  We study the problem of computing an Extensive-Form Perfect Equilibrium
(EFPE) in 2-player games. This equilibrium concept refines the Nash equilibrium
requiring resilience w.r.t. a specific vanishing perturbation (representing
mistakes of the players at each decision node). The scientific challenge is
intrinsic to the EFPE definition: it requires a perturbation over the agent
form, but the agent form is computationally inefficient, due to the presence of
highly nonlinear constraints. We show that the sequence form can be exploited
in a non-trivial way and that, for general-sum games, finding an EFPE is
equivalent to solving a suitably perturbed linear complementarity problem. We
prove that Lemke's algorithm can be applied, showing that computing an EFPE is
$\textsf{PPAD}$-complete. In the notable case of zero-sum games, the problem is
in $\textsf{FP}$ and can be solved by linear programming. Our algorithms also
allow one to find a Nash equilibrium when players cannot perfectly control
their moves, being subject to a given execution uncertainty, as is the case in
most realistic physical settings.
