Bayesian Holonic Systems: Equilibrium, Uniqueness, and Computation

TL;DR

This paper introduces the Bayesian Holonic Equilibrium (BHE) for modeling and controlling hierarchical multi-agent systems, establishing its theoretical properties and proposing a two-time scale learning algorithm validated through numerical experiments.

Contribution

It presents the novel BHE concept, proves its existence and uniqueness under certain conditions, and develops a scalable algorithm for computing it in complex holonic systems.

Findings

BHE ensures consistency between local and global system behavior.

The proposed algorithm converges to the BHE in numerical experiments.

The framework aids in designing strategic risk management in complex systems.

Abstract

This paper addresses the challenge of modeling and control in hierarchical, multi-agent systems, known as holonic systems, where local agent decisions are coupled with global systemic outcomes. We introduce the Bayesian Holonic Equilibrium (BHE), a concept that ensures consistency between agent-level rationality and system-wide emergent behavior. We establish the theoretical soundness of the BHE by showing its existence and, under stronger regularity conditions, its uniqueness. We propose a two-time scale learning algorithm to compute such an equilibrium. This algorithm mirrors the system's structure, with a fast timescale for intra-holon strategy coordination and a slow timescale for inter-holon belief adaptation about external risks. The convergence of the algorithm to the theoretical equilibrium is validated through a numerical experiment on a continuous public good game. This work provides a complete theoretical and algorithmic framework for the principled design and analysis of strategic risk in complex, coupled control systems.