Improved hardness of approximation for stackelberg shortest-path pricing

Authors:
Patrick Briest;Parinya Chalermsook;Sanjeev Khanna;Bundit Laekhanukit;Danupon Nanongkai
Affiliations:
Department of Computer Science, University of Paderborn, Germany;Department of Computer Science, University of Chicago, IL;Department of Computer and Information Science, University of Pennsylvania, PA;Department of Computer Science, McGill University, QC, Canada;College of Computing, Georgia Tech, Atlanta, GA
Venue:
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Year:
2010

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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 argue that the nicely structured type of instance resulting from our reduction captures most of the challenges we face in dealing with the problem in general and, in particular, we show that the gap between the revenue of an optimal pricing and the only known general upper bound can still be logarithmically large.