The Strategic Cost of Rationality

When predictions influence the outcomes they forecast, learning can become impossible: under adversarial responses, regret against an oracle that knows the response is $\Omega (T)$. We show that learnability is restored when the world is rational, meaning it best-responds to each published prediction by minimizing a convex cost under which acting more becomes relatively cheaper as the prediction rises. Rationality then makes the honest prediction self-certifying: the outcome at any prediction reveals its residual, whose square is the excess loss, and the rational response makes that residual monotone, so it points to a unique honest prediction identified from the data at that prediction alone. This gives regret $\Theta (\log T)$ at every response strength. Self-certification needs an honest prediction to exist, but when the world consists of agents of discrete types it may not: no prediction is calibrated, every learner's loss stays a constant above the noise, and zero bias and accuracy can no longer both be achieved. The same rationality that makes the world learnable also makes it predictable enough to steer. A learner with a stake in the outcome gains by steering it: at the honest prediction its marginal incentive splits into conflict of interest and manipulation in the ratio $1:\epsilon$, where $\epsilon$ is the elasticity of the world's response, and manipulation adds harm to users, beyond what a learner ignoring its influence would cause, exactly when $\epsilon >0$. But steering moves the learner away from the one prediction that certifies itself. The strategic target depends on the slope of the world's response, whereas the outcome at that target reveals only its level, so when the fundamental is unknown, learning the strategic target costs $\Theta (\sqrt{T})$ rather than $\Theta (\log T)$. Rationality thus makes honest prediction self-certifying, but leaves a strategic learner needing information its own outcomes do not reveal.