We consider a model for information theoretic games on interference channels introduced in previous work. The players in these games are the users, who autonomously select their encoding and decoding strategy with the objective of maximizing their own rate. In previous work, a Nash equilibrium region for this game was defined and completely characterized for two-user linear deterministic interference channels. In particular for such channels it was shown that there always exists an efficient Nash equilibrium. In this paper, we consider extending this to models with more than two users. We show that some of the analysis extends to networks with more than two users, however, significant differences also emerge. For example, it may no longer be the case that there are always efficient equilibria.