Earlier contributions have shown that imposing common knowledge of rationality is problematic when rationality is defined as choosing an admissible best response. Here we instead impose common knowledge of rational reasoning and define the concept of rationalizable sets. General existence (for any non-empty valued best response operator) is established, and a finite algorithm (eliminating strategy sets instead of strategies) is provided. Combined with the ordinary best response operator, Bernheim-Pearce rationalizability is fully characterized. Combined with the admissible best response operator, rationalizability is defined under the assumption of cautios and sequentially rational behavior, and a notion of forward induction is captured.