Boolean Network Games are iterated games played on a network, in which players choose a set of properties to present each round, with the aim of achieving some goal by way of a machine strategy. We define Boolean Games and Iterated Boolean Games as a brief background to the introduction of Boolean Network Games. We then discuss Boolean Network Games in detail, considering their definition and some basic properties. A translation between Boolean Network Games and Iterated Boolean Games is given, grounding the new model in existing frameworks. Finally, we consider a number of extensions to Boolean Network Games to allow for logical representations of machine strategies and the inclusion of epistemology in the games.