In this paper, we introduce the stable path topology control problem for routing in mobile multi-hop networks. We formulate the topology control problem of selective link-state broadcast as a graph pruning problem with restricted local neighborhood information. We develop a multi-agent optimiza- tion framework where the decision policies of each agent are restricted to local policies on incident edges and independent of the policies of the other agents. We show that under a condition called the positivity condition, these independent local policies preserve the stable routing paths globally. We then provide an efficient algorithm to compute an optimal local policy that yields a minimal pruned graph, which we call the Stable Path Topology Control (SPTC) algorithm. Using simulations, we demonstrate that this algorithm, when used with the popular ETX metric, outperforms topology control mechanisms commonly used for Mobile Ad Hoc Networks.