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Modelling lock-in of AI adoption through skill erosion

Renaud Lambiotte

Nov 3, 2026arXiv:2611.04886v1
cs.AIphysics.soc-ph
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Scorecard· 16/16
6.5/10 impact

Elegant, exact and timely minimal model with clear mechanistic insights on AI lock-in, but stylised, uncalibrated, and overlapping with concurrent independent work.

Abstract

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.

AI Impact Assessments

(1 model)

Core Contribution

The paper presents a minimal agent-based and mean-field model of AI adoption. Agents imitate successful peers via a linear pairwise comparison. Each agent carries an individual skill that grows with independent practice and decays with AI reliance. The AI payoff is b − c·x (benefit minus crowding), and the non-AI payoff equals the agent's own skill.

The main technical contribution is an exact stationary solution for the joint densities of skill among non-users and AI users. These are Beta-like densities tilted by an exponential factor, and they are closed-form even though switching rates depend on skill. Self-consistency then yields adoption branches and folds. The authors also derive a lone-holdout branching-process criterion for the "return" threshold, θ*(ρ). This gives a bistable window c + θ* < b < 1 in the rare-exploration limit.

Substantive conclusions:

  • Skill erosion produces bistability and hysteresis.
  • The invasion threshold (b > 1) is independent of the timescale ratio, while the return threshold depends on behavioural persistence.
  • Populations with the same adoption and mean skill can have very different skill polarisation.
  • Temporary boosts in AI benefit of sufficient duration can lock in adoption.
  • Adoption level alone does not diagnose lock-in.

    • Methodological Rigor

    The analytics are clean. The flux-balance argument, the integration to Beta/Kummer forms, and the self-consistency reduction to one equation are all sound and verified against agent-based simulations (fold locations agree within about 0.015). The holdout branching argument is neat and gives a microscopic interpretation.

    Limitations:

  • Stability of the branches is inferred from simulations rather than proven.
  • Monotonic connection of the unstable branch was checked numerically at twelve ρ values, with no general proof.
  • Lock-in statistics rest on only 20 runs per duration.
  • The simulated "locked-in" outcome is a finite-time notion.
  • Robustness checks (Fermi rule, imitate-if-better, asymmetric rates, complementarity) are reported in the appendix and are reassuring.
  • The model has no empirical calibration. The assumptions (skill-independent AI payoff, well-mixed population, homogeneous agents, linear payoffs) are strong, and the "five years" and "eight months" translations are only illustrative.

    • Potential Impact

    The work is mainly conceptual and theoretical, written for the statistical-physics, complex-systems and computational social science communities. It offers a vocabulary and a testable prediction: measure independent skill, not just adoption, to detect lock-in. It also gives a policy-relevant qualitative message, that temporary subsidies or price drops can create persistent dependence, and that complementary tools reduce the risk.

    Direct applied impact is limited because the model is uncalibrated and stylised. Its influence will probably come through follow-up models (networks, heterogeneity, strategic providers) and through citation in human–AI coevolution discussions.

    Timeliness & Relevance

    The topic is very timely: concerns about deskilling from generative AI are widespread, with recent empirical studies cited. The paper joins a cluster of contemporaneous modelling efforts, and it explicitly acknowledges that Frigerio et al. independently studied a closely related model with overlapping findings (bistability, hysteresis, polarisation). This reduces novelty and priority, though the paper differentiates itself with finite-selection exact distributions, the holdout criterion, and finite-duration lock-in simulations. It also reproduces Frigerio's criterion in a limit, which is a mild independent-corroboration element.

    Strengths

  • Exact, interpretable analytical solution in a model with individual memory, which is uncommon in evolutionary game dynamics.
  • The asymmetry insight, that skill erosion is a cost of returning rather than of adopting, is crisp and non-obvious.
  • The finding that identical adoption and mean skill can mask very different skill distributions is conceptually useful.
  • The lock-in-by-temporary-boost experiment shows the dynamic consequences clearly. The observation that adoption does not reveal lock-in status is a nice demonstration.
  • Code is available, and the paper is well organised and transparent, including disclosure of AI-assistant use.

    • Limitations

  • Parallel work reduces the novelty margin.
  • The model is highly stylised and has no empirical validation or data linkage.
  • Skill-independent AI payoff is central, and the complementarity extension is only briefly treated.
  • Well-mixed and homogeneous populations, with no network structure and no strategic or forward-looking agents.
  • Stability and branch-connectivity claims are not proven.
  • The practical lock-in timescales depend on arbitrary calibration.
  • The conclusion that lock-in is "difficult to reverse" follows largely from model assumptions, such as imitation of realised payoffs, rather than being discovered from data.

    • Other Observations

    The paper is a solid, careful theory contribution rather than a paradigm shift. Its value lies in analytic tractability and clear mechanism isolation, which makes it a reusable minimal model. Mathematical difficulty is moderate to high (stochastic processes, special functions, branching processes). Computational resources are minimal.

    Rating:6.5/ 10
    Significance 6Rigor 7Novelty 6Clarity 8

    Generated Nov 4, 2026

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