Basic neighbourhood logic is the modal logic in neighbourhood semantics where the neighbourhood functions are not necessarily upward-closed, therefore the modal operator is not necessarily monotonic. In this paper, we study a model comparison game for basic neighbourhood logic, in which there are two players, one of which claims that two pointed models are similar, and the other claims the opposite. The winning strategy of the first player is used to characterize the similarity between two pointed models. We give a definition of n-bisimulation, which characterizes n-modal equivalence and provides the ingredient for the model comparison game for basic neighbourhood logic.