The Stackelberg minimum spanning tree game on planar and bounded-treewidth graphs

Jean Cardinal, Erik D. Demaine, Samuel Fiorini, Gwenaël Joret, Ilan Newman, Oren Weimann

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)19-46
Number of pages28
JournalJournal of Combinatorial Optimization
Issue number1
StatePublished - Jan 2013


  • Baunded treewidth
  • Minimum spanning
  • Network pricing games
  • The Stackelberg games

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics


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