Time bounds for iterative auctions: a unified approach by discrete convex analysis

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Journaldiscrete optimization
DateAccepted/In press - 7 Jan 2016
DatePublished (current) - 7 Feb 2016
Volume19
Number of pages27
Pages (from-to)36-62
Original languageEnglish

Abstract

We investigate an auction model where there are many different goods, each
good has multiple units and bidders have gross substitutes valuations over
the goods. We analyze the number of iterations in iterative auction algo-
rithms for the model based on the theory of discrete convex analysis. By
making use of L♮-convexity of the Lyapunov function we derive exact bounds
on the number of iterations in terms of the ℓ1-distance between the initial
price vector and the found equilibrium. Our results extend and unify the
price adjustment algorithms for the multi-unit auction model and for the
unit-demand auction model, offering computational complexity results for
these algorithms, and reinforcing the connection between auction theory and
discrete convex analysis.

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