We present a new solution concept called evolutionarily stable Stackelberg equilibrium (SESS). We study the Stackelberg evolutionary game setting in which there is a single leading player and a symmetric population of followers. The leader selects an optimal mixed strategy, anticipating that the follower population plays an evolutionarily stable strategy (ESS) in the induced subgame and may satisfy additional ecological conditions. We consider both leader-optimal and follower-optimal selection among ESSs, which arise as special cases of our framework. Prior approaches to Stackelberg evolutionary games either define the follower response via evolutionary dynamics or assume rational best-response behavior, without explicitly enforcing stability against invasion by mutations. We present algorithms for computing SESS in discrete and continuous games, and validate the latter empirically. Our model applies naturally to biological settings; for example, in cancer treatment the leader represents the physician and the followers correspond to competing cancer cell phenotypes.

翻译：我们提出了一种名为进化稳定的Stackelberg均衡（SESS）的新解概念。我们研究了一类Stackelberg进化博弈设定，其中存在一个领导者玩家和一个对称的追随者群体。领导者选择一种最优混合策略，同时预期追随者群体在诱导子博弈中采取进化稳定策略（ESS），并可能满足额外的生态条件。我们考虑了ESS中领导者最优和追随者最优的选择，这些选择作为我们框架的特例出现。先前关于Stackelberg进化博弈的方法要么通过进化动力学定义追随者响应，要么假设理性的最佳响应行为，但未明确地强制执行对抗突变入侵的稳定性。我们提出了在离散和连续博弈中计算SESS的算法，并通过实证验证了后者。我们的模型自然地适用于生物学场景；例如，在癌症治疗中，领导者代表医生，追随者则对应于竞争中的癌细胞表型。