Computational comparisons of different formulations for the Stackelberg minimum spanning tree game

Abstract

Let (Formula presented.) be a given graph whose edge set is partitioned into a set R of red edges and a set B of blue edges, and assume that red edges are weighted and contain a spanning tree of G. Then, the Stackelberg minimum spanning tree game (StackMST) is that of pricing (i.e., weighting) the blue edges in such a way that the total weight of the blue edges selected in a minimum spanning tree of the resulting graph is maximized. In this paper, we present different new mathematical programming formulations for the StackMST based on the properties of the minimum spanning tree problem and the bilevel optimization. We establish a theoretical and empirical comparison between these new formulations that are able to solve random instances of 20–70 nodes. We also test our models on instances in the literature, outperforming previous results.