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On a Coupled Adoption-Opinion Framework for Competing Innovations

Martina Alutto, Fabrizio Dabbene, Angela Fontan, Karl H. Johansson, Chiara Ravazzi

TL;DR

This paper tackles diffusion of two competing technologies by coupling epidemic-like adoption dynamics with opinion formation on a two-layer network. The authors formulate a discrete-time model where susceptibles, adopters, and dissatisfied individuals interact across physical and social networks, and where adoption rates depend on technology-specific opinions via linear functions, while opinions evolve under a Friedkin–Johnsen–style process influenced by both predispositions and adoption outcomes. They prove the existence and uniqueness of an adoption-diffused equilibrium in which both technologies coexist ($s^*=0$, ${a^{[1]}}^*,{a^{[2]}}^*>0$), and show that partial-adoption or monopoly equilibria cannot occur; a key ratio ${a_i^{[2]}}^* = rac{oldsymbol{ au_i^{[1]}}}{oldsymbol{ au_i^{[2]}}}{a_i^{[1]}}^*$ links adoption across technologies. Numerical simulations reveal that final market shares depend primarily on user experience (dissatisfaction rates), not on marketing intensity, and that symmetric policy actions can produce asymmetric outcomes that favor the higher-quality technology. The work offers strategic insights for innovation management, emphasizing quality-focused interventions over aggressive marketing to shape long-term adoption in competitive settings.

Abstract

In this paper, we propose a two-layer adoption-opinion model to study the diffusion of two competing technologies within a population whose opinions evolve under social influence and adoption-driven feedback. After adopting one technology, individuals may become dissatisfied and switch to the alternative. We prove the existence and uniqueness of the adoption-diffused equilibrium, showing that both technologies coexist and that neither partial-adoption nor monopoly can arise. Numerical simulations show that while opinions shape the equilibrium adoption levels, the relative market share between the two technologies depends solely on their user-experience. As a consequence, interventions that symmetrically boost opinions or adoption can disproportionately favor the higher-quality technology, illustrating how symmetric control actions may generate asymmetric outcomes.

On a Coupled Adoption-Opinion Framework for Competing Innovations

TL;DR

This paper tackles diffusion of two competing technologies by coupling epidemic-like adoption dynamics with opinion formation on a two-layer network. The authors formulate a discrete-time model where susceptibles, adopters, and dissatisfied individuals interact across physical and social networks, and where adoption rates depend on technology-specific opinions via linear functions, while opinions evolve under a Friedkin–Johnsen–style process influenced by both predispositions and adoption outcomes. They prove the existence and uniqueness of an adoption-diffused equilibrium in which both technologies coexist (, ), and show that partial-adoption or monopoly equilibria cannot occur; a key ratio links adoption across technologies. Numerical simulations reveal that final market shares depend primarily on user experience (dissatisfaction rates), not on marketing intensity, and that symmetric policy actions can produce asymmetric outcomes that favor the higher-quality technology. The work offers strategic insights for innovation management, emphasizing quality-focused interventions over aggressive marketing to shape long-term adoption in competitive settings.

Abstract

In this paper, we propose a two-layer adoption-opinion model to study the diffusion of two competing technologies within a population whose opinions evolve under social influence and adoption-driven feedback. After adopting one technology, individuals may become dissatisfied and switch to the alternative. We prove the existence and uniqueness of the adoption-diffused equilibrium, showing that both technologies coexist and that neither partial-adoption nor monopoly can arise. Numerical simulations show that while opinions shape the equilibrium adoption levels, the relative market share between the two technologies depends solely on their user-experience. As a consequence, interventions that symmetrically boost opinions or adoption can disproportionately favor the higher-quality technology, illustrating how symmetric control actions may generate asymmetric outcomes.
Paper Structure (8 sections, 37 equations, 3 figures)

This paper contains 8 sections, 37 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Notation
  3. Model Description
  4. Equilibrium points and stability analysis
  5. Adoption-free equilibrium
  6. Adoption-diffused equilibrium
  7. Numerical Simulations
  8. Conclusion

Figures (3)

  • Figure 1: Coupled transition diagram for two competing technologies. Susceptible individuals can adopt either technology, moving to adoption compartments $A^{[1]}$ or $A^{[2]}$. Adopters may become dissatisfied, entering $D^{[1]}$ or $D^{[2]}$. Dissatisfied individuals can switch to the other technology at rates modulated by the opinion variables $x^{[k]}$.
  • Figure 2: Numerical simulation of adoption-opinion model \ref{['eq:vector_model']}.
  • Figure 3: Numerical simulation of adoption-opinion model \ref{['eq:vector_model']} where Technology $2$ enters the market after a delay $T=100$.