Adoption survival frontiers: Artificial intelligence, financing frictions, and market structure

Artificial intelligence and other general-purpose digital technologies often diffuse unevenly: large firms adopt early, while smaller firms delay adoption, contract, or abandon the active adoption option. This paper develops a survival-constrained theory of technology adoption in which firms choose when to adopt an irreversible technology while financing operations under uncertain implementation costs. Abandonment/exit is endogenous: firms leave the active adoption race when the value of preserving the adoption option falls below the passive legacy fallback (the value of abandoning the active adoption option, normalized to zero). The key object is an adoption survival frontier , a boundary in financing-cost–implementation-uncertainty space separating environments in which followers survive long enough to adopt from environments in which they abandon the active adoption option first. The Cournot block disciplines the price-pass-through component of follower payoff erosion; additional non-price appropriability losses, captured by a reduced-form term 𝜒 𝐴 (data accumulation, platform lock-in, switching frictions, and reduced access to post-adoption rents), remain reduced-form. Numerical characterization of the corrected nonhomogeneous stopping problem shows that a leader-induced regime shift moves the survival frontier inward and raises the risk that followers abandon the active adoption option before adoption. A welfare decomposition clarifies when this selection is efficient and when it reflects an accounting externality: a leader-induced payoff shift that the follower’s private stopping problem does not represent before the regime shift. We do not solve a dynamic adoption-timing game. Public EU aggregate data show that large-minus-small AI adoption gaps are measurable, but also illustrate that aggregate cross-country regressions are confounded by development gradients and cannot identify the firm-level survival-to-adoption channel; we treat this as a measurement-feasibility map for future linked-microdata tests rather than as a test of the mechanism. The paper contributes a computational theory of adoption survival and a transparent measurement-feasibility map.