Matjaž Perc

The Anh Han, Joel Z. Leibo, Tom Lenaerts et al.

Artificial intelligence (AI) systems are rapidly becoming more capable, autonomous, and deeply embedded in social life. As humans increasingly interact, cooperate, and compete with AI, we move from purely human societies to hybrid human-AI societies whose collective dynamics cannot be captured by existing behavioural models alone. Drawing on evolutionary game theory, cultural evolution, and Large Language Models (LLMs) powered simulations, we argue that these developments open a new research agenda for social physics centred on the co-evolution of humans and machines. We outline six key research directions. First, modelling the evolutionary dynamics of social behaviours (e.g. cooperation, fairness, trust) in hybrid human-AI populations. Second, understanding machine culture: how AI systems generate, mediate, and select cultural traits. Third, analysing the co-evolution of language and behaviour when LLMs frame and participate in decisions. Fourth, studying the evolution of AI delegation: how responsibilities and control are negotiated between humans and machines. Fifth, formalising and comparing the distinct epistemic pipelines that generate human and AI behaviour. Sixth, modelling the co-evolution of AI development and regulation in a strategic ecosystem of firms, users, and institutions. Together, these directions define a programme for using social physics to anticipate and steer the societal impact of advanced AI.

Yichao Yao, Minyu Feng, Matjaž Perc et al.

Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the node count remains constant, instead prioritizing node growth. In this work, we depart from the assumptions of node number variation and preferential attachment to present an innovative model that conceptualizes node degree fluctuations as a state-dependent random walk process with stasis and variable diffusion coefficient. We show that this model yields stochastic dynamic networks with stable scale-free properties. Through comprehensive theoretical and numerical analyses, we demonstrate that the degree distribution converges to a power-law distribution, provided that the lowest degree state within the network is not an absorbing state. Furthermore, we investigate the resilience of the fraction of the largest component and the average shortest path length following deliberate attacks on the network. By using three real-world networks, we confirm that the proposed model accurately replicates actual data. The proposed model thus elucidates mechanisms by which networks, devoid of growth and preferential attachment features, can still exhibit power-law distributions and be used to simulate and study the resilience of attacked fixed-size scale-free networks.