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演化稳定斯塔克尔伯格均衡（SESS）的新解概念。我们研究了一种斯塔克尔伯格演化博弈设定，其中存在一个领导者和一个对称的追随者群体。领导者选择一种最优混合策略，并预期追随者群体在诱导子博弈中采用演化稳定策略（ESS），且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两种选择，这两种选择均作为我们框架的特例出现。先前针对斯塔克尔伯格演化博弈的方法要么通过演化动力学定义追随者响应，要么假设理性最佳反应行为，而未明确强制抵御突变入侵的稳定性。我们提出了在离散和连续博弈中计算SESS的算法，并对其进行了实证验证。我们的模型自然适用于生物学场景；例如，在癌症治疗中，领导者代表医生，而追随者对应相互竞争的癌细胞表型。