Pure or Unstable: A Generic Dichotomy for Strong Stackelberg Commitments (opens in new tab)

We study the robustness of the Strong Stackelberg Equilibrium (SSE) in finite leader--follower games when the follower's best-response correspondence is set-valued. While optimistic tie-breaking (in the leader's favor) is commonly adopted, it can hinge on knife-edge indifferences. We formalize a stability notion: an SSE is unstable if, at the leader's committed strategy, the follower has an alternative best response that strictly reduces the lea...