  We show that the model-checking problem is decidable for a fragment of the
epistemic \mu-calculus. The fragment allows free variables within the scope of
epistemic modalities in a restricted form that avoids constructing formulas
embodying any form of common knowledge. Our calculus subsumes known decidable
fragments of epistemic CTL/LTL. Its modal variant can express winning
strategies in two-player games with one player having imperfect information and
non-observable objectives, and, with a suitable encoding, decidable instances
of the model-checking problem for ATL with imperfect information and perfect
recall can be encoded as instances of the model-checking problem for this
epistemic \mu-calculus.
