Modelling lock-in of AI adoption through skill erosion
Authors: Renaud Lambiotte
Organizations: Mathematical Institute, University of Oxford, Oxford, United Kingdom · Institute for New Economic Thinking, University of Oxford, Oxford, United Kingdom · Complexity Science Hub, Vienna, Austria
Generative AI can improve immediate performance but may erode the human skills required for future work. We study a model in which individuals tend to imitate successful peers, while their independent skills grow with practice and erode with reliance on AI. Because each agent's skill reflects their history, non-users and AI users develop different skill distributions, which we derive exactly. Skill erosion can produce bistability and hysteresis between a low-adoption, high-skill state and a high-adoption, low-skill state. When agents rarely change behaviour at random, the two transitions are asymmetric. A single AI user spreads through a population of experts only if AI-assisted work earns more than expert work, whatever the timescale of skill adaptation. A single non-user, by contrast, can lead an AI-dependent population back to independent work only if they regain enough skill before returning to AI, which becomes easier the more persistent behaviours are. As AI improves, adoption can jump abruptly, and a sufficiently long increase in its benefit, such as a period of low prices, can leave a population relying on AI after the benefit has returned to its initial value. Skill erosion thus creates a history-dependent switching cost that can make widespread AI adoption difficult to reverse.
Figures & tables
Figure 1: Feedbacks and individual memory. (a) Feedback structure. Reliance on AI erodes independent skill, and lower skill makes AI relatively more attractive. Crowding restrains adoption. (b,c) Illustrative skill trajectories of a single agent, coloured by behaviour, when behaviour changes often compared with the time skills need to adapt (b, ρ=0.1 ) and when behaviour is persistent (c, ρ=3 ). For these trajectories, switching is independent of skill and the rates are chosen so that the agent uses AI 40% of the time. The agent has the same mean skill in both cases (dashed line), but skill stays close to the mean in (b) and alternates between expertise and deep erosion in (c).
Figure 2: Same adoption and mean skill, different distributions of skill ( c=0.95 , a single stable state; b is tuned so that x=0.4 , and hence S=1−x=0.6 , in every panel). Histograms of skill in simulations of 2×104 agents, pooled over snapshots, and exact densities ( 7 ), for all agents and separately for non-users and AI users, as ρ increases. Each panel gives the adoption x and the mean skill S measured in the simulations, and the fraction of agents with skill below 0.2 predicted by the exact solution; simulations give 0.00 , 0.10 and 0.33 .
Figure 3: Bistability and hysteresis. (a) Stationary adoption as a function of the benefit b of AI-assisted work ( c=0.15 , ρ=0.39 ): exact solution (dashed on the unstable branch) and simulations of 104 agents in which b is slowly increased (circles) or decreased (squares). The arrow gives the width of the bistable window. (b) Phase diagram in the plane of the ratio of timescales ρ and the benefit b : folds of the exact solution for μ=0.02 (solid blue lines, bistable region shaded), folds measured in simulations (symbols), and boundaries of the bistable region for μ→0 (dashed, with ρ=2ε/ν ), at which a lone AI user invades a population of non-users ( b=1 ) and a lone non-user invades a population of AI users [ b=c+θ∗(ρ) , Eq. ( 8 )]. Below the bistable region, the only stable state has low adoption, and above it, high adoption; beyond the cusp, near ρ≈2.7 for μ=0.02 , adoption increases continuously with b .
Figure 4: Discontinuous adoption and lock-in ( c=0.15 , ρ=0.39 , simulations of 104 agents). (a) Adoption against the benefit b when b rises from 0.3 to 1.15 at a rate r , remains at 1.15 for 300 time units and falls back at the same rate, for four values of r , with the exact stationary solution (grey, dashed on the unstable branch) and the thresholds ( 8 ) for μ→0 (dotted). (b) Adoption over time in single runs in which b is raised from 0.7 to 1 for a duration D and then restored to 0.7 ; dots mark the end of the increase. Inset: fraction of 20 runs that remain at high adoption, against D , with binomial standard errors.