Some new types of knowledge constructions in epistemic logic are defined, and semantics given by combining game-theoretic notions with modal models. One such notion introduced is focussed knowledge, which arises from imperfect information in quantified epistemic logics. This notion is useful in knowledge representation schemes in artificial intelligence and multi-agent systems with uncertainty. In general, in all the logics considered here, the imperfect information is seen to give rise to partiality, including partial common and partial distributed knowledge. A game-theoretic method of creating non-monotonicity will then be suggested, based on the partialised notion of ‘only knowing’ and inaccessible possible worlds. The overall purpose is to show the extent in which games combine with a given variety of knowledge constructions.