Backward Induction and Subgame Perfection . The justi fi cation of a “ folk algorithm . ”

I introduce axiomatically infinite sequential games that extend von Neumann and Kuhn’s classic axiomatic frameworks. Within this setup, I define a modified backward induction procedure that is applicable to all games. A strategy profile that survives backward pruning is called a backward induction equilibrium (BIE). The main result compares the sets of BIE and subgame perfect equilibria (SPE). Remarkably, and similarly to finite games of perfect information, BIE and SPE coincide both for pure strategies and for a large class of behavioral strategies. This result justifies the “folk algorithm” of finding SPEs in games with backward induction.