A multi-agent system consisting of hetero-geneous agents, described by nonlinear dynamics andwith inter-agent communication characterised by a directedacyclic graph, is considered in this paper. A frameworkfor designing distributed control strategies obtained viathe combination oflocal non-cooperative differential gamesis provided. The resulting dynamic (local) state-feedbackcontrol laws can be computed offline and in a decentralisedmanner. Conditions for ensuring stability of the overallclosed-loop system are provided, before the proposed gametheoretic framework is applied to a formation control problem.