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Title: Frugality in set-system auctions
Author: McCabe, Antony
ISNI:       0000 0004 2734 5770
Awarding Body: University of Liverpool
Current Institution: University of Liverpool
Date of Award: 2012
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We study the topic Frugality in Set System auctions; examining the payments that are given by truthful mechanisms when buying selections of items at auction. Firstly, we examine a simple single-commodity auction, where the auctioneer wishes to buy some given quantity of identical items. We show methods of quickly computing a winning set, as well as the benchmark NTUmin. We then show, for certain special cases, a mechanism that improves on the frugality of VCG, and is within a constant factor of optimal for mechanisms in its class. We then consider the general case, and see a relatively large lower-bound for a class of similar mechanisms. We propose a new type of auction, based on finding the shortest-path in a graph with 'bundles' of edges. We show that finding an optimal solution to this problem is NP-hard, for any bundle-size (k) of 2 or more, showing that there is no polynomial time algorithm that can compute an exact solution, subject to the commonly-held assumption that P! =NP. However, we give a simple k approximation and use this to design a truthful mechanism and give its frugality ratio. We consider the benchmarks that have been used in the literature as first-price auctions, and examine a range of other possibilities that should aim to meet the same 'fairness' criteria. We show that not all of the proposals will meet these criteria, and give the ranges of values possible for these other benchmarks. We also give information on their computational complexity, including a new result showing approximation hardness for a new benchmark as well as an existing one used in the literature. We then briefly examine the meaning of the benchmarks we used for frugality if they are rewritten for use in the more traditional 'forward' auctions (that is, selling items by auction).
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral