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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.18112 |
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| _version_ | 1866909972184432640 |
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| author | Pan, Yunian Zhu, Quanyan |
| author_facet | Pan, Yunian Zhu, Quanyan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian Holonic Systems: Equilibrium, Uniqueness, and Computation Pan, Yunian Zhu, Quanyan Systems and Control 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. |
| title | Bayesian Holonic Systems: Equilibrium, Uniqueness, and Computation |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2512.18112 |