Interactive epistemology in games with payoff uncertainty

We adopt an interactive epistemology perspective to analyse 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, P., 2003. Rationalizability in infinite, dynamic games of incomplete information. Research in Economics 57, 1-38; Battigalli, P., Siniscalchi, M., 2003. Rationalization and incomplete information. Advances in Theoretical Economics 3 (Article 3). http://www.bepress.com/bejte/advances/vol3/iss1/art3]. We first show that weakΔ-rationalizability is characterized by initial common certainty of rationality and of the restrictions Δ, whereas strongΔ-rationalizability is characterized by common strong belief in rationality and the restrictions Δ (cf. [Battigalli, P., Siniscalchi, M., 2002. Strong belief and forward induction reasoning. Journal of Economic Theory 106, 356-391]). The latter result allows us to obtain an epistemic characterization of the iterated intuitive criterion. Then we use the framework to analyse 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.