We consider a dynamical approach to sequential games. The lazy improvement dynamics are given through a very simple individual updating rule, and, for finite games, are guaranteed to converge to a Nash equilibrium (provided that the preferences are acyclic). Moreover, even if some players have cyclic preferences, the remaining ones will still finite time. Thus, lazy improvement even induces a notion of rational play in the presence of irrational actors. For infinite sequential games we can retain convergence to a Nash equilibrium (in some sense), if the preferences are given by continuous payoff functions; or obtain a trans finite convergence if the outcome sets of the game are Delta^_02-sets. Joint work with Arno Pauly.