Subgame-Perfect ϵ-Equilibria in Perfect Information Games with Common Preferences at the Limit

We prove the existence of a pure subgame-perfect epsilon-equilibrium, for every epsilon > 0, in multiplayer perfect information games, provided that the payoff functions are bounded and exhibit common preferences at the limit. If, in addition, the payoff functions have finite range, then there exists a pure subgame-perfect 0-equilibrium. These results extend and unify recent existence theorems for bounded and semicontinuous payoffs.