Subgame perfect equilibrium in continuous games of perfect information: An elementary approach to existence and approximation by discrete games
Abstract This paper relates infinite-action (continuous) games of perfect information to finite-action approximations of such games and thereby obtains a new existence proof for subgame-perfect equilibrium (SPE) in the infinite-action case. Accumulation points of SPE paths of approximating finite-action games are shown to be SPE paths of the limiting infinite-action game. However, no such upper hemi-continuity property holds for SPE strategies. The discontinuity in strategies corresponds to a need for forward induction in the SPE construction for the infinite-action game, thus conflicting with the Harsanyi-Selten principle of subgame-consistency.