Edge Computing brings flexibility and scalability of virtualization technologies at the edge of the network, enabling service providers to deploy new applications over a richer network infrastructure. However, the coexistence of such variety of applications on the same infrastructure exacerbates the already challenging problem of coordinating resource allocation while preserving the resource assignment optimality. In fact, (i) each application can potentially require different optimization criteria due to their heterogeneous requirements, and (ii) we may not count on a centralized orchestrator due to the highly dynamic nature of edge networks. To solve this problem, we present DRAGON, a Distributed Resource AssiGnment and OrchestratioN algorithm that seeks optimal partitioning of shared resources between different applications running over a common edge infrastructure. We designed DRAGON to guarantee both a bound on convergence time and an optimal (1-1/e)-approximation with respect to the Pareto optimal resource assignment. We evaluate convergence and performance of DRAGON on a prototype implementation, assessing the benefits compared to traditional orchestration approaches.