Interactive Epistemology in Games with Payoff Uncertainty

We adopt an interactive epistemology perspective to analyze dynamic games with partially unknown payoff functions. We consider solution procedures that iteratively delete strategies conditional on private information about the state of nature. In particular we focus on a weak and a strong version of the Δ-rationalizability solution concept, where Δ represents given restrictions on players' beliefs about state of nature and strategies (Battigalli, 2003, Battigalli and Siniscalchi, 2003). We first show that weak Δ-rationalizability is characterized by initial common certainty of rationality and of the restrictions Δ, whereas strong Δ-rationalizability is characterized by common strong belief in rationality and the restrictions Δ (cf. Battigalli and Siniscalchi, 2002). The latter result allows us to obtain an epistemic characterization of the iterated intuitive criterion. Then we use the framework to analyze the robustness of complete-information rationalizability solution concepts to the introduction of "slight" uncertainty about payoffs. If the set of conceivable payoff functions is sufficiently large, the set of strongly rationalizable strategies with slight payoff uncertainty coincides with the set of complete-information, weakly rationalizable strategies.