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Stepwise randomized combinatorial auctions achieve revenue monotonicity

Stepwise randomized combinatorial auctions achieve revenue monotonicity
Stepwise randomized combinatorial auctions achieve revenue monotonicity
In combinatorial auctions that use VCG, a seller can sometimes increase revenue by dropping bidders (see e.g. [5]). In our previous work [26], we showed that such failures of “revenue monotonicity” occur under an extremely broad range of deterministic strategyproof combinatorial auction mechanisms, even when bidders have “known single-minded” valuations. In this work we consider the question of whether revenue monotonic, strategyproof mechanisms for such bidders can be found in the broader class of randomized mechanisms. We demonstrate that—surprisingly—such mechanisms do exist, show how they can be constructed, and consider algorithmic techniques for implementing them in polynomial time.

More formally, we characterize a class of randomized mechanisms defined for known single-minded bidders that are strategyproof and revenue monotonic, and furthermore satisfy some other desirable properties, namely participation, consumer sovereignty and maximality, representing the mechanism as a solution to a quadratically constrained linear program (QCLP). We prove that the QCLP is always feasible (i.e., for all bidder valuations) and give its solution analytically. Furthermore, we give an algorithm for running such a mechanism in time polynomial in the number of bidders and goods; this is interesting because constructing an instance of such mechanisms from our QCLP formulation in a naive way can require exponential time.
PR132
738-747
Society for Industrial and Applied Mathematics
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Condon, Anne
a1c1e645-b4b0-4449-a18e-6e43a440cce8
Leyton-brown, Kevin
bbf18b1f-b857-48b6-b33c-5b26a6ed6b13
Mathieu, Claire
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Condon, Anne
a1c1e645-b4b0-4449-a18e-6e43a440cce8
Leyton-brown, Kevin
bbf18b1f-b857-48b6-b33c-5b26a6ed6b13
Mathieu, Claire

Rastegari, Baharak, Condon, Anne and Leyton-brown, Kevin (2009) Stepwise randomized combinatorial auctions achieve revenue monotonicity. In, Mathieu, Claire (ed.) Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms. (Proceedings, , (doi:10.1137/1.9781611973068.81), PR132) Philadelphia. Society for Industrial and Applied Mathematics, pp. 738-747. (doi:10.1137/1.9781611973068.81).

Record type: Book Section

Abstract

In combinatorial auctions that use VCG, a seller can sometimes increase revenue by dropping bidders (see e.g. [5]). In our previous work [26], we showed that such failures of “revenue monotonicity” occur under an extremely broad range of deterministic strategyproof combinatorial auction mechanisms, even when bidders have “known single-minded” valuations. In this work we consider the question of whether revenue monotonic, strategyproof mechanisms for such bidders can be found in the broader class of randomized mechanisms. We demonstrate that—surprisingly—such mechanisms do exist, show how they can be constructed, and consider algorithmic techniques for implementing them in polynomial time.

More formally, we characterize a class of randomized mechanisms defined for known single-minded bidders that are strategyproof and revenue monotonic, and furthermore satisfy some other desirable properties, namely participation, consumer sovereignty and maximality, representing the mechanism as a solution to a quadratically constrained linear program (QCLP). We prove that the QCLP is always feasible (i.e., for all bidder valuations) and give its solution analytically. Furthermore, we give an algorithm for running such a mechanism in time polynomial in the number of bidders and goods; this is interesting because constructing an instance of such mechanisms from our QCLP formulation in a naive way can require exponential time.

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Published date: 2009

Identifiers

Local EPrints ID: 426397
URI: https://eprints.soton.ac.uk/id/eprint/426397
PURE UUID: 9326bfa0-b72c-4b77-b5f0-61cafd59539c
ORCID for Baharak Rastegari: ORCID iD orcid.org/0000-0002-0985-573X

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Date deposited: 27 Nov 2018 17:30
Last modified: 10 Dec 2019 01:22

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