Policymakers often design regulatory incentives without evidence on how they will shift behavior. We introduce agentic AI policy prototyping, a method that configures a large language model as a goal-directed strategic agent inside a stylized regulatory environment. The LLM receives descriptions of policy parameters and makes a discrete choice, allowing analysts to stress-test incentive designs rapidly and at low cost before real-world implementation. We demonstrate the method on an AI governance dilemma: under what conditions will a competitive developer invest in ethical features of its system? Calibrating parameters derived from game theoretic model with governance indicators from 79 countries, we find that recognition probability dominates other levers, that rewards are ineffective without credible monitoring, and that the LLM's choices align with a theoretical benchmark in approximately 75% of cases. The contribution is primarily methodological: a transparent and replicable sandbox that bridges formal theory and costly field pilots, applicable across policy domains.