Stackelberg Network Pricing Games [article]

Patrick Briest, Martin Hoefer, Piotr Krysta
2008 arXiv   pre-print
We study a multi-player one-round game termed Stackelberg Network Pricing Game, in which a leader can set prices for a subset of m priceable edges in a graph. The other edges have a fixed cost. Based on the leader's decision one or more followers optimize a polynomial-time solvable combinatorial minimization problem and choose a minimum cost solution satisfying their requirements based on the fixed costs and the leader's prices. The leader receives as revenue the total amount of prices paid by
more » ... he followers for priceable edges in their solutions, and the problem is to find revenue maximizing prices. Our model extends several known pricing problems, including single-minded and unit-demand pricing, as well as Stackelberg pricing for certain follower problems like shortest path or minimum spanning tree. Our first main result is a tight analysis of a single-price algorithm for the single follower game, which provides a (1+ϵ) m-approximation for any ϵ >0. This can be extended to provide a (1+ϵ)( k + m)-approximation for the general problem and k followers. The latter result is essentially best possible, as the problem is shown to be hard to approximate within O(^ϵ k + ^ϵ m). If followers have demands, the single-price algorithm provides a (1+ϵ)m^2-approximation, and the problem is hard to approximate within O(m^ϵ) for some ϵ >0. Our second main result is a polynomial time algorithm for revenue maximization in the special case of Stackelberg bipartite vertex cover, which is based on non-trivial max-flow and LP-duality techniques. Our results can be extended to provide constant-factor approximations for any constant number of followers.
arXiv:0802.2841v1 fatcat:wmo5umfwyvfshpwemvsseiwktm