Role differentiation as ignition of a collective information engine: Structuration in Agent Populations

Informational active matter shows how measurement-informed decisions produce collective order, so far in systems that reach consensus. We design collective information engines structured by differentiation instead, and construct a minimal instance using anti-coordination games where differentiated role information has value. Within many coexisting games, agents infer their role from a noisy social signal grounded in a persistent identity, and role-following action feeds back into that signal, which shapes the incentive to follow roles. Resources accrued through coordinated role-play combine with identity variability to reinforce the schemas that generated them. The model thereby operationalizes Sewell's duality of schemas and resources in Structuration, a resolution to structure--agency debates across social science. The engine ignites when a social loop gain---the product of identity persistence, cognitive capacity, channel fidelity, and schema strength---exceeds one. For a repertoire of such schemas, roles emerge with increasing gain in a bifurcation cascade whose functional form is fixed by the repertoire's eigenvalue spectrum, ranging from monitorable logarithmic sequences to avalanches that arrive without warning. Resource accumulation supplies the fitness of a replicator dynamics on schema strengths, which selects the cascade type endogenously. Subcritical identity covariance reveals that type before onset, enabling early detection, while feedback channel parameters bias which type is selected. Platform design then becomes a control lever to throttle emergent coordination. This theory grounds distributional AGI takeoff in a mechanism and provides a monitor-based solution. Joining game theory, collective dynamics, and information engines, we open a route to an information thermodynamics of agent populations.