Abstract
In this paper, I examine dynamic evolutionary processes driven by perpetual random shocks on extensive form games with perfect information. Every period, n individuals are randomly chosen from n finite populations to play an extensive form game. Each individual observes a sample from the memory of past plays. Then she either plays a best reply to that sample or imitates by choosing the action with the highest or the highest average payoff in the sample on the reached nodes. Occasionally, individuals also experiment or make mistakes and choose a pure local strategy at random on the reached nodes. For finite n-player games, I prove that in the limit, as the probability of experimentation tends to zero, the backward induction outcomes occur with positive probability in the best reply and the imitation cases. Moreover, for a special class of games, the backward induction outcome is the unique prediction.