Interactive epistemology in simple dynamic games with a continuum of strategies

We extend the epistemic analysis of dynamic games of Battigalli and Siniscalchi (1999, 2002, 2007) from finite dynamic games to all simple games, that is, finite and infinite-horizon multistage games with finite action sets at non-terminal stages and compact action sets at terminal stages. We prove a generalization of Lubin's (1974) extension result to deal with conditional probability systems and strong belief. With this, we can provide a short proof of the following result: in every simple dynamic game, strong rationalizability characterizes the behavioral implications of rationality and common strong belief in rationality.