A topology for a class of multistage games is introduced. Some properties of this topology are studied. In particular it is shown that all multistage games can be approximated by finite multistage games. The main result then says that the correspondence mapping multistage games into their subgame-perfect equilibrium outcomes is upper hemicontinuous with respect to the introduced topology. It is also demonstrated that some recent results from the literature are special cases of the general upper hemicontinuity result. © 1990.
Börgers, T. (1991). Upper hemicontinuity of the correspondence of subgame-perfect equilibrium outcomes. Journal of Mathematical Economics, 20(1), 89–106. https://doi.org/10.1016/0304-4068(91)90019-P