We propose a model of network games with heterogeneity introduced by endowing players with types that generate preferences among their choices. We study two classes of games: strategic complements or substitutes in payoffs. The payoff function depends on the network structure, and we ask how does heterogeneity shape players' decision making, what is its effect on equilibria, conditions of stability, and welfare. Heterogeneity in players' type establishes the existence of thresholds which determine the Nash equilibrium conditions in a network game. Network configurations in equilibrium can be satisfactory if each player chooses the action corresponding to her type or frustrated when at least one player is not. Also, equilibria can be specialized if all players are choosing the same action (only in strategic complements), or hybrid when both actions coexist. A refinement of the Nash equilibria through stochastic mutations of pairs of neighbors limits multiplicity to a subset of Stable Equilibrium Configurations. The absorbing state networks lead, in most cases, to a frustrated hybrid configuration. This class corresponds to the risk dominant equilibrium