Anmerkungen:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments October 5, 2022 erstellt
Beschreibung:
The minimum-cost-spanning-tree (m.c.s.t.) game is a classical cooperative game model that has been extensively studied. We consider the problem of decreasing the connection costs as much as possible in an m.c.s.t. game such that its core does not change. We define the desired m.c.s.t. game as the matrix-exact cover of the original m.c.s.t. game, and show its existence and uniqueness by providing an explicit formula. Our results also imply that the set of all m.c.s.t. games with the same core possesses a meet-semilattice structure: if two m.c.s.t. games have the same core, and we construct a new m.c.s.t. game by defining the cost of each edge as the minimum between the corresponding connection costs of the two games, then the new game has the same core too