Understanding mobility dynamics and the effects of urban transportation management policies requires examining how individual travel decisions, traffic conditions, and policy interventions influence one another over time. We present AgenticMobility, an open-source experimental platform for studying how mobility AI agents and other AI agents interact, adapt through repeated experience, and collectively shape mobility outcomes. Persistent agents retain identities and relevant states across rounds, with explicit interfaces defining information access, admissible actions, and decision schedules; linked records trace decisions, execution, and feedback. In the current implementation, large language model (LLM) agents act as travelers choosing routes and departure times and as a manager periodically adjusting link charges within MATSim. A preliminary demonstration spans 100 simulated days in each of five configurations, with one run per configuration and a shared simulation seed. In the joint traveler--manager run, all 1,179,300 finalized target decisions satisfied action constraints; execution checks verified implementation of accepted choices and preservation of personal memories across days. Trajectories show stable route choices alongside departure-time adjustments and differences between controlled-trip and population-wide outcomes. The platform supports experiments on individual adaptation, collective outcomes, and management interventions by varying information access, retained experience, and management feedback. Source code is available at https://github.com/Agentic-City-Research/Agentic-Mobility

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