When a Few Misfits Trigger Digital Adoption Cascades: Network Reach, Threshold Heterogeneity, and Performance-Conditioned Complex Contagion in an Agent-Based Model of Firms

Abstract

Why does a superior technology sometimes spread and sometimes stall, even when its expected returns are much higher? We develop an agent-based model in which firms adopt a digital technology by imitating successful neighbours through a fast-and-frugal heuristic. We compare frequency-based imitation, where firms follow the local majority, with performance-conditioned imitation, where they follow better-performing neighbours. We define a cascade as high final adoption reached through rapid, accelerating takeoff rather than slow accumulation. In the calibrated regime, four results emerge. First, dynamic cascades arise under performance-conditioned imitation, but not under an exogenous adoption hazard or frequency-based imitation. Second, on degree-controlled networks, adoption tips once the network provides sufficient reach, at a small-world rewiring threshold near 0.41, with a 95 percent bootstrap confidence interval of 0.39 to 0.43. This reflects short paths, low clustering, and high-reach nodes rather than one graph statistic. Third, at a fixed mean threshold, concentrating receptiveness in the lower tail can generate cascades that homogeneous thresholds cannot. Fourth, cascade probability depends strongly on the positions of initial adopters and low-threshold pioneers. At human-scale observation degrees, the mechanism is genuine complex contagion: adoption requires reinforcement from multiple successful exemplars, survives a requirement of at least two successful digital neighbours when seeded by a clustered critical mass, and weakens beyond Dunbar-scale neighbourhoods. The model identifies where interventions may have leverage rather than forecasting industries. Broad cultural change is not required for system-wide adoption: a small minority of receptive firms, positioned where the network can transmit success, can be enough. In short, a few misfits can change the world.