The Stackelberg Minimum Spanning Tree Game on Planar and Bounded-Treewidth Graphs

Authors:
Jean Cardinal;Erik D. Demaine;Samuel Fiorini;Gwenaël Joret;Ilan Newman;Oren Weimann
Affiliations:
Université Libre de Bruxelles (ULB), Brussels, Belgium B-1050;MIT, Cambridge, USA 02139;Université Libre de Bruxelles (ULB), Brussels, Belgium B-1050;Université Libre de Bruxelles (ULB), Brussels, Belgium B-1050;University of Haifa, Haifa, Israel 31905;Weizmann Institute of Science, Rehovot, Israel 76100
Venue:
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Year:
2009

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Abstract

The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem introduced at WADS'07. The game is played on a graph, whose edges are colored either red or blue, and where the red edges have a given fixed cost. The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest 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. We study this problem in the cases of planar and bounded-treewidth graphs. We show that the problem is NP-hard on planar graphs but can be solved in polynomial time on graphs of bounded treewidth.