Verification is an important technique to ensure quality of a system and detect scenarios in which requirements can be violated. For complex systems with multiple interacting components, one of the crucial requirements is a component's ability to achieve a given goal. However, verification of strategic abilities is computationally hard, and the existing model checking algorithms cope with it only partially. This applies especially to systems where components have limited knowledge of the global state of the world.In this project, we propose to advance verification of strategic interaction by focusing more on models, and less on algorithms. Our research hypothesis is that model checking algorithms are approaching the limits of their potential when applied to arbitrary abstract models. On the other hand, certain representations can be more succinct or provide better structural properties. For instance, Reaction Systems encourage the modeler to abstract away from features of individual components. Likewise, Modular Interpreted Systems support additional structural information about separation of interacting components.In order to systematically explore different representations, we identify 3 basic modeling levels for interaction and knowledge. The Agent Level focuses on actions, mental states, and social features of components. The Effectivity Level provides a uniform mathematical representation in terms of abstract effectivity. The population level focuses on interaction between large groups of similar components, and abstracts away from sporadic behaviors. We will begin by establishing mappings between models (and classes of models) from different levels. Based on these mappings, we will identify suitable model equivalences and abstractions that produce more succinct and/or structurally well-behaved models. Finally, we will investigate application of symbolic model checking algorithms to the resulting representations.