Interacting non-linear reinforced stochastic processes: Synchronization and no-synchronization

Irene Crimaldi (1) , Pierre-Yves Louis (2, 3, 4) , Ida Germana Minelli (5)

1 IMT Institute for Advanced Studies [Lucca]
2 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]
3 PMB - Procédés Microbiologiques et Biotechnologiques
4 IMB - Institut de Mathématiques de Bourgogne [Dijon]
5 UNIVAQ - University of L'Aquila [Italy]

Rich get richer rule comforts previously often chosen actions. What is happening to the evolution of individual inclinations to choose an action when agents do interact ? Interaction tends to homogenize while each individual dynamics tends to reinforce its own position. Interacting stochastic systems of reinforced processes were recently considered in many papers, where the asymptotic behavior was proven to exhibit a.s. synchronization. We consider in this paper models where, even if interaction among agents is present, absence of synchronization may happen due to the choice of an individual non-linear reinforcement. We show how these systems can naturally be considered as models for coordination games, technological or opinion dynamics.

Mots clés: Interacting agents; Interacting stochastic processes; Reinforced stochastic process; Urn model; Non-linear Pólya urn; Generalized Pólya urn; Reinforcement learning; Stochastic approximation; Evolutionary-game theory; Coordination games; Technological dynamics; CODA models

Domaines: Probabilités [math.PR]; Informatique et théorie des jeux [cs.GT]; Applications [stat.AP]

Irene Crimaldi, Pierre-Yves Louis, Ida Germana Minelli. Interacting non-linear reinforced stochastic processes: Synchronization and no-synchronization. Advances in Applied Probability, 2023, 55 (1), ⟨10.1017/apr.2022.18⟩. ⟨hal-02910341⟩