Three-person spanning tree games

There are many situations where allocation of costs among the users of a minimum spanning tree network is a problem of concern. In [1], formulation of this problem as a game theoretic model, spanning tree games, has been considered. It is well known that st games have nonempty cores. Many researchers have studied other solutions related to st games. In this paper, we study three-person st games. Various properties connected to the convexity or no-convexity, and τ-value is studied. A characterization of the core and geometric interpretation is given. In special cases, the nucleolus of the game is given.