Competition, Switching, and Control in Coupled Adoption-Opinion Dynamics
Abstract
We propose a Multi-technology AdopTion-opinion co-Evolution (MATE) model to describe the diffusion of m ≥ 2 competing alternatives within a networked population whose opinions evolve under social influence and the feedback generated by adoption. Communities interact through two layers: a physical network governing exposure to adoption, and a social network shaping opinion evolution through social imitation. Individuals can adopt a technology, eventually becoming dissatisfied at a rate reflecting the quality of the technology, and switch to an alternative at a rate driven by their opinion of that alternative. For an arbitrary number of competing technologies m ≥ 2, we characterize the equilibria and establish the existence of an adoption-diffused equilibrium in which all technologies coexist. For m > 2, the equilibrium configuration depends on the broader competitive environment: unlike the two-technology case, within-community relative adoption generally depends also on equilibrium opinions and on the other alternatives. Finally, we formulate finite-horizon opinion-shaping control problems, derive necessary optimality conditions via the discrete-time Pontryagin maximum principle, and compute numerical extremals using a forward-backward sweep method.
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BibTeX
@misc{alutto2026competition,
title = {{Competition, Switching, and Control in Coupled Adoption-Opinion Dynamics}},
author = {Martina Alutto and Fabrizio Dabbene and Angela Fontan and Karl H. Johansson and Chiara Ravazzi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04407},
eprint = {2611.04407},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04407},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Competition, Switching, and Control in Coupled Adoption-Opinion Dynamics
AU - Martina Alutto
AU - Fabrizio Dabbene
AU - Angela Fontan
AU - Karl H. Johansson
AU - Chiara Ravazzi
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04407
UR - https://arxiv.org/abs/2611.04407
AB - We propose a Multi-technology AdopTion-opinion co-Evolution (MATE) model to describe the diffusion of m ≥ 2 competing alternatives within a networked population whose opinions evolve under social influence and the feedback generated by adoption. Communities interact through two layers: a physical network governing exposure to adoption, and a social network shaping opinion evolution through social imitation. Individuals can adopt a technology, eventually becoming dissatisfied at a rate reflecting the quality of the technology, and switch to an alternative at a rate driven by their opinion of that alternative. For an arbitrary number of competing technologies m ≥ 2, we characterize the equilibria and establish the existence of an adoption-diffused equilibrium in which all technologies coexist. For m > 2, the equilibrium configuration depends on the broader competitive environment: unlike the two-technology case, within-community relative adoption generally depends also on equilibrium opinions and on the other alternatives. Finally, we formulate finite-horizon opinion-shaping control problems, derive necessary optimality conditions via the discrete-time Pontryagin maximum principle, and compute numerical extremals using a forward-backward sweep method.
ER -