Reinforced dynamics for interacting agents in competitive or cooperative environments

Michele Aleandri; Paolo Dai Pra; Ida Germana Minelli

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arXiv · 2509.13493

Reinforced dynamics for interacting agents in competitive or cooperative environments

Michele Aleandri·Paolo Dai Pra·Ida Germana Minelli

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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.

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BibTeX RIS

Michele Aleandri, Paolo Dai Pra, Ida Germana Minelli. 2025-09-16. Reinforced dynamics for interacting agents in competitive or cooperative environments. https://arxiv.org/abs/2509.13493

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