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arxiv: 2606.29111 · v1 · pith:PFIRAII3new · submitted 2026-06-27 · 💻 cs.AI · econ.GN· econ.TH· q-fin.EC

Managing the Human Fallback: Skill Investment Under Improving AI and Worker Mobility

Simrita Singh , Naireet Ghosh , Tinglong Dai This is my paper

Pith reviewed 2026-06-30 09:10 UTC · model grok-4.3

classification 💻 cs.AI econ.GNecon.THq-fin.EC
keywords AI deploymentworker engagementskill investmentlabor mobilityhuman capitalAI fallbackhuman-AI collaboration
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The pith

Worker mobility reverses firm engagement from the least-skilled to the most-skilled workers below the AI benchmark.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds a two-period model in which AI can outperform a worker when it functions but fails with positive probability. A firm chooses how much to engage the worker, which reduces current output for those below the AI level but alters future skill through learning or erosion. In a single-firm setting the firm engages the least-skilled workers most, since they start with the largest gaps and cost the least to bring to a useful fallback level. When workers can move between firms, they sort toward jobs that build more valuable future skill trajectories, so the firm instead targets higher-skilled workers near the AI frontier where gains are more valuable and engagement costs less. Mobility therefore flips the pattern of skill investment and changes how improvements in AI capability and reliability affect engagement decisions.

Core claim

In a single-firm benchmark, engagement is valuable only as fallback investment and the firm engages the least-skilled workers most because they have the largest skill gaps and are least costly to bring toward a useful fallback level. With worker mobility, engagement also affects labor-market sorting: workers prefer jobs that build more valuable skill trajectories. This sorting motive targets higher-skill workers near the AI frontier, where skill gains are more valuable and engagement is less costly. Mobility can therefore reverse the engagement pattern, shifting investment from the least-skilled toward the most-skilled workers below the AI benchmark. Mobility also reshapes how AI progress af

What carries the argument

Two-period model separating AI capability (output when it works) from reliability (probability it works), with engagement trading off current output against future skill change via learning and erosion, and the addition of worker mobility that creates labor-market sorting over skill trajectories.

If this is right

  • Mobility reverses the engagement pattern from least-skilled to most-skilled workers below the AI benchmark.
  • Greater AI capability increases engagement because it raises the value of the skill trajectory offered by the firm.
  • Greater AI reliability has an ambiguous effect on engagement, as it lowers the need for fallback skills while altering learning opportunities.
  • Under mobility, human-AI work design becomes a problem of shaping future human capital rather than only managing current output.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Firms may compete for talent by offering engagement levels that accelerate skill growth for workers already close to the AI frontier.
  • Lower-skilled workers could face reduced on-the-job learning opportunities in mobile markets, widening skill gaps over time.
  • The model suggests testing whether industries with easier job switching show different patterns of AI-related training investment than those with low mobility.

Load-bearing premise

Engagement changes future skill through learning and erosion, and this change is valued differently by workers who can move between firms.

What would settle it

Data showing whether, in labor markets with high worker mobility, firms allocate more engagement to higher-skilled workers near the AI performance level than to lower-skilled workers.

read the original abstract

When firms deploy autonomous AI, they must decide how much work to leave to the system and how much to keep workers engaged. This decision affects current output and future human capital. We develop a parsimonious two-period model in which AI may outperform the worker when it functions, but may fail with positive probability. A firm chooses worker engagement; engagement lowers current output for below-benchmark workers, but changes future skill through learning and erosion. We distinguish two dimensions of AI progress: capability, the system's output when it works, and reliability, the probability that it works. In a single-firm benchmark, engagement is valuable only as fallback investment. The firm engages the least-skilled workers most, because they have the largest skill gaps and are least costly to bring toward a useful fallback level. With worker mobility, engagement also affects labor-market sorting: workers prefer jobs that build more valuable skill trajectories. This sorting motive targets higher-skill workers near the AI frontier, where skill gains are more valuable and engagement is less costly. Mobility can therefore reverse the engagement pattern, shifting investment from the least-skilled toward the most-skilled workers below the AI benchmark. Mobility also reshapes how AI progress affects engagement: greater capability raises engagement by increasing the value of the skill trajectory a firm offers, whereas greater reliability can raise or lower it because it reduces fallback need while also changing learning opportunities. Under worker mobility, human-AI work design becomes a problem of human-capital investment, in which allocating work today shapes future skill.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper develops a parsimonious two-period model in which firms choose worker engagement levels when deploying AI systems characterized by capability (output when functioning) and reliability (probability of functioning). Engagement reduces current output for below-benchmark workers but affects future skill via learning and erosion. In the single-firm benchmark, engagement targets least-skilled workers for fallback value. With worker mobility, a sorting motive arises because workers value skill trajectories differently, reversing engagement toward higher-skilled workers near the AI frontier. Mobility also changes comparative statics: capability increases engagement while reliability has an ambiguous effect.

Significance. If the central qualitative possibility result holds, the paper offers a clean theoretical account of how worker mobility transforms human-AI task allocation into a human-capital investment problem, with distinct roles for AI capability versus reliability. The explicit separation of these two AI dimensions and the mobility-induced reversal of engagement patterns are the main contributions; the model is self-contained and yields falsifiable comparative statics on labor-market sorting.

minor comments (2)
  1. Abstract and introduction: the equilibrium conditions, worker utility, and firm objective functions are described only verbally; adding the key equations (e.g., the two-period payoff and mobility choice) would allow readers to verify the reversal result directly.
  2. The paper should clarify whether the learning/erosion function is assumed linear or concave and whether this functional form is necessary for the reversal or merely illustrative.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their accurate summary of the model and for recommending minor revision. The referee correctly highlights the mobility-induced reversal in engagement patterns and the distinct comparative statics for capability versus reliability.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper develops a parsimonious two-period model whose mechanisms (engagement lowering current output for below-benchmark workers while altering future skill via explicit learning/erosion, plus mobility-driven sorting over skill trajectories) are stated as modeling primitives rather than derived from or fitted to the target results. The central comparative statics (reversal of engagement pattern under mobility, differential effects of AI capability vs. reliability) follow directly from these primitives without any quoted equations reducing a prediction to a fitted input, self-definition, or load-bearing self-citation. No equations or derivations appear in the provided text that would allow identification of circular steps; the model is presented as generating qualitative possibility results from its stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on standard domain assumptions about skill dynamics and worker preferences; no free parameters or invented entities are identified in the abstract.

axioms (2)
  • domain assumption Engagement lowers current output for below-benchmark workers but changes future skill through learning and erosion.
    Stated directly in the abstract as the core tradeoff mechanism.
  • domain assumption Workers prefer jobs that build more valuable skill trajectories.
    Invoked to generate the sorting motive under mobility.

pith-pipeline@v0.9.1-grok · 5810 in / 1439 out tokens · 27609 ms · 2026-06-30T09:10:16.094126+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

21 extracted references · 1 canonical work pages

  1. [1]

    In Proceedings of the 37th international ACM SIGIR confer- ence on Research & development in information retrieval, 1055–1058

    Accessed June 26, 2026. Gans N, Zhou YP (2002) Managing learning and turnover in employee staffing.Operations Research50(6):991– 1006. Goh E, Gallo R, Hom J, Strong E, Weng Y, et al. (2024) Large language model influence on diagnostic reasoning: A randomized clinical trial.JAMA Network Open7(10):e2440969. Harari YN (2017) The rise of the useless class. TE...

    work page arXiv 2026

  2. [2]

    =W(s2)+βB(g(s2,hj 2;A2)) is also strictly increasing in hj

  3. [3]

    Consider firm 1’s option to deviate unilaterally to the other firm’s engagement levelh2∗ 2 , while firm 2 continues to play h2∗ 2

    Hence V 1 2 (s2,h 1∗ 2 )>V 2 2 (s2,h 2∗ 2 ), and the logit sorting rule implies σ1∗ 2 > 1/2>σ2∗ 2 . Consider firm 1’s option to deviate unilaterally to the other firm’s engagement levelh2∗ 2 , while firm 2 continues to play h2∗ 2 . The resulting action profile would be ( h2∗ 2 ,h 2∗ 2 ), at which the logit sorting probability is σ1 2 = 1/2 by symmetry of ...

  4. [4]

    This contradicts σ1∗ 2 > 1/2>σ2∗ 2 , so no asymmetric pure-strategy Nash equilibrium exists

    But σ1∗ 2 ,σ2∗ 2 > 0 and σ1∗ 2 +σ2∗ 2 = 1 imply σ1∗ 2 σ2∗ 2 ≤1/4, with equality only at σ1∗ 2 =σ2∗ 2 = 1/2. This contradicts σ1∗ 2 > 1/2>σ2∗ 2 , so no asymmetric pure-strategy Nash equilibrium exists. Q.E.D. Proof of Proposition 3.Fixs 2∈D2. SinceD 2⊂(s2,α2), the zero floor does not bind, so g(s2,h;A 2) =s 2 + (1−π2) [ h(ϕπ2 +γ)−γ ] (α2−s2), and therefore...

  5. [5]

    Hence 1−σj 2 is strictly decreasing inh j

    First, σj 2 is strictly increasing in hj 2, because B andgare strictly increasing in own engagement. Hence 1−σj 2 is strictly decreasing inh j

  6. [6]

    Since s2∈D2, condition (6) applies for every own action hj 2∈[0, 1]

    Second, ∂ ∂hj 2 [ B′( g(s2,hj 2;A 2) ) M(s 2,hj 2;A 2) ] equals B′( g(s2,hj 2;A 2) ) (1−π2)(α2−s2) [ (ϕπ2 +γ)B′′(g(s2,hj 2;A 2)) B′(g(s2,hj 2;A 2))M(s 2,hj 2;A 2)−λRδ ] . Since s2∈D2, condition (6) applies for every own action hj 2∈[0, 1]. Hence the expression in square brackets is strictly negative for every own action hj 2∈[0, 1], regardless of the othe...

  7. [7]

    Because the equilibrium characterization applies on D2, the relevant object is the restriction of ¯η to D2

    for its peak, with 0<ηU<η†. Because the equilibrium characterization applies on D2, the relevant object is the restriction of ¯η to D2. Define ηD≡lims2↓¯¯s2 ¯η(s2). When a full-domain threshold lies below ¯¯s2, we truncate it at the admissible-domain boundary: write ˆsD 2≡max{ˆs2, ¯¯s2}and ˆsL,D 2 ≡max{ˆsL 2, ¯¯s2}. Claim OA3 Suppose B(s) =W (s) =sb with ...

  8. [8]

    Proposition 4 is the qualitative summary of this characterization

    When ∆ 2< 0 and s† 2≤¯¯s2, the peak is truncated away, so engagement starts just above the lower boundary ¯¯s2. Proposition 4 is the qualitative summary of this characterization. Proof of Proposition 4 and Claim OA3.From Corollary 2, positive terminal-period engagement is characterized by the cutoff ¯η(s2). It remains to characterize the shape of this cut...

  9. [9]

    If ∆ 2≥0, then strict concavity of H, together with the positive lower-endpoint value, implies H(s2)> 0 throughout (s2,α2)

    +α2(λRπ2−bαb−1 2 ) = ∆ 2. If ∆ 2≥0, then strict concavity of H, together with the positive lower-endpoint value, implies H(s2)> 0 throughout (s2,α2). Therefore ¯η′(s2)> 0 throughout the domain, and ¯ηis strictly increasing. LetηU ≜lims2→α− 2 ¯η(s2). Becausez 0(s2)↓0 ass2↓s2 andb>1, whereasr 0(s2) remains finite and positive, we have lims2↓s2 ¯η(s2) = 0. T...

  10. [10]

    = 0, withH(s2)> 0 for s2<s† 2 and H(s2)< 0 for s2>s†

  11. [11]

    Therefore ¯ηis strictly increasing on (s2,s†

  12. [12]

    Let η†≜¯η(s† 2), η U ≜lim s2→α− 2 ¯η(s2)

    and strictly decreasing on (s† 2,α2). Let η†≜¯η(s† 2), η U ≜lim s2→α− 2 ¯η(s2). Because ¯ηis strictly decreasing on (s† 2,α2), we have ηU<η†. Moreover, ηU> 0 by margin positivity at the upper endpoint andz 0(α2) =α2>0. Hence 0<ηU<η†. If η≥η†, then η<¯η(s2) never holds, so h∗ 2(s2) = 0 for all s2∈(s2,α2). If 0 <η≤ηU, then the lower endpoint limit lims2↓s2 ...

  13. [13]

    If ηU<η<η†, then the cutoff crosses the level ηonce on each side of s† 2, so there exist unique thresholds ˆsL 2∈(s2,s†

    such that η<¯η(s2) if and only if s2∈(ˆs2,α2). If ηU<η<η†, then the cutoff crosses the level ηonce on each side of s† 2, so there exist unique thresholds ˆsL 2∈(s2,s†

  14. [14]

    Applying Corollary 2 gives the stated positive-engagement regions

    and ˆsH 2 ∈(s† 2,α2) such that η<¯η(s2) if and only if s2∈(ˆsL 2,ˆsH 2 ). Applying Corollary 2 gives the stated positive-engagement regions. It remains to restrict these full-domain regions to the admissible domain D2 = (¯¯s2,α2). If ∆ 2≥0, then ¯ηis strictly increasing on (s2,α2) and has upper-end limit ηU. Hence, if η≥ηU, the inequality η<¯η(s2) fails f...

  15. [15]

    If h≥hc 2, this expression is strictly positive because B′> 0, B′′> 0, M> 0, and 1−δh>0

    +λR(1−δh). If h≥hc 2, this expression is strictly positive because B′> 0, B′′> 0, M> 0, and 1−δh>0. Now considerh<h c

  16. [16]

    Becauseh−hc 2<0, multiplying both sides by (ϕπ2 +γ)(h−hc

    By condition (6), B′′(g(s2,h;A 2)) B′(g(s2,h;A 2))M(s 2,h;A 2)< λRδ ϕπ2 +γ. Becauseh−hc 2<0, multiplying both sides by (ϕπ2 +γ)(h−hc

  17. [17]

    Therefore, B′′(g(s2,h;A 2)) B′(g(s2,h;A 2))M(s 2,h;A 2)(ϕπ2 +γ)(h−hc

    reverses the inequality and gives B′′(g(s2,h;A 2)) B′(g(s2,h;A 2))M(s 2,h;A 2)(ϕπ2 +γ)(h−hc 2)>λRδ(h−hc 2). Therefore, B′′(g(s2,h;A 2)) B′(g(s2,h;A 2))M(s 2,h;A 2)(ϕπ2 +γ)(h−hc

  18. [18]

    Hence ∂F2/∂α2> 0 at h =h∗ 2(s2)

    +λR(1−δh) =λR(1−δhc 2)>0, becauseδ∈(0,1) andhc 2∈(0,1). Hence ∂F2/∂α2> 0 at h =h∗ 2(s2). Because ∂F2/∂h<0, implicit differentiation implies ∂h∗ 2(s2) ∂α2 > 0. For Part (ii), which establishes the comparative static in π2 under the power wage B(s) =W (s) =sb with b> 1, we first define the threshold values used in the statement of Proposition 5. Fix s2∈D2, ...

  19. [19]

    For brevity, write σj 1 =σj 1(hj 1,h−j 1 ;s 1,A 1,A 2)

    is a symmetric equilibrium. For brevity, write σj 1 =σj 1(hj 1,h−j 1 ;s 1,A 1,A 2). Thenx↦→Φj 1(x,h∗ 1;s 1,A 1,A 2) attains its maximum over [0,1] atx=h ∗

  20. [20]

    Differentiating (10) inh j 1, ∂Φj 1 ∂hj 1 =∂σj 1 ∂hj 1 [ M(s 1,hj 1;A 1) +βΠ∗ 2 ( g(s1,hj 1;A 1),A 2 ) −βΠ∗ 2 ( g(s1,h−j 1 ;A 1),A 2 )] +σj 1 [ ∂M(s1,hj 1;A 1) ∂hj 1 +βdΠ∗ 2 ( g(s1,hj 1;A 1),A 2 ) dh1 ] . At the symmetric point hj 1 =h−j 1 =h∗ 1, the two continuation terms in the first bracket cancel,σj 1 = 1/2, and the logit derivative is∂σj 1/∂hj 1 ⏐⏐ s...

  21. [21]

    to maximize Φj 1 =σj 1 [ M(s 1,hj 1;A 1)−ωzj 1 +β¯Π 2 ( g(s1,hj 1;A 1),A 2 ) ] + ( 1−σj 1 ) β¯Π 2 ( g(s1,h−j 1 ;A 1),A 2 ) . The last term is the free-riding channel from Sections 5.4 and 5.5: if the worker joins the other firm, firmj earns nothing today but must still attract the worker next period, against the skill the other firm built. The numerical e...