We consider a game-theoretical variant of the Steiner forest problem in which each player j, out of a set of k players, strives to connect his terminal pair (sj, tj) of vertices in an undirected, edge-weighted graph G. In this paper we show that a natural adaptation of the primaldual Steiner forest algorithm of Agrawal, Klein and Ravi [When trees collide: An approximation algorithm for the generalized Steiner problem in networks, SIAM Journal on Computing, 24(3):445