arXiv:2608.07940v2 Announce Type: replace-cross Abstract: We develop a formal framework for analyzing indirect geoeconomic influence. The influencing state (sender) does not attempt to change a target nation's policy directly. Instead, the sender restructures the target's internal political economy so that its own citizens, firms, and institutions generate the compliance pressure. The framework rests on a switching dynamical system (SDS) in which a target's political economy evolves under mode-dependent rules. We analyze two modes: a permissive mode, in which a mechanism transmits pressure toward the sender's preferred policy, and a contested mode, entered naturally once the target detects and attributes the mechanism. Crucially, the sender's mechanism design shapes the transition into the contested mode. Our approach inverts the usual regime-switching problem in which analysts estimate a latent transition kernel from data. The indirect influence approach is to have the designer engineer a kernel to steep regime occupancy over a planning horizon. A structured switch vector decomposes any mechanism along discrete design dimensions, and a combinatorial optimizer searches this space for high-performing archetypes scored on compliance, time-to-threshold, and a durability ratio. We characterize mode-conditional equilibria and derive comparative statics on credibility and legibility, showing that the legibility penalty is scaled by the salience of the government channel and interacts with the mechanism's cost incidence. We illustrate the framework with two stylized mechanisms and report a two-part proof of concept: a simulation of 972 archetypes, and a fully crossed study of the pipeline's optional generative stage in which language models write and blindly classify candidate instruments for archetypes.