Reliability, Embeddedness, and Agency: A Utility-Driven Mathematical Framework for Agent-Centric AI Adoption
This work addresses the challenge of designing AI systems that are reliably adopted over time, which is incremental as it builds on existing adoption models with new mathematical formalizations and analyses.
The paper tackles the problem of sustained adoption of agent-centric AI systems by formalizing design axioms and modeling adoption as a sum of decaying novelty and growing utility, deriving phase conditions with proofs and introducing multiple analytical components such as identifiability analysis and benchmark evaluations.
We formalize three design axioms for sustained adoption of agent-centric AI systems executing multi-step tasks: (A1) Reliability > Novelty; (A2) Embed > Destination; (A3) Agency > Chat. We model adoption as a sum of a decaying novelty term and a growing utility term and derive the phase conditions for troughs/overshoots with full proofs. We introduce: (i) an identifiability/confounding analysis for $(α,β,N_0,U_{\max})$ with delta-method gradients; (ii) a non-monotone comparator (logistic-with-transient-bump) evaluated on the same series to provide additional model comparison; (iii) ablations over hazard families $h(\cdot)$ mapping $ΔV \to β$; (iv) a multi-series benchmark (varying trough depth, noise, AR structure) reporting coverage (type-I error, power); (v) calibration of friction proxies against time-motion/survey ground truth with standard errors; (vi) residual analyses (autocorrelation and heteroskedasticity) for each fitted curve; (vii) preregistered windowing choices for pre/post estimation; (viii) Fisher information & CRLB for $(α,β)$ under common error models; (ix) microfoundations linking $\mathcal{T}$ to $(N_0,U_{\max})$; (x) explicit comparison to bi-logistic, double-exponential, and mixture models; and (xi) threshold sensitivity to $C_f$ heterogeneity. Figures and tables are reflowed for readability, and the bibliography restores and extends non-logistic/Bass adoption references (Gompertz, Richards, Fisher-Pry, Mansfield, Griliches, Geroski, Peres). All code and logs necessary to reproduce the synthetic analyses are embedded as LaTeX listings.