  We consider a dynamical approach to game in extensive forms. By restricting
the convertibility relation over strategy profiles, we obtain a semi-potential
(in the sense of Kukushkin), and we show that in finite games the corresponding
restriction of better-response dynamics will converge to a Nash equilibrium in
quadratic (finite) time. Convergence happens on a per-player basis, and even in
the presence of players with cyclic preferences, the players with acyclic
preferences will stabilize. Thus, we obtain a candidate notion for rationality
in the presence of irrational agents. Moreover, the restriction of
convertibility can be justified by a conservative updating of beliefs about the
other players strategies.
  For infinite games in extensive form we can retain convergence to a Nash
equilibrium (in some sense), if the preferences are given by continuous payoff
functions; or obtain a transfinite convergence if the outcome sets of the game
are $\Delta^0_2$-sets.
