Evolutionarily Stable Stackelberg Equilibrium

TL;DR

This paper introduces the evolutionarily stable Stackelberg equilibrium (SESS), a new solution concept for leader-follower games that accounts for evolutionary stability of follower strategies, with algorithms for computation and biological applications.

Contribution

It defines SESS, a novel equilibrium concept combining Stackelberg and evolutionary stability, with algorithms for discrete and continuous games, validated empirically.

Findings

Algorithms successfully compute SESS in various game settings.

The model applies to biological scenarios like cancer treatment.

SESS accounts for mutation invasion stability in leader-follower dynamics.

Abstract

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.