On finding curb sets in extensive games

We characterize strategy sets that are closed under rational behavior (curb) in extensive games of perfect information and finite horizon. It is shown that any such game possesses only one minimal curb set, which necessarily includes all its subgame perfect Nash equilibria. Applications of this result are twofold. First, it lessens computational burden while computing minimal curb sets. Second, it implies that the profile of subgame perfect equilibrium strategies is always stochastically stable in a certain class of games.