Game theory is a formal approach to behavior that focuses on the strategic aspect of situations. The game theoretic approach originates in economics but has been embraced by scholars across disciplines, including many philosophers and biologists. This approach has an important weakness: the strategic aspect of a situation, which is its defining quality in game theory, is often not its most salient quality in human (or animal) cognition. Evidence from a wide range of experiments highlights this shortcoming. Previous theoretical and empirical work has sought to address this weakness by considering learning across an ensemble of multiple games simultaneously. Here we extend this framework, incorporating artificial neural networks, to allow for an investigation of the interaction between the perceptual and functional similarity of the games composing the larger ensemble. Using this framework, we conduct a theoretical investigation of a population that encounters both stag hunts and prisoner’s dilemmas, two situations that are strategically different but which may or may not be perceptually similar.