The diffusion of new technologies such as operating systems can be analyzed using game-theoretic frameworks.While previous studies have primarily focused on the spread of a single technology, in practice, multipletechnologies―such as Windows and Unix-based systems (including macOS and Linux)―coexist. In this study, wedevelop a tractable model based on the stochastic block model to investigate the conditions under which such coexistenceemerges, taking into account community structures within a network. First, we show that when communitystructure is strong, the Nash equilibrium shifts from single-technology dominance to coexistence of multiple technologies.Second, we observe critical slowing down near the transition point in the time it takes for the system toreach equilibrium, suggesting the presence of a phase transition (bifurcation phenomenon). Third, we analyticallyconfirm the existence of such bifurcations using dynamical systems theory.
Onaga et al. (Sat,) studied this question.