 Just as with Backward Induction, there are connections between iterated announcements and fixed-point logics. The set of strategy profiles that survive iterated announcements of strong rationality can be defined in modal μ-calculi (Kozen 1983; Venema 2008). If announcements are generalized to arbitrary formulas, so-called deflationary fixed-point logics are needed for studying limit behavior (Ebbinghaus &amp; Flum 1995; Dawar, Grädel, &amp; Kreutzer 2004).