On the outcome equivalence of backward induction and extensive form rationalizability

Pearce’s (Econometrica 52:1029-1050, 1984) extensive-form rationalizablity (EFR) is a solution concept embodying a best-rationalization principle (Battigalli, Games Econ Behav 13:178-200, 1996; Battigalli and Siniscalchi, J Econ Theory 106:356-391, 2002) for forward-induction reasoning. EFR strategies may hence be distinct from backward-induction (BI) strategies. We provide a direct and transparent proof that, in perfect-information games with no relevant ties, the unique BI outcome is nevertheless identical to the unique EFR outcome, even when the EFR strategy profile and the BI strategy profile are distinct.