The resource-based view of strategy (RBV) seeks to explain why some firms consistently outperform rivals in the same industry by acquiring a unique set of strategic assets (or resources). We suggest firms achieve competitive advantage through ‘cognitive asymmetries’ (differences between dominant managerial mental models) that lead rival management teams to implement distinct resource building strategies. This managerial and cognitive view of competition and rivalry lends itself to investigation through problem structuring methods. We suggest that resource maps, as a problem structuring method, can be used to interpret managerial mental models for strategic decision-making in terms of resource building processes. Through resource maps, we represent the system of asset stocks believed to be most important for driving business performance. We illustrate the framework by comparing and contrasting maps of the system of resources (asset stocks) that best characterise the four leading firms in the UK Commercial Radio Broadcasting Industry.