Mathematical Programming

, Volume 21, Issue 1, pp 1-18

First online:

Minimum cost spanning tree games

  • Daniel GranotAffiliated withUniversity of British Columbia
  • , Gur HubermanAffiliated withUniversity of Chicago

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We consider the problem of cost allocation among users of a minimum cost spanning tree network. It is formulated as a cooperative game in characteristic function form, referred to as a minimum cost spanning tree (m.c.s.t.) game. We show that the core of a m.c.s.t. game is never empty. In fact, a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem. For m.c.s.t. games with efficient coalition structures we define and construct m.c.s.t. games on the components of the structure. We show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli, respectively, of the induced games on the components of the efficient coalition structure.

Key words

Game Theory Cost Allocation Spanning Tree