Does Backwards Induction Imply Subgame Perfection?

In finite games subgame perfect equilibria are precisely those that are obtained by a backwards induction procedure. In large extensive form games with perfect information this equivalence does not hold: Strategy combinations fulfilling the backwards induction criterion may not be subgame perfect in general. The full equivalence is restored only under additional (topological) assumptions. This equivalence is in the form of a one-shot deviation principle for large games, which requires lower semi-continuous preferences. As corollaries we obtain one-shot deviation principles for particular classes of games, when each player moves only finitely often or when preferences are representable by payoff functions that are continuous at infinity.