Abstract
<p>Informational active matter research has shown how measurement-informed decisions produce collective order, so far in systems that reach consensus. We identify a collective information engine that orders by differentiation instead, and construct a minimal instance using anti-coordination games, the simplest game class in which differentiated role information has value. Agents infer their role from a noisy social signal, and role-following action feeds back into that signal, shaping the incentive to follow roles. The schemas prescribing roles are themselves dynamic: resources accrued through coordinated role-play combine with population variability to shape and reinforce the schemas that generated them. The model thereby operationalizes Sewell's duality of schemas and resources, the influential but hitherto qualitative resolution of sociology's structure--agency debate. The engine ignites when a loop gain $\Lambda$---the product of identity persistence, cognitive capacity, and social feedback channel fidelity---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 deceptive spike-then-avalanche onsets. Resource accumulation turns schema competition into a replicator dynamics that, in mean field, selects the cascade type endogenously. Subcritical behavioral covariance reveals that type before onset, enabling early detection, and feedback channel parameters bias which type is selected. For agents interacting on a platform, adaptive platform design then becomes a control lever to throttle emergent coordination, e.g. for mitigating risks from distributional AI. Joining game theory, collective dynamics, and information engines, we open a route to an information thermodynamics of agent populations.</p>