Internet and Network Economics

Volume 6484 of the series Lecture Notes in Computer Science pp 444-454

Improved Hardness of Approximation for Stackelberg Shortest-Path Pricing

  • Patrick BriestAffiliated withDepartment of Computer Science, University of Paderborn
  • , Parinya ChalermsookAffiliated withDepartment of Computer Science, University of Chicago
  • , Sanjeev KhannaAffiliated withDepartment of Computer and Information Science, University of Pennsylvania
  • , Bundit LaekhanukitAffiliated withDepartment of Computer Science, McGill University
  • , Danupon NanongkaiAffiliated withCollege of Computing, Georgia Tech

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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.