In many social and economic situations, networks are the primary vehicle for strategic interactions among multiple players. On the one hand, networks connect individuals and represent how they interact with each other. On the other hand, networks describe relations between objects that are of interest to multiple decision-makers. The aims of the thesis are two-fold: first, to describe how the underlying network structures affect the existence of desirable outcomes of strategic interactions; and second, to discuss computational issues that arise when considering problems with connectivity constraints imposed by a network. In particular, we will consider two settings in which networks play a critical role: coalition formation and fair division restricted by networks. Specifically, we will study a model in which the space of feasible outcomes is restricted to the connected subgraphs of an underlying network. In essence, we show that acyclicity of a network is a necessary and sufficient condition for desirable outcomes to exist and to be efficiently computable.