In this paper, we introduce the stable path topology control problem for routing in Mobile Ad Hoc Networks (MANETs). We formulate the problem as a constrained multiagent optimization problem with only local neighborhood information. We develop and prove local pruning strategies that solve this problem. We also introduce the notion of distorted pruning, which offers a systematic method to trade path stability off against the hop count metric. Finally, we quantify the performance of our pruning algorithms using several simulation scenarios.