Both conventional computable general equilibrium (CGE) models and game-theoretic models have been widely used in examining federal systems. There has been little attempt, however, at linking such models. In this paper we seek to combine the two approaches. We model the effects of a change in a federal government's inter-regional transfers within the context of a CGE model of a federal system in which regional governments act to maximise the welfare of the residents of their region. The model is a small two-region one. Simulations are conducted with six versions of the model, each calibrated for a particular Australian state and the rest of the nation. We show that a change in the level of transfers has little influence on per-capita private consumption, government consumption and welfare, and that its main effect is to induce migration from the donor region to the recipient region.