Archive for October, 2010

Improved Hardness of Approximation for Stackelberg Shortest-Path Pricing

Author: Patrick Briest, Parinya Chalermsook, Sanjeev Khanna, Bundit Laekhanukit, Danupon Nanongkai
(Alphabetical order)

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Conference: WINE 2010: 6th Workshop on Internet & Network Economics [wiki].  Published in LNCS Vol. 6484.

Abstract:

 

We consider the Stackelberg shortest-path pricing problem, which is defined as follows. Given a graph G with fixed-cost and pricable edges and two distinct vertices s and t, we may assign
prices to the pricable edges. Based on the predefined fixed costs and our prices, a customer purchases a cheapest s-t-path in G and we receive payment equal to the sum of prices of pricable
edges belonging to the path. Our goal is to find prices maximizing the payment received from the customer. While Stackelberg shortest-path pricing was known to be APX-hard before, we provide
the first explicit approximation threshold and prove hardness of approximation within 2 − o(1). We also prove that for the nicely structured type of instance resulting from our reduction, the
gap between the revenue of an optimal pricing and the only known general upper bound can still be logarithmically large.

Update History

[v1] October 1, 2010 (Conference version)

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