Minimum-cost spanning tree game
From Wikipedia, the free encyclopedia
A minimum-cost spanning-tree game (MCST game) is a kind of a cooperative game. 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. Each edge in the graph has a cost, and the players build the minimum cost 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. The cost of each coalition S is the minimum cost of a spanning tree connecting only the nodes in S to the supply node s. The value of S is minus the cost of S. Using these definitions, various solution concepts from cooperative game theory can be applied. MCST games were introduced by Bird in 1976.[1]