distributed valuations for the items, the canonical long-standing open problem in the area. We propose a deterministic selling mechanism called straight-jacket auction (SJA), which we prove to be exactly optimal for up to six items, and conjecture its optimality for any number of goods. The duality framework is used not only for proving optimality, but perhaps more importantly for deriving the optimal mechanism itself; as a result, SJA is defined by natural geometric constraints.
APA:
Giannakopoulos, Y., & Koutsoupias, E. (2018). Duality and optimality of auctions for uniform distributions. SIAM Journal on Computing, 47(1), 121-165. https://dx.doi.org/10.1137/16M1072218
MLA:
Giannakopoulos, Yiannis, and Elias Koutsoupias. "Duality and optimality of auctions for uniform distributions." SIAM Journal on Computing 47.1 (2018): 121-165.
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