For extensive form games with perfect information, consider a learning process in which, at any iteration, each player unilaterally deviates to a best response to his current conjectures of others’ strategies; and then updates his conjectures in accordance with the induced play of the game. We show that, for generic payoﬀs, the outcome of the game becomes stationary in ﬁnite time, and is consistent with Nash equilibrium. In general, if payoﬀs have ties or if players observe more of each others’ strategies than is revealed by plays of the game, the same result holds provided a rationality constraint is imposed on unilateral deviations: no player changes his moves in subgames that he deems unreachable, unless he stands to improve his payoﬀ there. Moreover, with this constraint, the sequence of strategies and conjectures also becomes stationary, and yields a self-conﬁrming equilibrium.
Dubey, Pradeep and Haimanko, Ori, "Unilateral Deviations with Perfect Information" (2000). Cowles Foundation Discussion Papers. 1533.