Self-Organizing Multi-Agent Systems (SO-MAS)

Updated 7 December 2025

Self-Organizing Multi-Agent Systems are distributed frameworks where global order emerges from simple, localized interactions without centralized control.
They employ formal frameworks such as logic-based, graph-theoretic models and modular learning to enable dynamic coordination and self-deployment.
Applications span adaptive communication networks, LLM-based collaborative reasoning, and real-world control systems, demonstrating scalable and robust performance.

Self-Organizing Multi-Agent Systems (SO-MAS) comprise a class of distributed systems in which multiple autonomous agents achieve global coordination, organization, or problem-solving capacity without centralized control or prespecified organizational schema. In SO-MAS, global order emerges through repeated local interactions according to simple agent-specific or environment-driven rules, resulting in scalable, robust, and adaptable macroscopic behaviors (Abbas et al., 2015). This paradigm contrasts fundamentally with traditional organization-centered MAS that impose explicit, top-down role structures, coordination protocols, or supervisory controls (Luo et al., 2021, Li et al., 5 Feb 2025). SO-MAS theory and practice encompass formal frameworks for agent independence and contribution, dynamic graph-based coordination, compositional and modular learning, runtime agent self-adaptation, decentralized meta-design, and real-world applications spanning LLM-based collaboration, critical infrastructure control, and adaptive network management.

1. Formal Definitions and Theoretical Foundations

The core defining characteristic of SO-MAS is endogenous, bottom-up reorganization: agents modify only their local interactions or state based on local rules or feedback, and are generally unaware of any global plan or organizational structure (Abbas et al., 2015). A SO-MAS is formally described as a population of agents $\Sigma = \{a_1,\dots,a_k\}$ interacting in a deterministic or stochastic environment, where global patterns arise from the system $\mathcal{S} = (\Sigma, Q, \pi, A, D, \delta, \Gamma)$ , with:

$Q$ the (possibly infinite) state-space;
$\pi: Q \rightarrow 2^\Pi$ labels each state with atomic properties;
$A$ the shared action space or set of possible actions;
$D(q)$ the joint move set at each state;
$\delta: Q \times D(q) \rightarrow Q$ the (possibly stochastic) transition rule;
$\Gamma$ the collection of agent-specific local rules, $\Gamma = \{(\tau_a, \gamma_a) | a \in \Sigma\}$ , specifying who each agent "listens to" in $q$ and how it computes its next move from local messages.

In this framework, the system evolves only through agent-based, local decision mechanisms, and coalitional or system-level properties are reasoned about through explicit logic (not agent-internal representation) (Luo et al., 2021). Global behavior, such as the satisfaction of complex temporal logic properties, is emergent and not directly encoded as agent objectives.

SO-MAS are distinguished from organization-centered MAS (OCMAS) by the absence of an explicit organizational model, global roles or groups, or central scheduling. Agents possess local policies $\pi_i$ , states, and often local learning algorithms $\mathcal{L}_i$ , but no awareness of, or reasoning over, a system-wide structure (Li et al., 5 Feb 2025, Abbas et al., 2015).

2. Methodological Frameworks and Formal Models

2.1 Logic and Graph-Based Reasoning on Independence

Recent advances establish logic-based frameworks for reasoning about the independence and full contribution of agent coalitions in SO-MAS (Luo et al., 2021). In these formalisms, queries such as "Which minimal coalition of agents is both structurally and semantically independent in achieving a global specification $\psi$ ?" are represented in a temporal logic similar to ATL but constrained by agent-specific local rules:

Structural independence: defined graph-theoretically on the dependence graph $G_{out}$ , where for a coalition $A$ to be independent, no edge enters $A$ from $\Sigma\setminus A$ across all possible compatible runs.
Semantic independence: encoded by temporal operators $\langle A\rangle\psi$ , signifying $A$ can guarantee $\psi$ by only following $\Gamma_A$ .
Full contribution: the smallest coalition that is both structurally and semantically independent for $\psi$ .

The complexity of verifying full contribution is shown to be EXPTIME-complete in $|\Sigma|$ , but tractable in system state and formula size. Layered decomposition of the dependence graph into $L_0, L_1, \dots, L_h$ layers with no intra-layer dependencies permits efficient enumeration of independent coalitions per layer, dropping the search space from $2^k$ to $\sum_i 2^{w_i}$ , with $w_i$ the maximal layer width (Luo et al., 2021).

2.2 Self-Deployment and Goal Dependency Structures

The SO-MAS framework generalizes to a unifying, data-driven agent-based structure comprising:

Goals Dependency Network (GDN): a directed acyclic graph capturing goal/subgoal or resource/task dependencies among all agents.
Rational Activity Algorithm (RAA): a canonical agent decision process, parameterized by utility/urgency and available producers or trading partners, recursively scheduling activities to self-satisfy or negotiate for goals.
Activity Deployment Simulator (ADS): a simulation engine assembling agents and producers directly from the GDN and RAA (Jaraiz, 2020).

This architecture enables not only spontaneous organization but also "self-deployment" of new producers/tasks as dictated by current resource flow, need, or market signals. It encompasses both goal-driven (e.g., economic) and non-goal-driven (e.g., gradient-following, swarm) systems.

2.3 Modular Learning and Multi-Tier Decomposition

Compositional and modular approaches in SO-MAS structure agent populations into layered controllers—e.g., cell-level and cell-pair-level agents—each trained by compositional deep RL (CDRL) or predictive decision-making (CPDM) to manage parameter interdependencies and multi-objective tradeoffs (Liao et al., 3 Jun 2025). Critics and actors are decomposed into submodules aligned with performance metrics (throughput, latency, anomaly rates), with joint reward decomposition and alternating training for multi-level agents.

Empirically, this compositionality delivers superior scaling, convergence, and safety, outperforming monolithic multi-agent RL in large, self-organizing communication networks.

3. Self-Organization Mechanisms: Decentralization, Coordination, and Adaptation

3.1 Decentralized Coordination and Local Rule Design

In SO-MAS, all coordination emerges from localized agent rules, message passing, and environmental cues. Profiles such as those in MorphAgent evolve dynamically through role clarity, role differentiation, and task-role alignment scores, driving decentralized negotiation of specializations via LLM-based or algorithmic text rewriting, without a central authority (Lu et al., 19 Oct 2024).

Attention-inspired dynamic graph routing, as operationalized in frameworks like Orchestrator, leverages per-agent information gain (variational free energy) and cost to adaptively re-weight edges in the inter-agent graph at runtime, emulating emergent attention or value propagation (Beckenbauer et al., 6 Sep 2025). In stochastic settings, frameworks such as SelfOrg iteratively build DAGs of communication based on approximate Shapley value contributions (via response embedding cosine similarity), directing information flow from correct agents to suppress noise and amplify consensus (Tastan et al., 1 Oct 2025). These approaches are scalable, robust under partial observability, and empirically outperform fixed-topology or centrally planned MAS.

3.2 Coalitional Dynamics, Norms, and Evolving Objectives

SO-MAS admit dynamic adaptation of objectives, relationship graphs, and coalition structures via ongoing social and environmental feedback (Li et al., 5 Feb 2025). Each agent may revise its objective $J_i$ based on learned impact, peer expectations, or environmental signals, with protocols and norms (e.g., resource-sharing penalties) evolving continuously according to norm-agent dynamical couplings:

$J_i(t+1) = f\left(J_i(t), s(t), S_i(t)\right)$

$\frac{d\mathcal{P}}{dt} = -\gamma(\mathcal{P} - \mathcal{P}^*)$

Coalitions $C$ form organically as relationship strengths $w_{ij}$ (updated per event) reach critical thresholds, and agents may engage in Nash-style bargaining within coalition structures (Li et al., 5 Feb 2025). This provides formal and algorithmic bases for the organic emergence of both cooperation and negotiation in critical domains such as traffic optimization and distributed energy grids.

3.3 Runtime Composition, Meta-Level Adaptation, and Robustness

Recent SO-MAS architectures (e.g., MAS-ZERO, BiRouter, MAS $^2$ ) add explicit meta-level agents or next-hop routing modules that execute closed-loop processes of system composition, evaluation, and rectification at inference time:

Meta-design loop: Iteratively generates, evaluates, and refines agent teams based on meta-feedback metrics (solvability, completeness) tailored to the current query (Ke et al., 21 May 2025).
BiRouter: Distributed next-hop routing using hybrid criteria (ImpScore for long-term importance; GapScore for local continuity) and dynamic, reputation-based credit updates, supporting robust, token-efficient task routing even in unreliable or adversarial agent pools (Yang et al., 30 Nov 2025).
MAS²: Ensemble of generator, implementer, and rectifier meta-agents, recursively instantiating and repairing MAS templates in response to task feedback, with rigorous collaborative tree optimization for meta-agent specialization (Wang et al., 29 Sep 2025).

These designs eliminate static, hand-coded organizational bottlenecks and admit dynamic reorganization, specialization, and self-correction during operation.

4. Emergent Structure, Hierarchies, and Organizational Metrics

Self-organization in MAS can result in dynamic, context-dependent emergence of dependency hierarchies, coalitions, or modular subpopulations, even when no such structure is imposed. Dependency hierarchies can be quantified via gradients of agent actions with respect to teammates' states:

$D_{ij}(t) = \left\| \frac{\partial a_i(t)}{\partial s_j(t)} \right\|, \qquad D_i(t) = \sum_{j\neq i} (|D_{ji}(t)| - |D_{ij}(t)|)$

Dynamic leadership, role alternation, or persistent dominance (determined by initialization "Talent" or episodic "Effort") naturally arise and adapt to environmental changes, enabling robust collective task achievement (Chen et al., 13 Aug 2025). Analysis of such emergent structures guides both theoretical paper and engineering of scalable, resilient SO-MAS.

Universal, scale-invariant metrics—emergence $E(X)$ (Shannon entropy), self-organization $S(X)$ , complexity $C(X) = 4ES$ , homeostasis $H$ , autopoiesis $A$ (relative complexity to environment)—support quantitative assessment and phase identification in simulated and real-world SO-MAS (Fernandez, 2015).

5. Applications and Benchmarking

SO-MAS exhibit high utility in domains where decentralization, scalability, and adaptability are required. Notable deployments include:

Large-scale pursuit and search: Distributed algorithms using fuzzy clustering, cooperative coevolution, and actor-critic RL achieve near-perfect performance with thousands of agents under occlusion and partial observability, matching or surpassing monolithic and flat RL baselines (Sun et al., 2022).
Adaptive communication and infrastructure control: Two-tier modular SO-MAS with compositional RL optimize handover success, throughput, latency, and anomaly avoidance in urban wireless networks, universally outperforming monolithic baselines (Liao et al., 3 Jun 2025).
LLM-based collaborative reasoning, code synthesis, and QA: Self-organizing frameworks (BiRouter, MAS-ZERO, MAS $^2$ , MorphAgent, Orchestrator) achieve superior accuracy and resource utilization, are robust to unreliable nodes, and generalize across backbones and problem classes (Yang et al., 30 Nov 2025, Ke et al., 21 May 2025, Wang et al., 29 Sep 2025, Lu et al., 19 Oct 2024, Beckenbauer et al., 6 Sep 2025).
Forecasting in large self-organizing agent systems: Deep learning architectures leverage the locality of agent interactions to efficiently predict future local states without full system reconstruction, dramatically reducing computational cost (Kang et al., 2022).

Experimental results consistently show improvements of 4–20 percentage points in accuracy or other domain metrics relative to state-of-the-art, as well as enhancements in token usage, convergence time, and fault tolerance.

6. Limitations, Open Problems, and Future Directions

Current SO-MAS paradigms face several open technical and theoretical challenges:

Autonomy vs. control trade-offs: Fully emergent structures may underperform for tightly coordinated global objectives; balancing self-organization with soft constraints or incentives is an open research area (Abbas et al., 2015).
Verification and validation: Lack of explicit global models hampers formal assurance; EXPTIME-complete verification algorithms exist only for certain logical frameworks (Luo et al., 2021).
Unpredictability and safety: Open-ended adaptation may yield undesired macro-patterns (resource monopolies, oscillations, collusion), and theoretical tools for monitoring and correcting such behaviors are underdeveloped (Li et al., 5 Feb 2025).
Compositional and meta-learning: While compositional critics and meta-level design yield improved scaling and adaptability, their convergence properties and robustness to adversarial environments warrant further research (Liao et al., 3 Jun 2025, Ke et al., 21 May 2025).
Communication cost and time-to-convergence: Local peer-to-peer or broadcast communication can become costly in large teams; methods such as selective neighbor gossip or hierarchical structuring represent potential improvements (Lu et al., 19 Oct 2024).
Human-agent collaboration: Extending SO-MAS theory to human-in-the-loop settings, with mixed-initiative protocol co-development and auditability, is an essential area for safe and responsible deployment in societal applications (Li et al., 5 Feb 2025).

Research continues to seek general meta-models unifying static, dynamic, emergent, and designed organization; improved runtime composition and rectification policies; and scalable, safety-assured middleware for real-world, critical deployments (Abbas et al., 2015, Wang et al., 29 Sep 2025, Yang et al., 30 Nov 2025).

7. References: Selected Frameworks and Empirical Results

Framework	Key Features	Reference
Logic-based SOMAS	Full-contribution, layered decomposition	(Luo et al., 2021)
SO-MAS (ADS+RAA+GDN)	Self-deployment, goal dependency	(Jaraiz, 2020)
BiRouter	Decentralized, ImpScore+GapScore, reputation	(Yang et al., 30 Nov 2025)
MAS-ZERO/SELF-MAS	Meta-level design, meta-reward feedback	(Ke et al., 21 May 2025)
MorphAgent	Self-evolving role profiles, P2P adaptation	(Lu et al., 19 Oct 2024)
Modular SO-MAS (CPDM/CDRL)	Two-tier RL, compositional critics	(Liao et al., 3 Jun 2025)
SelfOrg	Dynamic DAG via Shapley approximation	(Tastan et al., 1 Oct 2025)
Orchestrator	Active inference, attention routing	(Beckenbauer et al., 6 Sep 2025)
MAS $^2$	Generator-Implementer-Rectifier self-evolution	(Wang et al., 29 Sep 2025)
DECOMAS	Minimal-invasive coordination modules	(Sudeikat et al., 2010)

These frameworks collectively define the frontiers of SO-MAS research, offering a spectrum of tools and methodologies for the analysis, implementation, and verification of decentralized, self-organizing agent systems in diverse domains.