Reinforced dynamics for interacting agents in competitive or cooperative environments
Abstract
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.
Keywords
Cite
@article{arxiv.2509.13493,
title = {Reinforced dynamics for interacting agents in competitive or cooperative environments},
author = {Michele Aleandri and Paolo Dai Pra and Ida Germana Minelli},
journal= {arXiv preprint arXiv:2509.13493},
year = {2025}
}