Evolutionarily Stable Stackelberg Equilibrium
This is an incremental theoretical extension for game theory and biological applications like cancer treatment.
The paper introduces evolutionarily stable Stackelberg equilibrium (SESS) to address Stackelberg evolutionary games, where a leader optimizes strategy while followers play evolutionarily stable strategies, and provides algorithms for computation with empirical validation.
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.