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Reaching consensus and convergence to equilibrium are two major challenges of multi-agent systems. Although each has attracted significant attention, relatively few studies address both challenges at the same time. This paper examines the connection between the notions of consensus and equilibrium in a multi-agent system where multiple interacting sub-populations coexist. We argue that consensus can be seen as an intricate component of intra-population stability, whereas equilibrium can be seen as encoding inter-population stability. We show that smooth fictitious play, a well-known learning model in game theory, can achieve both consensus and convergence to equilibrium in diverse multi-agent settings. Moreover, we show that the consensus formation process plays a crucial role in the seminal thorny problem of equilibrium selection in multi-agent learning.

In the realm of multi-agent reinforcement learning (MARL), achieving high performance is crucial for a successful multi-agent system.Meanwhile, the ability to avoid unsafe actions is becoming an urgent and imperative problem to solve for real-life applications. Whereas, it is still challenging to develop a safety-aware method for multi-agent systems in MARL. In this work, we introduce a novel approach called Multi-Agent First Order Constrained Optimization in Policy Space (MAFOCOPS), which effectively addresses the dual objectives of attaining satisfactory performance and enforcing safety constraints. Using data generated from the current policy, MAFOCOPS first finds the optimal update policy by solving a constrained optimization problem in the nonparameterized policy space. Then, the update policy is projected back into the parametric policy space to achieve a feasible policy. Notably, our method is first-order in nature, ensuring the ease of implementation, and exhibits an approximate upper bound on the worst-case constraint violation. Empirical results show that our approach achieves remarkable performance while satisfying safe constraints on several safe MARL benchmarks.

Recent advancements in large language models, such as GPT-4, have demonstrated remarkable capabilities in processing standard queries. Despite these advancements, their performance substantially declines in advanced mathematical problems requiring complex, multi-step logical reasoning. To enhance their inferential capabilities, current research has delved into prompting engineering, exemplified by methodologies such as the Tree of Thought and Graph of Thought.Nonetheless, these existing approaches encounter two significant limitations. Firstly, their effectiveness in tackling complex mathematical problems is somewhat constrained. Secondly, the necessity to design distinct prompts for individual problems hampers their generalizability.In response to these limitations, this paper introduces the Multi-Agent System for conditional Mining (MACM) prompting method. It not only resolves intricate mathematical problems but also demonstrates strong generalization capabilities across various mathematical contexts.With the assistance of MACM, the accuracy of GPT-4 Turbo on the most challenging level five mathematical problems in the MATH dataset increase from $\mathbf{54.68\\%}

Fairness is essential for human society, contributing to stability and productivity. Similarly, fairness is also the key for many multi-agent systems. Taking fairness into multi-agent learning could help multi-agent systems become both efficient and stable. However, learning efficiency and fairness simultaneously is a complex, multi-objective, joint-policy optimization. To tackle these difficulties, we propose FEN, a novel hierarchical reinforcement learning model. We first decompose fairness for each agent and propose fair-efficient reward that each agent learns its own policy to optimize. To avoid multi-objective conflict, we design a hierarchy consisting of a controller and several sub-policies, where the controller maximizes the fair-efficient reward by switching among the sub-policies that provides diverse behaviors to interact with the environment. FEN can be trained in a fully decentralized way, making it easy to be deployed in real-world applications. Empirically, we show that FEN easily learns both fairness and efficiency and significantly outperforms baselines in a variety of multi-agent scenarios.

Large Language Model Multi-Agent Systems (LLM-MAS) have greatly progressed in solving complex tasks. It communicates among agents within the system to collaboratively solve tasks, under the premise of shared information. However, when agents' collaborations are leveraged to perform multi-person tasks, a new challenge arises due to information asymmetry, since each agent can only access the information of its human user.

We demonstrate how collective memory emerges in decentralized multi-agent systems through the interplay between individual agent memory and environmental trace communication. Our agents maintain internal memory states while depositing persistent environmental traces, creating a spatially distributed collective memory without centralized control. Comprehensive validation across five environmental conditions (20x20 to 50x50 grids, 5-20 agents, 50 runs per configuration) reveals a critical asymmetry: individual memory alone provides 68.7% performance improvement over no-memory baselines (1563.87 vs 927.23, p < 0.001), while environmental traces without memory fail completely. This demonstrates that memory functions independently but traces require cognitive infrastructure for interpretation. Systematic density-sweep experiments (rho in [0.049, 0.300], up to 625 agents) validate our theoretical phase transition prediction. On realistic large grids (30x30, 50x50), stigmergic coordination dominates above rho ~ 0.20, with traces outperforming memory by 36-41% on composite metrics despite lower food efficiency. The experimental crossover confirms the predicted critical density rho_c = 0.230 within 13% error.

Multi-agent systems play a central role in area coverage tasks across search-and-rescue, environmental monitoring, and precision agriculture. Achieving non-uniform coverage, where spatial priorities vary across the domain, requires coordinating agents while respecting dynamic and communication constraints. Density-driven approaches can distribute agents according to a prescribed reference density, but existing methods do not ensure connectivity. This limitation often leads to communication loss, reduced coordination, and degraded coverage performance. This letter introduces a connectivity-preserving extension of the Density-Driven Optimal Control (D2OC) framework. The coverage objective, defined using the Wasserstein distance between the agent distribution and the reference density, admits a convex quadratic program formulation. Communication constraints are incorporated through a smooth connectivity penalty, which maintains strict convexity, supports distributed implementation, and preserves inter-agent communication without imposing rigid formations. Simulation studies show that the proposed method consistently maintains connectivity, improves convergence speed, and enhances non-uniform coverage quality compared with density-driven schemes that do not incorporate explicit connectivity considerations.

Unlike most primary headaches, secondary headaches need specialized care and can have devastating consequences if not treated promptly. Clinical guidelines highlight several 'red flag' features, such as thunderclap onset, meningismus, papilledema, focal neurologic deficits, signs of temporal arteritis, systemic illness, and the 'worst headache of their life' presentation. Despite these guidelines, determining which patients require urgent evaluation remains challenging in primary care settings. Clinicians often work with limited time, incomplete information, and diverse symptom presentations, which can lead to under-recognition and inappropriate care. We present a large language model (LLM)-based multi-agent clinical decision support system built on an orchestrator-specialist architecture, designed to perform explicit and interpretable secondary headache diagnosis from free-text clinical vignettes. The multi-agent system decomposes diagnosis into seven domain-specialized agents, each producing a structured and evidence-grounded rationale, while a central orchestrator performs task decomposition and coordinates agent routing. We evaluated the multi-agent system using 90 expert-validated secondary headache cases and compared its performance with a single-LLM baseline across two prompting strategies: question-based prompting (QPrompt) and clinical practice guideline-based prompting (GPrompt). We tested five open-source LLMs (Qwen-30B, GPT-OSS-20B, Qwen-14B, Qwen-8B, and Llama-3.1-8B), and found that the orchestrated multi-agent system with GPrompt consistently achieved the highest F1 scores, with larger gains in smaller models. These findings demonstrate that structured multi-agent reasoning improves accuracy beyond prompt engineering alone and offers a transparent, clinically aligned approach for explainable decision support in secondary headache diagnosis.

The emerging "agentic web" envisions large populations of autonomous agents coordinating, transacting, and delegating across open networks. Yet many agent communication and commerce protocols treat agents as low-cost identities, despite the empirical reality that LLM agents remain unreliable, hallucinated, manipulable, and vulnerable to prompt-injection and tool-abuse. A natural response is "agents-at-stake": binding economically meaningful, slashable collateral to persistent identities and adjudicating misbehavior with verifiable evidence. However, heterogeneous tasks make universal verification brittle and centralization-prone, while traditional reputation struggles under rapid model drift and opaque internal states. We propose a protocol-native alternative: insured agents. Specialized insurer agents post stake on behalf of operational agents in exchange for premiums, and receive privileged, privacy-preserving audit access via TEEs to assess claims. A hierarchical insurer market calibrates stake through pricing, decentralizes verification via competitive underwriting, and yields incentive-compatible dispute resolution.