The analysis of the replicator dynamic in generic perfect information games yields the following results. In the long run, players play a Nash equilibrium provided that initially all strategies are present. There is at most one ``stable'' component (formally, an interior asymptotically stable set), play in this component will follow the backwards induction path. Existence of such a component is guaranteed in games with at most three consecutive decision nodes. An example of a ``longer'' game is provided where some trajectories starting close to the backwards induction component lead away and never come back.
The evolutionary basis for predicting the backwards induction solution in generic finite extensive-form games with perfect information is examined. Evolution is modelled using the replicator dynamic in combination with rare mutations that introduce a small change in the proportion of each strategy. The criterion for our judgement is whether this dynamic stabilizes over time at the subgame perfect equilibrium outcome. We find that the backwards induction solution is fully justified by this process only in simple games; simple meaning two players, two actions at each node and at most three consecutive decisions in the game. Examples of more complex games are given in which this process does not select between the subgame perfect equilibrium outcome and alternative Nash equilibrium outcomes.
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