Role Differentiation in a Coupled Resource Ecology under Multi-Level Selection

Self-optimizing behaviors can lead to outcomes where collective benefits are ultimately destroyed, a well-known phenomenon known as the ``tragedy of the commons". These scenarios are widely studied using game-theoretic approaches to analyze strategic agent decision-making. In this paper, we examine this phenomenon in a bi-level decision-making hierarchy, where low-level agents belong to multiple distinct populations, and high-level agents make decisions that impact the choices of the local populations they represent. We study strategic interactions in a context where the populations benefit from a common environmental resource that degrades with higher extractive efforts made by high-level agents. We characterize a unique symmetric Nash equilibrium in the high-level game, and investigate its consequences on the common resource. While the equilibrium resource level degrades as the number of populations grows large, there are instances where it does not become depleted. We identify such regions, as well as the regions where the resource does deplete.

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.

Language-model agents are increasingly deployed to act on behalf of people in settings where individual decisions shape shared outcomes. We examine whether five production models adapt their contributions to changing risks and partner behaviour, or instead follow a relatively fixed strategy. In a collective-risk dilemma game (CRG), six players contribute to a shared pool over ten rounds; if the pool falls short of its target, a catastrophe may destroy their remaining resources. Four models contributed approximately an equal share at every positive risk level, and four of the five also contributed when risk was zero, even though contributing could not improve their payoff. Explicitly stating that only the agent's own payoff mattered reduced zero-risk contributions for most models, while a more neutral prompt did not. Several models correctly identified which action offered the higher expected payoff at different risk levels, yet their contributions changed little. Against fixed partners, no model consistently chose the payoff-maximising response, and in mixed-model groups, a single agent's shortfall in the final round could cause an otherwise successful group to fail. Payoff-based selection also depended on population composition: in a single six-agent group, it favoured the model that contributed least and reduced group success, whereas in larger, randomly mixed populations, it favoured an exact fair-share model at moderate and high risk. These findings show that cooperative self-play alone is not evidence of strategic adaptability. Consistent with a machine-behaviour approach, evaluations of agents in multi-agent systems should test how they respond to incentives, partner actions, and population composition.