Informational active matter shows how measurement‑driven decisions generate collective order, yet most studies focus on systems that reach consensus. We instead design a collective information engine structured by role differentiation and instantiate it with anti‑coordination games where differentiated role information carries intrinsic value.\ \ Within many coexisting games, agents infer their role from a noisy social signal anchored in a persistent identity. Role‑following actions feed back into that signal, shaping the incentive to adhere to roles.\ \ Resources accrued through coordinated role‑play combine with identity variability to reinforce the schemas that generated them, operationalizing Sewell’s duality of schemas and resources in structuration theory.\ \ We define the social‑loop gain as\ $$G = \rho \cdot C \cdot \phi \cdot S$$\ where $\rho$ denotes identity persistence, $C$ cognitive capacity, $\phi$ channel fidelity, and $S$ schema strength. The engine ignites once $G>1$.\ \ For a repertoire of such schemas, roles emerge via a bifurcation cascade whose functional form is fixed by the repertoire’s eigenvalue spectrum, ranging from monitorable logarithmic sequences to sudden avalanches.\ \ Resource accumulation supplies fitness for a replicator dynamics on schema strengths, endogenously selecting the cascade type. Subcritical identity covariance reveals the impending type before onset, enabling early detection, while feedback‑channel parameters bias which type is ultimately selected.\ \ Consequently, platform design becomes a control lever to throttle emergent coordination by tuning $\rho$, $C$, $\phi$, and $S$. This theory grounds distributional AGI takeoff in a concrete mechanism and offers a monitor‑based solution.\ \ By joining game theory, collective dynamics, and information engines, we open a route to an information thermodynamics of agent populations.\ \ Review: The role‑differentiation framework provides a tractable mathematical foundation for predicting and steering large‑scale intelligent agent systems, especially for early warning of abrupt coordination and for designing platform interventions.