💰 quantitative finance

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

This paper develops a two-period model demonstrating that while firms in isolation engage least-skilled workers as a fallback against AI failure, worker mobility reverses this pattern by incentivizing engagement of higher-skilled workers to build valuable future human capital.

Original authors: Simrita Singh, Naireet Ghosh, Tinglong Dai

Published 2026-06-30

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Simrita Singh, Naireet Ghosh, Tinglong Dai

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Core Problem: The "Safety Net" Dilemma

Imagine you are a coach for a soccer team. You have a new, incredibly advanced robot player (AI) that is faster and more accurate than your human players.

The robot is great, but it’s not perfect. Sometimes it glitches, gets confused, or simply isn’t available. When that happens, you need a human player to step in and save the day. This human is your "fallback."

The paper asks a tricky question: How much should you let your human players practice?

If they practice a lot: They stay sharp and ready to step in when the robot fails. But, while they are practicing, they aren’t letting the robot do the work. Since the robot is better, the team’s current performance drops. You are paying for practice that hurts today’s score.
If they don’t practice: The robot does all the work, so today’s score is high. But, if the human players sit on the bench too long, they get rusty. Their skills erode. If the robot fails later, they might be too weak to help.

This is the "Human Fallback" problem. You are trying to balance today’s output against tomorrow’s safety net.

Scenario 1: The Island Firm (No Job Hopping)

First, the authors imagine a world where workers can’t quit and go to another company. They are stuck with you.

In this world, you only care about keeping the robot’s backup ready.

Who do you train? You train the weakest players.
Why? The weakest players have the most room to improve. A little bit of practice goes a long way for them. The strongest players are already good enough to be a fallback, so spending money to train them further is a waste. You just want them to be "good enough" to catch the ball if the robot drops it.

The Result: You invest heavily in the least skilled workers to keep them from getting too rusty.

Scenario 2: The Open Market (Workers Can Quit)

Now, imagine workers can quit and join a rival team. This changes everything.

Workers don’t just care about the current game; they care about their career trajectory. They want to join a team that makes them better, because being better means they can get a higher salary later (even if they leave your team).

This creates a new motive called "Sorting." You aren’t just training them to be a fallback for your robot; you are training them to be attractive to the labor market.

Who do you train now? Surprisingly, you start training the strongest players (those closest to the robot’s skill level).
Why?
1. Cost: Training a weak player is "expensive" in terms of lost productivity because the robot is so much better than them. Training a strong player is "cheaper" because they are already close to the robot’s level.
2. Value: A strong player who gets even stronger is very valuable in the job market. If you help them grow, they are more likely to choose your team over the rival team.

The "Engagement Reversal":
This is the paper’s big finding.

Without job hopping: You train the weakest workers.
With job hopping: You train the strongest workers (below the robot’s level).

The direction of your investment flips completely based on whether workers can leave.

The Two Knobs of AI Progress

The paper also looks at how AI improves. AI gets better in two ways:

Capability: How good the robot is when it works (e.g., it scores more goals).
Reliability: How often the robot works without glitching (e.g., it rarely breaks down).

1. Capability (Getting Smarter)
If the robot gets smarter, you actually increase training for your workers (in the open market). Why? Because a smarter robot raises the bar. To stay competitive and attractive to workers, you need to offer a steeper learning curve. You want to show workers, "Join me, and I’ll help you reach this new, higher level."

2. Reliability (Getting More Stable)
This is tricky.

If the robot is unreliable (glitches often), workers have lots of chances to practice when the robot fails. They learn a lot.
If the robot is perfectly reliable (never glitches), workers never get to practice. They get rusty.
If the robot is too unreliable (glitches all the time), it’s barely worth having a robot at all, and the team’s performance suffers too much.

The Result: Training is often highest at medium reliability. You want the robot to work most of the time (so you make money), but fail just enough so the humans get practice. If the robot becomes too reliable, you might actually have to force humans to practice more to keep them from forgetting how to play.

The "Free Rider" Problem

Finally, the paper looks at what happens when two identical teams compete.

Because skills are portable (a player can take their skills to the other team), one team might decide: "I’m not going to spend money training anyone. I’ll just wait for the other team to train their players, and then I’ll hire those skilled players away."

This is called free-riding.

One team becomes the "Skill Builder" (spending money to train).
The other team becomes the "Free Rider" (saving money, but stealing the trained talent).

In some cases, the Free Rider actually makes more profit than the Builder, because they get the benefit of skilled workers without paying for the training. This shows that in a competitive market, companies might under-invest in training because they can’t keep all the rewards of that training.

Summary

AI is a tool, but it’s imperfect. Humans are the backup plan.
Training hurts today’s score but helps tomorrow’s safety net.
If workers can’t quit: Train the weakest people to keep them from getting rusty.
If workers can quit: Train the strongest people to attract them and keep them happy.
AI getting smarter makes training more valuable.
AI getting more reliable has a complex effect: too reliable, and humans forget how to work; too unreliable, and the business loses money. The sweet spot is in the middle.

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

1. Problem and Motivation
The paper addresses the strategic decision firms face when deploying autonomous AI systems: determining the optimal level of human engagement in AI-assisted tasks. While AI often outperforms workers on routine tasks, it is imperfect and may fail or encounter edge cases. Consequently, human workers serve as a "fallback." However, sustained reliance on AI can lead to skill erosion (deskilling), while active engagement preserves and builds human capital.

The authors argue that this decision is not merely an operational trade-off between current output and future fallback capacity but also a human-capital investment problem influenced by labor market dynamics. Specifically, when workers are mobile and wages are standardized (preventing firms from competing solely on pay), firms must compete by offering jobs that build valuable skill trajectories. The paper investigates how the interplay between AI progress (defined by capability and reliability) and worker mobility reshapes firm engagement policies.

2. Methodology
The authors develop a parsimonious two-period analytical model ( $T=1, 2$ ) featuring a continuum of workers with initial skill $s_1$ and a firm employing an AI system with technology level $A_t$ .

AI Technology: AI progress is modeled along two distinct dimensions:
- Capability ( $\alpha_t$ ): The effective throughput of the AI when it functions.
- Reliability ( $1-\pi_t$ ): The probability that the AI functions; $\pi_t$ is the failure probability.
- Assumption: Technology improves over time ( $A_2 \ge A_1$ ), implying $\alpha_2 \ge \alpha_1$ and $\pi_2 \le \pi_1$ .
Production and Engagement: The firm chooses an engagement level $h_t \in [0,1]$ . For workers below the AI benchmark ( $s_t < \alpha_t$ ), engagement lowers current operational revenue because the AI is more efficient. However, engagement affects future skill.
Skill Dynamics: Skill evolves via a transition function $s_{t+1} = g(s_t, h_t; A_t)$ $s_{t + 1} = g (s_{t}, h_{t}; A_{t})$ . This function captures two opposing forces:
- Erosion: Passive reliance on AI reduces skill, proportional to the gap $(\alpha_t - s_t)$ and the lack of engagement.
- Learning: Active engagement builds skill, proportional to the gap $(\alpha_t - s_t)$ and the interaction between AI functioning and failure ( $\pi_t(1-\pi_t)$ ), reflecting that learning requires both exposure to AI and practice in fallback scenarios.
Labor Market and Mobility:
- Wages: Workers receive a market-clearing wage $W(s_t)$ , which is strictly increasing and convex in skill. Firms cannot offer idiosyncratic wage premiums.
- Sorting: In the mobility scenario, two ex ante identical firms compete for workers. Workers sort based on the expected skill trajectory (and thus future wages) offered by each firm’s engagement policy. This sorting is modeled using a logit choice framework with a friction parameter $\eta$ .

3. Key Contributions and Results

The paper derives three main findings by comparing a single-firm benchmark (no mobility) to a competitive market with mobile workers.

A. The Engagement Reversal (Targeting of Workers)

Single-Firm Benchmark (Fallback Motive): Without mobility, the firm engages workers only to preserve fallback skill for when AI fails. The firm targets the least-skilled workers. These workers have the largest skill gap to close, meaning a unit of engagement yields the highest marginal skill gain at the lowest marginal wage cost. Engagement is non-increasing in initial skill.
With Mobility (Sorting Motive): When workers can move, firms also engage to attract talent by offering superior skill trajectories. This "sorting motive" targets higher-skilled workers near the AI frontier. For these workers, the portable skill built is more valuable in the labor market (due to convex wages), and the operational cost of engagement is lower (smaller skill gap).
Result: Worker mobility can reverse the engagement pattern. Instead of focusing on the least-skilled, firms may shift investment toward the most-skilled workers below the AI benchmark.

B. Divergent Effects of AI Progress
The paper distinguishes between AI capability and reliability, showing they affect engagement differently under mobility:

Capability: An increase in AI capability ( $\alpha$ ) raises engagement under mobility. A more capable AI widens the performance gap, allowing workers to learn more from engagement, thereby strengthening the skill trajectory the firm can offer as a competitive draw.
Reliability: The effect of reliability ( $1-\pi$ $1 - π$ ) is non-monotonic.
- Higher reliability reduces the need for fallback skill (lowering engagement).
- However, learning is strongest at intermediate reliability (where AI works often enough to be useful but fails often enough to require practice).
- Consequently, engagement may be highest at intermediate reliability. If AI is too reliable, there is no fallback practice; if too unreliable, the operational cost of failures outweighs the learning benefits.

C. Impact of Mobility on Investment Levels and Equilibrium Structure

Investment Levels: Consistent with Becker’s (1962) theory of general training, mobility generally depresses investment because firms cannot fully appropriate the returns to portable skill. When workers respond weakly to skill trajectories (high sorting friction $\eta$ ), engagement falls below the single-firm benchmark.
Timing Reversal: Mobility can reverse the timing of engagement. A firm might disengage a worker in Period 1 (to avoid spillover costs) but fully engage them in Period 2 (the terminal period) to attract them for the final horizon, a pattern not seen in the single-firm case.
Asymmetric Specialization: The model allows for asymmetric equilibria where ex ante identical firms differentiate. One firm may specialize in building skill (high engagement), while the other free-rides on the portable skill built by the first firm (low engagement). In such cases, the free-rider can earn higher profits despite offering a weaker skill trajectory, as it avoids the cost of training while still accessing the skilled labor pool.

4. Significance and Implications
The authors claim this work is among the first analytical models to integrate the dynamic skill consequences of AI-assisted production with labor market sorting under wage standardization. By treating human-AI work design as a human-capital investment problem, the paper highlights that:

Operational efficiency is not the sole driver: Firms must balance current output against future skill preservation and labor market competitiveness.
Policy nuances matter: Treating AI progress as a single index is insufficient; capability and reliability have distinct, sometimes opposing, effects on human engagement.
Mobility changes the game: The presence of mobile workers shifts the target of skill investment from the bottom of the skill distribution (fallback) to the top (sorting), fundamentally altering how firms manage human capital in the age of improving AI.

The framework provides testable predictions for settings where task-level human-AI allocation and worker movement can be observed, such as software development, radiology, and autonomous driving.