A bilevel model of taxation and its application to optimal highway pricing
Management Science
Some APX-completeness results for cubic graphs
Theoretical Computer Science
SIAM Journal on Computing
Using sparsification for parametric minimum spanning tree problems
Nordic Journal of Computing
Pricing network edges for heterogeneous selfish users
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Stackelberg Scheduling Strategies
SIAM Journal on Computing
Beyond VCG: Frugality of Truthful Mechanisms
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The effectiveness of Stackelberg strategies and tolls for network congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A survey on networking games in telecommunications
Computers and Operations Research
On two-stage stochastic minimum spanning trees
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Pricing network edges to cross a river
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Near-optimal pricing in near-linear time
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Computational Aspects of a 2-Player Stackelberg Shortest Paths Tree Game
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
On Stackelberg Pricing with Computationally Bounded Consumers
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
The Stackelberg Minimum Spanning Tree Game on Planar and Bounded-Treewidth Graphs
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Improved hardness of approximation for stackelberg shortest-path pricing
WINE'10 Proceedings of the 6th international conference on Internet and network economics
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We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or StackMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor's prices). The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest possible minimum spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. This game is the minimum spanning tree analog of the well-studied Stackelberg shortest-path game. We analyze the complexity and approximability of the first player's best strategy in StackMST. In particular, we prove that the problem is APX-hard even if there are only two different red costs, and give an approximation algorithm whose approximation ratio is at most min {k,3 + 2lnb,1 + lnW}, where k is the number of distinct red costs, b is the number of blue edges, and W is the maximum ratio between red costs. We also give a natural integer linear programming formulation of the problem, and show that the integrality gap of the fractional relaxation asymptotically matches the approximation guarantee of our algorithm.