This thesis investigates mean field games and related models of dynamic agent behaviour, along with applications to network models. To begin, small time horizon and many--agent limits are taken of stochastic dynamic games. The limits are show to converge to a mean field game and a best reply strategy model. For stationary versions of each model, novel proofs of existence and uniqueness are given. Then the models are simulated for some particular examples that highlight the similarities and differences between the two models. After studying the best reply strategy approximation of mean field games, next an application of mean field games to an economic model of knowledge spillovers is considered. A multi--population mean field game is constructed, with interactions between populations encoded in a network structure. For this model, proofs of existence and uniqueness are given, and simulations are made. The simulations provide some predictions about the effect of the network structure on company productivity, which are then tested using an econometric analysis of patent data. Finally, econometric and network analysis is used to estimate supply network climate risk, through a calculation of company--level embodied emissions.