In this paper, diagrammatic systems for logical concept modelling are investigated. These systems include Charles S. Peirce's existential graphs, conceptual graphs, extensive semantic games, and discourse representation theory (DRT). It is argued that the fundamental difference between these systems is that unlike in the other graphical methods of logic, in the theory of extensive semantic games one is able to model concepts that call for some strategic, i.e. game-theoretic deliberations. They are needed among other things in properly understanding the linguistic concept of anaphora and its interplay with negation. Furthermore, it is shown how Peirce's existential graphs transform into extensive semantic games. This has important consequences to the game-theoretic visualisation of logic and semantics and enables one to represent uncertainty in existential graphs.