A memory-based three-state model of competing technology adoption: substitution regimes, multi-homing, and churn
Technologies, products, platforms, and behavioral routines often compete through gradual adoption, reinforcement-dependent use, and temporary multi-homing. We formulate a homogeneous, well-mixed, three-state agent-based model of competition between an incumbent option (X) and a challenger (Y). Agents are exclusive users of (X), exclusive users of (Y), or dual adopters (Z). Adoption is memory-based: an exclusive user adds the alternative only after enough adoption-relevant encounters within a finite learning window. Retention is also memory-based: a dual adopter continues to use both options only if each is sufficiently reinforced within a finite retention window. This microscopic mechanism reproduces aggregate usage signatures analogous to the four Adner--Kapoor technology-substitution regimes---creative destruction, robust coexistence, the illusion of resilience, and robust resilience---without explicitly representing ecosystems, complementors, prices, or strategic investment. Starting from the same small challenger seed, the benchmark simulations differ only in adoption burden, retention burden, post-adoption usage preference, and the teaching role of dual adopters. Rolling usage shares reproduce the four aggregate substitution patterns, while state-resolved trajectories and phase portraits reveal distinct microscopic pathways. Thus, similar market-level substitution curves need not have unique causal interpretations: although ecosystem mechanisms may be essential in many empirical cases, finite-memory learning and retention alone can generate qualitatively similar regimes. The model provides a compact baseline linking technology-substitution trajectories to observable individual-level adoption, multi-homing, and discontinuance.