Game Logic, coalgebraic completeness and automata Game Logic (Parikh, 1985) is a multi-modal, monotonic modal logic for reasoning about strategic ability in 2-player determined games. Game Logic can be seen as a monotonic generalisation of Propositional Dynamic Logic (PDL) in which games are interpreted as monotonic neighbourhood functions, and game operations include all the PDL program operations together with the operation dual (which denotes role swap of the two players). We have recently shown that both Game Logic and PDL can be seen as instances of a coalgebraic framework of dynamic logics in which the completeness of PDL and dual-free Game Logic can be proved uniformly (cf. Hansen, Kupke). Completeness of full Game Logic, however, remains an open challenge, nevermind completeness for the coalgebraic generalisations. Recent results in the theory of coalgebraic fixpoint logics (cf. Enqvist, Venema, Seifan) have made crucial use of automata in proving completeness and other results. An automata-theoretic characterisation of Game Logic is therefore of interest. In this talk, I will first introduce Game Logic, and show that it is an instance of a coalgebraic dynamic logic. Then I will state the (restricted) coalgebraic completeness theorem, and discuss the difficulty with completeness of full Game Logic. Finally, I will present a class of modal automata that characterise Game Logic as a fragment of the monotonic modal mu-calculus, and discuss future steps towards completeness. This is joint work with Clemens Kupke, Johannes Marti and Yde Venema.