2025/09/16 by Michele Aleandri, Aleandri, Michele, Paolo Dai Pra +3
Computer Science · Physics and Astronomy · #60F15 #60K35 #62L20 #91D30 #Distributed Control Multi-Agent Systems #FOS: Mathematics #Neural Networks Stability and Synchronization #Opinion Dynamics and Social Influence #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2509.13493
openalex publication_date 2025/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study systems of interacting reinforced stochastic processes, where agents' decisions evolve under reinforcement, network-mediated interactions, and environmental influences. In competitive environments with irreducible networks, we prove almost sure convergence of agents' states, with bipartite graphs leading to non-deterministic limits and non-bipartite graphs to deterministic ones. These results are extended to reducible networks with cooperative or competitive substructures, using a hierarchical graph representation in which higher-level agents perceive lower-level agents as forcing inputs. A general framework for interacting agents under external forcing is also provided, offering a rigorous characterization of long-term behavior and synchronization phenomena in such systems.