Technology Adoption and Network Externalities in Financial Systems: A Spatial-Network Approach

ArXiv ID: 2601.04246 “View on arXiv”

Authors: Tatsuru Kikuchi

Abstract

This paper develops a unified framework for analyzing technology adoption in financial networks that incorporates spatial spillovers, network externalities, and their interaction. The framework characterizes adoption dynamics through a master equation whose solution admits a Feynman-Kac representation as expected cumulative adoption pressure along stochastic paths through spatial-network space. From this representation, I derive the Adoption Amplification Factor – a structural measure of technology leadership that captures the ratio of total system-wide adoption to initial adoption following a localized shock. A Levy jump-diffusion extension with state-dependent jump intensity captures critical mass dynamics: below threshold, adoption evolves through gradual diffusion; above threshold, cascade dynamics accelerate adoption through discrete jumps. Applying the framework to SWIFT gpi adoption among 17 Global Systemically Important Banks, I find strong support for the two-regime characterization. Network-central banks adopt significantly earlier ($ρ= -0.69$, $p = 0.002$), and pre-threshold adopters have significantly higher amplification factors than post-threshold adopters (11.81 versus 7.83, $p = 0.010$). Founding members, representing 29 percent of banks, account for 39 percent of total system amplification – sufficient to trigger cascade dynamics. Controlling for firm size and network position, CEO age delays adoption by 11-15 days per year.

Keywords: technology adoption, network externalities, master equation, Levy jump-diffusion, cascade dynamics, Technology/Banking

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic processes, Feynman-Kac representations, and Lévy jump-diffusion models, while also providing a concrete empirical application with SWIFT gpi adoption data, regression analysis, and statistical significance testing.

  flowchart TD
    A["Research Goal: Analyze technology adoption in financial networks considering spatial spillovers, network externalities, and their interaction."] --> B["Methodology: Develop a unified framework with Master Equation and Feynman-Kac representation"]
    B --> C["Computational Process: Derive Adoption Amplification Factor (expected cumulative pressure)"]
    C --> D["Extension: Apply Lévy jump-diffusion for critical mass analysis"]
    D --> E["Data: SWIFT gpi adoption across 17 Global Systemically Important Banks"]
    E --> F["Outcomes: 1) Network-central banks adopt earlier (ρ = -0.69) 2) Pre-threshold adopters have higher amplification (11.81 vs 7.83) 3) Founding members drive 39% of system amplification 4) CEO age delays adoption by 11-15 days/year"]