🤖 AI Summary
This study investigates the trade-offs among collective output, stability, and adaptability in multi-agent systems to achieve optimal order. To this end, it proposes a unified analytical framework grounded in agent influence (power) and response functions, incorporating task dependency and system relativity into formal measures of order, entropy, and information. The framework reveals an intrinsic trade-off between synchrony and system fragility. By integrating multi-agent modeling, macroscopic variable derivation, and risk-preference parameterization, the work optimizes system utility, thereby enhancing the predictability and controllability of collective behavior. It further delineates the precise conditions under which collective intelligence emerges and optimal order is attained.
📝 Abstract
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.