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Stackelberg network pricing games (2008)
| Content Provider | CiteSeerX |
|---|---|
| Author | Briest, Patrick Hoefer, Martin Krysta, Piotr |
| Description | 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 pricable 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 the followers for pricable edges in their solutions. 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 singleprice algorithm for the single follower game, which provides a (1+ε)log m-approximation for any ε> 0. This can be extended to provide a (1 + ε)(log k + log 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(log ε k + log 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. |
| File Format | |
| Language | English |
| Publisher Date | 2008-01-01 |
| Publisher Institution | In Proceedings of the 25th International Symposium on Theoretical Aspects of Computer Science (STACS |
| Access Restriction | Open |
| Subject Keyword | Log M-approximation Unit-demand Pricing Singleprice Algorithm Minimum Cost Solution Latter Result Stackelberg Bipartite Vertex Cover Stackelberg Network Pricing Game First Main Result Several Known Pricing Problem Minimum Spanning Tree General Problem Log Log Polynomial-time Solvable Combinatorial Minimization Problem Lp-duality Technique Tight Analysis Single Follower Game Constant Number Pricable Edge Stackelberg Pricing Revenue Maximization Fixed Cost Leader Price Special Case Leader Decision Second Main Result Multi-player One-round Game Single-price Algorithm Total Amount Constant-factor Approximation Polynomial Time Algorithm |
| Content Type | Text |
| Resource Type | Article |
