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First-passage percolation on a ladder graph, and the path cost in a VCG auction

Flaxman, Abraham, Gamarnik, David and Sorkin, Gregory B. (2011) First-passage percolation on a ladder graph, and the path cost in a VCG auction. Random Structures and Algorithms, 38 (3). pp. 350-364. ISSN 1042-9832

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Abstract

This paper studies the time constant for first-passage percolation, and the Vickrey-Clarke-Groves (VCG) payment, for the shortest path on a ladder graph (a width-2 strip) with random edge costs, treating both in a unified way based on recursive distributional equations. For first-passage percolation where the edge costs are independent Bernoulli random variables we find the time constant exactly; it is a rational function of the Bernoulli parameter. For first-passage percolation where the edge costs are uniform random variables we present a reasonably efficient means for obtaining arbitrarily close upper and lower bounds. Using properties of Harris chains we also show that the incremental cost to advance through the medium has a unique stationary distribution, and we compute stochastic lower and upper bounds. We rely on no special properties of the uniform distribution: the same methods could be applied to any well-behaved, bounded cost distribution. For the VCG payment, with Bernoulli-distributed costs the payment for an n-long ladder, divided by n, tends to an explicit rational function of the Bernoulli parameter. Again, our methods apply more generally.

Item Type: Article
Official URL: http://eu.wiley.com/WileyCDA/WileyTitle/productCd-...
Additional Information: © 2010 Wiley Periodicals, Inc.
Library of Congress subject classification: H Social Sciences > HF Commerce
Q Science > QA Mathematics
Sets: Research centres and groups > Management Science Group
Departments > Management
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 13 Apr 2011 10:47
URL: http://eprints.lse.ac.uk/35055/

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