In an MCST game, each player is a node in a complete graph.
The graph contains an additional node - the supply node - denoted by s. The goal of the players is that all of them will be connected by a path to s. To this end, they need to construct a spanning tree.
The question then arises, how to allocate the cost of this MCST among the players?
The solution offered by cooperative game theory is to consider the cost of each potential coalition - each subset of the players.
In general, the core of an MCSF game may be empty.