Survival and Cascades in Geoeconomic Networks: A Graph-Embedded Hazard Framework

This paper develops a theoretical framework for modelling survival dynamics in interconnected economic systems. The model introduces a graph-embedded hazard model (GEHM) in which node-level survival emerges from nonlinear diffusion over a network structure. The dynamics are governed by a graph p–Laplacian operator combined with a stochastic aggregate process, allowing the economic state of each agent to evolve endogenously through local interactions and aggregate shocks. Crucially, failure is modelled not as a passively recorded event but as an endogenous state transition that feeds back into the system: When a node fails, it injects additional stress into its neighbourhood and may sever its economic links, raising the failure intensity of the agents to which it is connected. The survival probability of an economic agent therefore depends not only on its own characteristics but also on the evolving conditions and the realised failures of its neighbourhood. This feedback turns the system of node-level hazards into a network self-exciting point process, in which each failure mechanically increases the hazard of still-active neighbours. The model characterises conditions under which local shocks dissipate, propagate through neighbouring nodes, or trigger systemic cascades. By integrating survival analysis with network diffusion dynamics and failure feedback, the GEHM framework provides a bridge between duration models, network economics, and nonlinear dynamics on graphs. The approach offers a structural perspective for analysing systemic fragility, contagion, and cascade phenomena in complex economic networks.