We introduce a novel model construction, cascaded games, that is intended to allow us to study the notion of steady states algebraically and structurally. The model construction is inspired by the chemical underpinning and the prevailing conceptualisation of mitogenactivated protein kinase (MAPK) cascades. To analyse the models, we use the recent notion of change-of-mind equilibria. We exemplify our proposal with gene regulation and MAPK cascades, capturing basic as well as advanced issues such as prophage induction and tauopathy causation.