Fairness in multi-agent systems (MAS) focuses on equitable reward distribution among agents in scenarios involving sensitive attributes such as race, gender, or socioeconomic status. This paper introduces fairness in Proximal Policy Optimization (PPO) with a penalty term derived from a fairness definition such as demographic parity, counterfactual fairness, or conditional statistical parity. The proposed method, which we call Fair-PPO, balances reward maximisation with fairness by integrating two penalty components: a retrospective component that minimises disparities in past outcomes and a prospective component that ensures fairness in future decision-making. We evaluate our approach in two games: the Allelopathic Harvest, a cooperative and competitive MAS focused on resource collection, where some agents possess a sensitive attribute, and HospitalSim, a hospital simulation, in which agents coordinate the operations of hospital patients with different mobility and priority needs. Experiments show that Fair-PPO achieves fairer policies than PPO across the fairness metrics and, through the retrospective and prospective penalty components, reveals a wide spectrum of strategies to improve fairness; at the same time, its performance pairs with that of state-of-the-art fair reinforcement-learning algorithms. Fairness comes at the cost of reduced efficiency, but does not compromise equality among the overall population (Gini index). These findings underscore the potential of Fair-PPO to address fairness challenges in MAS.

Recent interest in Multi-Agent Systems of Large Language Models (MAS LLMs) has led to an increase in frameworks leveraging multiple LLMs to tackle complex tasks. However, much of this literature appropriates the terminology of MAS without engaging with its foundational principles. In this position paper, we highlight critical discrepancies between MAS theory and current MAS LLMs implementations, focusing on four key areas: the social aspect of agency, environment design, coordination and communication protocols, and measuring emergent behaviours. Our position is that many MAS LLMs lack multi-agent characteristics such as autonomy, social interaction, and structured environments, and often rely on oversimplified, LLM-centric architectures. The field may slow down and lose traction by revisiting problems the MAS literature has already addressed. Therefore, we systematically analyse this issue and outline associated research opportunities; we advocate for better integrating established MAS concepts and more precise terminology to avoid mischaracterisation and missed opportunities.

In this paper, we interpret Deep Neural Networks with Complex Network Theory. Complex Network Theory (CNT) represents Deep Neural Networks (DNNs) as directed weighted graphs to study them as dynamical systems. We efficiently adapt CNT measures to examine the evolution of the learning process of DNNs with different initializations and architectures: we introduce metrics for nodes/neurons and layers, namely Nodes Strength and Layers Fluctuation. Our framework distills trends in the learning dynamics and separates low from high accurate networks. We characterize populations of neural networks (ensemble analysis) and single instances (individual analysis). We tackle standard problems of image recognition, for which we show that specific learning dynamics are indistinguishable when analysed through the solely Link-Weights analysis. Further, Nodes Strength and Layers Fluctuations make unprecedented behaviours emerge: accurate networks, when compared to under-trained models, show substantially divergent distributions with the greater extremity of deviations. On top of this study, we provide an efficient implementation of the CNT metrics for both Convolutional and Fully Connected Networks, to fasten the research in this direction.