Yes, if predictors can influence the world in addition to making a prediction, they can go make their predictions more accurate. The nice thing about working with predictive models is that by default the only action they can take is making predictions.
AI safety via market making, which Evan linked in another comment, touches on the analogy where agents are making predictions but can also influence the outcome. You might be interested in reading through it.
Yes, if predictors can influence the world in addition to making a prediction, they can go make their predictions more accurate. The nice thing about working with predictive models is that by default the only action they can take is making predictions.
AI safety via market making, which Evan linked in another comment, touches on the analogy where agents are making predictions but can also influence the outcome. You might be interested in reading through it.