Specializations and generalizations of the Stackelberg minimum spanning tree game

Specializations and Generalizations of the Stackelberg Minimum Spanning Tree Game

Let be given a graph G = (V,E) 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 form a spanning tree of G. Then, the Stackelberg Minimum Spanning Tree (StackMST) problem 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 r...

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

The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem introduced at WADS’07. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where 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 buy...

The irreducible Core of a minimum cost spanning tree game

It is a known result that for a minimum cost spanning tree (mcst) game a Core allocation can be deduced directly from a mcst in the underlying network. To determine this Core allocation one only needs to determine a mcst in the network and it is not necessary to calculate the coalition values of the corresponding mcst game. In this paper we will deduce other Core allocations directly from the n...

Fair cost-sharing methods for the minimum spanning tree game

The optimistic TU game in minimum cost spanning tree problems

We associate an optimistic TU game with each minimum cost spanning tree problem. We define the worth of a coalition S as the cost of connecting agents in S to the source assuming that agents in N\S are already connected to the source, and agents in S can connect through agents in N\S. We study the Shapley value of this new game.