We discuss the MM* condition in game theory, where players lack a single secure pure strategy to guarantee their best possible worst-case outcome. The text explains how repeated games satisfying this condition can lead to pathological learning behaviors like non-convergence and chaotic adaptation between players, because agents are forced into complex or randomized strategies. However, the sources argue that real-world interactions involving Large Language Model (LLM) agents often avoid these issues due to structural features such as built-in safe fallback strategies, institutional rules, and partial common interests, ensuring at least one participant has a reliable action to secure a baseline outcome. This means LLM interactions typically do not meet the MM condition, promoting more stable learning dynamics and preventing the disruptive cycles seen in strictly adversarial settings. Therefore, the presence of a guaranteed safe option helps steer LLM agent behavior toward more predictable and less pathological outcomes.

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