Duality and optimality of auctions for uniform distributions

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.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 72 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.