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

TL;DR

This paper investigates the Stackelberg Minimum Spanning Tree Game on planar and bounded-treewidth graphs, showing NP-hardness in the former and polynomial solvability in the latter, advancing understanding of strategic pricing in network design.

Contribution

It proves NP-hardness for planar graphs and polynomial-time algorithms for graphs with bounded treewidth, extending the theoretical understanding of the game.

Findings

NP-hard on planar graphs

Polynomial-time solvable on bounded-treewidth graphs

Advances strategic pricing in network design

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.