We construct a game-theoretic account of AI-mediated cognitive decoupling in the production and consumption of knowledge content.Extending Spence's costly signalling framework to environments where production costs collapse asymmetrically, we prove that AI-mediated decoupling is a \emph{strictly dominant strategy}under a broad class of utility functions (\emph{Dominant Decoupling Theorem}).This dominance holds not because agents are deceived, but because the observable signal --- a lengthy, well-structured document ---is \emph{decoupled} from its previously costly production process,rendering the signal cheap for all types. We then model the resulting market for cognitive depth as a dynamic signalling game.We show that as AI adoption increases, the market passes through three distinct regimes: a \emph{separating equilibrium} (high-depth agents are distinguishable), a \emph{pooling equilibrium} (all agents produce identical signals), and finally a \emph{Lemons collapse} in which no credible signal remains and the market for deep content unravels (\emph{Signalling Inflation Theorem}).We characterise the speed of this collapse as a function of AI adoption rate and derive the critical adoption threshold $q^*$ beyond which the separating equilibrium is irreversibly destroyed. Finally, we identify two equilibrium escape routes:(i) \emph{certified costliness} --- institutional mechanisms that artificially re-introduce production cost (peer review, Turing-style verification) --- and (ii) \emph{market stratification} --- the emergence of a high-trust, low-volume premium market for ``AI-free'' content.We characterise conditions under which each escape route is stable, and show that without external intervention, the system converges to a pooling equilibrium with socially sub-optimal information production.