Game theory usually assumes that followers are rational -- that they choose strategies maximizing their payoffs given what the leader has committed to. Sam Ganzfried's new framework, the evolutionarily stable Stackelberg equilibrium, replaces this assumption with something older and stranger: followers adopt strategies that survive invasion by mutants. The leader -- modeled as a physician choosing a treatment protocol, or a regulator setting policy -- optimizes against a population whose behavior is shaped not by calculation but by evolutionary stability. The resulting equilibrium can differ sharply from the standard Stackelberg solution, because an evolutionarily stable strategy in the follower population need not be a best response in the classical sense.
The structural insight is that the leader's power actually depends on the followers being governed by dynamics the leader cannot directly command. In a standard game, the leader announces a strategy and followers rationally comply; the leader's advantage comes from commitment. Here, the leader's advantage comes from prediction of a process that runs on its own logic. The evolutionary dynamics are not a simplification of rationality -- they are a different kind of regularity, one that makes the follower population's behavior more constrained in some directions and less controllable in others. The leader must optimize against a population that is stable in a specific, invasion-proof sense, and this stability narrows the set of reachable outcomes while making those outcomes more robust. In the cancer treatment application, the physician cannot instruct cell phenotypes to adopt a strategy; she can only shape the selective landscape and rely on the evolutionary process to settle. The leash works precisely because it is not a chain.
(arXiv:2603.18385)