Generative agents have proven to be powerful assistants in a wide variety of contexts. Given this success, users are now deploying agents with minimal restrictions in open ended, multi-agent environments. Current methods for monitoring the dynamics of open-ended multi-agent systems are limited to qualitative inspection. In this paper, we extend the process-theoretic notion of adaptive control charts to multi-agent systems to enable automated monitoring. Using simulation, we demonstrate that adaptive control charts are necessary for monitoring multi-agent systems that can learn from their environment. We further demonstrate, both empirically and theoretically, that adaptive control charts are susceptible to adversarial agents that defect sufficiently slowly. These results illustrate a fundamental tradeoff in multi-agent system control: either agents in a system cannot learn or the system is susceptible to adversaries.