Subgame-perfection in free transition games

We prove the existence of a subgame-perfect ε-equilibrium, for every ε > 0, in a class of multi-player games with perfect information, which we call free transition games. The novelty is that a non-trivial class of perfect information games is solved for subgame-perfection, with multiple non-terminating actions, in which the payoff structure is generally not (upper or lower) semi-continuous. Due to the lack of semi-continuity, there is no general rule of comparison between the payoffs that a player can obtain by deviating a large but finite number of times or, respectively, infinitely many times. We introduce new techniques to overcome this difficulty.