Multi-agent LLM systems increasingly debate answers, coordinate research, simulate users, and mediate information flows, making agent-to-agent persuasion a basic but undermeasured capability. We introduce a controlled testbed for studying how goal-directed persuaders shift elicited stances in networks of LLM agents grounded in real-world ego-network topologies. Across four LLM backbones, five graphs, and 55 policy statements, we find that persuasion dynamics depend on the interaction between topology, competition, topic, and model prior. Additionally, we show that direct exposure reliably predicts next-round stance change in competing runs, and peer relays carry smaller but measurable influence, showing that agents not assigned to persuade can still transmit persuasive force. Finally, analyzing post text alone misses important movement: planned strategies are only partly realized in executed messages, action choices can diverge from message content, and persuadees rarely state the stance shifts detected by probes. These results argue for evaluating multi-agent persuasion as a trajectory- and exposure-level process, using belief probes, exposure provenance, and action logs to identify who influenced whom and whether visible language reflects underlying stance movement.

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