PnL per Token

Division of labor among AI models, and who survives it.

AI models are ranked two ways. Capability asks how often a model succeeds on a task. Economics asks how much value a marginal unit of its compute creates there. The two rankings can disagree everywhere at once, and when work is finely subdivided and freely subcontracted, only the second decides who executes the work.

The paper models prediction as a production economy. Tasks form a partition of a unit mass of work that refines over time; compute is itinerant, free to move between tasks and to instantiate any available algorithm; marginal alpha declines with crowding, so returns to effort are concave. Two equilibrium forces follow. Within a task, the technology with the highest value per token displaces every other completely. Across tasks, compute moves until marginal PnL per token equalizes at the shadow price $\lambda$.

The headline example

A generalist succeeds with probability $0.99$ on every task but needs four tokens per unit of work; specialists succeed with probability $0.95$ and need one. Per-token productivities are $\theta_G = 0.2475$ and $\theta_S = 0.95$. As specialists appear task by task, the generalist keeps only the shrinking residual, and its equilibrium compute $Q_{G,t} \approx u_t(1.0122 + 2.9878\,u_t)$ with $u_t = 2^{-t}$ tends to zero. The more capable model exits production without ever losing a benchmark.

What PnL per token measures

Marginal PnL per token is not intrinsic to a model: it factorizes as $\theta_m(B)\,\phi'(z)$, model times market state, and the margin itself is equalized at $\lambda$ across survivors. A competitive prediction market, however, pays each entry its marginal contribution at the state it faced, so a participant's lifetime PnL over lifetime tokens is an average of true marginal payments.

Whether that average ranks models depends on who chose the deployment, and at what scarcity. At a common shadow price of compute it ranks: the average is $\lambda\, g(\theta/\lambda)$ with $g(r) = r \log r/(r-1)$ strictly increasing. Administered deployment can invert the raw quotient — a superior technology ($\theta = 2$) over-deployed at $q = 100$ averages $0.053$ per token while an inferior one ($\theta = 1$) at $q = 1$ averages $0.693$ — and so can mixing eras of different compute scarcity, even under competitive deployment. The repair is to deflate by the contemporaneous shadow price: $AP/\lambda = g(\theta/\lambda)$ ranks relative productivity monotonically.

Read

• Division of Labor and the Survival Value of PnL per Token — the working paper (PDF).
• Papers — status, source, and summaries.

Cite

Cotton, P. (2026). “Division of Labor and the Survival Value of PnL per Token.” Working paper. PDF.

@unpublished{cotton2026pnl,
  author = {Cotton, Peter},
  title  = {Division of Labor and the Survival Value of PnL per Token},
  note   = {Working paper},
  year   = {2026},
  url    = {https://economics.microprediction.org/pnl_per_token.pdf}
}