Intrinsic motivations are receiving increasing attention, i.e. behavioral incentives that are not engineered, but emerge from the interaction of an agent with its surroundings. In this work we study the emergence of behaviors driven by one such incentive, empowerment, specifically in the context of more than one agent. We formulate a principled extension of empowerment to the multi-agent setting, and demonstrate its efficient calculation. We observe that this intrinsic motivation gives rise to characteristic modes of group-organization in two qualitatively distinct environments: a pair of agents coupled by a tendon, and a controllable Vicsek flock. This demonstrates the potential of intrinsic motivations such as empowerment to not just drive behavior for only individual agents but also higher levels of behavioral organization at scale.
A key challenge for the safety of advanced AI systems is the possibility that multiple simpler agents might inadvertently form a collective agent with capabilities and goals distinct from those of any individual. More generally, determining when a group of agents can be viewed as a unified collective agent is a foundational question in the study of interactions and incentives in both biological and artificial systems. We adopt a behavioral perspective in answering this question, ascribing collective agency to a group when viewing the group's joint actions as rational and goal-directed successfully predicts its behavior. We formalize this perspective on collective agency using causal games -- which are causal models of strategic, multi-agent interactions -- and causal abstraction -- which formalizes when a simple, high-level model faithfully captures a more complex, low-level model. We use this framework to solve a puzzle regarding multi-agent incentives in actor-critic models and to make quantitative assessments of the degree of collective agency exhibited by different voting mechanisms. Our framework aims to provide a foundation for theoretical and empirical work to understand, predict, and control emergent collective agents in multi-agent AI systems.
Frederik Hytting Jørgensen, Sebastian Weichwald, Lewis Hammond
Multi-agent simulations are widely used to study complex social and ecological systems, where rich and often unexpected emergent behaviors arise from local interactions. A large body of prior work has focused on analyzing such emergent dynamics across domains. In this paper, we move beyond analyzing emergent behavior and introduce a learning-based mechanism for actively shaping it via social reward modeling. We introduce Multi-Agent Reward Prediction (MARP), a simple framework that extends preference-based reward modeling to multi-agent reinforcement learning. While the framework is designed to be applicable across multi-agent settings, the present empirical validation is limited to a single environment, and we therefore present MARP as a proof of concept within the studied domain. Rather than relying on handcrafted rewards, MARP learns a shared reward model from episode-level evaluations of collective outcomes, enabling decentralized agents to align their behavior with global social objectives. We study MARP in the Harvest Game, a canonical sequential social dilemma modeling common-pool resource management and related real-world challenges. Our results show that MARP can be tuned to produce behavior that is more closely aligned with target social metrics than standard reward-based baselines, while the learned reward model captures subtle environmental structure without explicit programming. Crucially, MARP supports multiple and composite social objectives within a single training regime. By modifying only the high-level evaluation metric, the same framework seamlessly aligns agent behavior with diverse goals, including sustainability, equality, and peace, as well as combinations of individual and group-level objectives. These findings demonstrate that emergent multi-agent behavior can be treated not only as a phenomenon to study, but as a target of principled, data-driven regulation.
This paper develops a general framework for analyzing multi-agent systems with feedback loops between agents actions and collective observations. The framework is built on two fundamental agent-level variables: power, which measures agent influence on collective outcomes, and response functions, which determine how agents react to observations. We derive how macroscopic properties, including total power, useful power, entropy, order, fragility, and mobility, emerge from these two variables of heterogeneous agents. To study the trade off between growth and resilience, we introduce a system-level utility function parameterized by a risk-appetite coefficient and derive an optimal degree of order that balances productivity, stability, and adaptability. The analysis suggests that stronger synchronization can increase collective output but may also increase systemic fragility and reduce mobility. We further argue that order, entropy, information, and useful energy are task-dependent and system-relative concepts whose meanings depend on the objectives of the system. By measuring and designing agent power distributions and response functions, it may be possible to better understand, predict, and optimize collective behavior and identify the conditions under which collective intelligence and optimal order emerge.