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Designing and Learning Optimal Finite Support Auctions

Designing and Learning Optimal Finite Support Auctions
Designing and Learning Optimal Finite Support Auctions
A classical paper of Myerson shows how to construct an optimal (revenue-maximizing) auction in a model where bidders' values are drawn from known continuous distributions. In this paper we show how to adapt this approach to finite support distributions. We demonstrate that a Myerson-style auction can be constructed in time polynomial in the number of bidders and the size of the support sets. Also, we consider the scenario where the mechanism designer knows the support sets, but not the probability of each value. In this situation, we show that the optimal auction may be learned in polynomial time using a weak oracle that, given two candidate auctions, returns one with a higher expected revenue. To prove this, we introduce a new class of truthful mechanisms which we call order-based auctions. We show that the optimal mechanism is an order-based auction and use the internal structure of this class to prove the correctness of our learning algorithm as well as to bound its running time.
736-745
Elkind, Edith
7a013473-5cd0-4e41-b907-66b30a04a400
Gabow, Harold
157b578e-539b-46be-a773-373426cb36f2
Elkind, Edith
7a013473-5cd0-4e41-b907-66b30a04a400
Gabow, Harold
157b578e-539b-46be-a773-373426cb36f2

Elkind, Edith (2007) Designing and Learning Optimal Finite Support Auctions. Gabow, Harold (ed.) Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, New Orleans, Louisiana, United States. 07 - 09 Jan 2007. pp. 736-745 .

Record type: Conference or Workshop Item (Paper)

Abstract

A classical paper of Myerson shows how to construct an optimal (revenue-maximizing) auction in a model where bidders' values are drawn from known continuous distributions. In this paper we show how to adapt this approach to finite support distributions. We demonstrate that a Myerson-style auction can be constructed in time polynomial in the number of bidders and the size of the support sets. Also, we consider the scenario where the mechanism designer knows the support sets, but not the probability of each value. In this situation, we show that the optimal auction may be learned in polynomial time using a weak oracle that, given two candidate auctions, returns one with a higher expected revenue. To prove this, we introduce a new class of truthful mechanisms which we call order-based auctions. We show that the optimal mechanism is an order-based auction and use the internal structure of this class to prove the correctness of our learning algorithm as well as to bound its running time.

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More information

Published date: 2007
Additional Information: Event Dates: January 7-9, 2007
Venue - Dates: Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, New Orleans, Louisiana, United States, 2007-01-07 - 2007-01-09
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 263443
URI: http://eprints.soton.ac.uk/id/eprint/263443
PURE UUID: 5467ce6a-a5e5-4609-be59-043ffd3e8bda

Catalogue record

Date deposited: 15 Feb 2007
Last modified: 14 Mar 2024 07:32

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Contributors

Author: Edith Elkind
Editor: Harold Gabow

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