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:

  • Département d'Informatique, CP 212, Université Libre de Bruxelles (ULB), Brussels, Belgium 1050;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, USA 02139;Département de Mathématique, CP 216, Université Libre de Bruxelles (ULB), Brussels, Belgium 1050;Département d'Informatique, CP 212, Université Libre de Bruxelles (ULB), Brussels, Belgium 1050;Department of Computer Science, University of Haifa, Haifa, Israel 31905;Department of Computer Science, University of Haifa, Haifa, Israel 31905

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2013

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Abstract

The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem played on a graph representing a network. Its edges are colored either red or blue, and 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 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.