In most of the literature on games on networks, players do not differ in their individual characteristics and can only be distinguished by their structural position in the network. We introduce heterogeneity by allowing players to have individual preferences over available actions. Extending the framework of Hernandez et al. (2013), we analyze equilibria outcomes for a much wider range of games. We show that, in most of the cases, the set of equilibria in a heterogeneous network is different from the analogous set in a homogeneous network, and that there is no inclusion in either direction. In the new framework, we develop a new efficiency measure, apart from the standard aggregate payoff, and use both of them for comparison of possible equilibria.