Dynamic stability in symmetric extensive form games

Dynamic stability under the replicator dynamic of evolutionary game theory is investigated for certain symmetric extensive form games whose subgame structure exhibits a high degree of decomposability. It is shown that a pervasive equilibrium strategy is locally asymptotically stable (l.a.s.) if and only if it is given by backwards induction applied to the l.a.s. pervasive equilibria of the subgames and their corresponding truncations. That is, this dynamic backwards induction procedure provides a rational basis on which to predict the evolutionary outcome of the replicator dynamic for these symmetric games.