What are the externalities of predictions on wars?

This depends on who's predicting, who's listening, and various actors' models of how other actors will react to the prediction. For this reason, it's very hard to accurately predict conflict type and severity - this is not completely zero-sum, but it's close enough to be anti-inductive.

Conditional predictions about who will be hurt by how much for wars _might_ reduce the chance of wars. Better knowledge of how badly one will lose (or be hurt in a win) can certainly lead participants to be more willing to submit rather than fighting.

My prior is that predictions are useful in general, and I have the impression this is also true for wars in general too, but I have no idea really, I just spent a few minutes thinking about it.

And I imagine it changes depending on the war dynamic. For example, predictions on mutually assure destructions would probably escalate really quickly (although not sure where it would stabilize; not necessarily high). Reason: If a prediction market predicts with slightly too high probability that a great power will do a nuclear first strike, predictors will slightly update that the other great power might also do a first strike to avoid being the recipient of a first strike, etc. in a way that can spiral and overall increase the risk of a first strike.

On the other hand, if a prediction markets signal wars would be more likely if countries had less economic trades with each other, then predicting this would be useful to inform countries to increase economic trades, and hence reducing the risk of wars.

I think it depends on the amount of money involved in the predictions! If the reward for correct predictions is high enough, people with political power might be incentivised to perform a military version of 'insider trading' and escalate/call off a war.