Improved Hardness of Approximation for Stackelberg Shortest-Path Pricing

TL;DR

This paper improves the understanding of the computational difficulty of the Stackelberg shortest-path pricing problem by establishing a new approximation threshold and proving hardness of approximation within a factor of 2-o(1).

Contribution

It provides the first explicit approximation threshold and demonstrates hardness of approximation for the problem within a factor of 2-o(1).

Findings

Established the first explicit approximation threshold.

Proved hardness of approximation within 2-o(1).

Enhanced the theoretical understanding of the problem's complexity.

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).