On non-monotonic strategic reasoning
Strong-Δ-Rationalizability introduces first-order belief restrictions in the analysis of forward induction reasoning. Without actual restrictions, it coincides with Strong Rationalizability (Battigalli, 2003; Battigalli and Siniscalchi, 2003). These solution concepts are based on the notion of strong belief (Battigalli and Siniscalchi, 2002). The non-monotonicity of strong belief implies that the predictions of Strong-Δ-Rationalizability can be inconsistent with Strong Rationalizability. I show that Strong-Δ-Rationalizability refines Strong Rationalizability in terms of outcomes when the restrictions correspond to belief in a distribution over terminal nodes. Moreover, under such restrictions, the epistemic priority between rationality and belief restrictions is irrelevant for the predicted outcomes.