The crazy thing is that unlike a weather forecast, if people start to trust your economic forecast, then their actions will likely throw it off again, so your new forecast then needs to include the reactions to the first forecast (and other forecasts) and so on, sorta like solving coupled differential equations (or the plot of Dune, with "levels" of prescience). Hopefully you'll get some fix point at the end, e.g. via a Nash equilibrium, where a new forecast doesn't change anybody's reaction any more.
Let's assume the forecast is sufficiently coarse, just economy will go up/down/stay as is. Now you can just compute the future based on the past plus the reaction to your forecast, for each of your forecasts. That gives you three pairs of (announced prediction, predicted outcome). Now choose any where announced prediction == predicted outcome. This leads you to the same Nash equilibrium that you described, with a simpler model. Of course it's now obvious that an equilibrium is far from guaranteed. If reactions were distributed like dice rolls, 12.5% of days don't contain any equilibrium. I guess at that point just choose whatever leads to the desired outcome (lots of opportunity for "insider trading" here).
With a more detailed forecast you need a better approach like you described. I just found the limited case easier to reason about.
Yep, it's interesting to wonder about the implications of that. Maybe the only reachable fix-point would be economic disaster, i.e. 'the only way to be right with certainty is to get people to panic by telling them they'll panic'. At least it's much easier to imagine a stable negative feedback-loop than a positive one.
I've read Soros' work on this idea, he described it as 'reflexivity'. It's a meaty problem that, from my limited point of view anyway, keeps investing from being a trivial exercise. Every bet one takes on the future of the market going a specific direction changes the order-book, and thus the market direction.
There probably is no fixed point, however: imagine a game with two players, the hunter and the prey where the turn consists of choosing whether to go place A or to place B. If both players end up in the same place, the hunter wins, otherwise the prey wins. Keep revealing to them the other player's decision, and they will keep adjusting their decisions without ever reaching any fixed point because logical negation doesn't have a fixed point. So I would wager this result generalizes to almost any antagonistic game.
> where a new forecast doesn't change anybody's reaction any more
That's the original proposition I was working with. Obviously, if the amount of published forecasts finite, then the amount of decision changes in response to such publications will be finite too.
Now that I think about it, a forecast that causes nobody to change any plans is pretty useless and is effectively indistinguishable from the trivial "empty" forecast which got to be the unique fixed point of this whole forecasting exercise.
Yeah, the forecast itself has to factor the changing of plans, e.g. don't pick a solution that won't get picked. If there is low trust placed onto the forecasting system, then no viable solutions is the only answer. There is a scale of influence to it as well, if the forecaster is giving a forecast to someone who can only purchase $1000 worth of shares, that won't influence the economy in any meaningful way. Someone with a $1B dollars who can actually present adversarial strategies to other players in the market? A lot less opportunities can be presented (assuming other players also have a forecaster), and a lot more trust in the forecaster would be required. Equilibrium only exists if everyone wins, and moreover, everyone is satisfied with the victory that they have been given.
It's all based on trust though, if one forecaster suspects that another forecaster has been hacked to optimize profits for that individual player, the equilibrium is broken.
Even with everyone in the world having an all powerful genie, the greed of a few but powerful can ruin the entire thing.
If and when ML agents control the bulk of transactions, it will be interesting to see the emergent oscillations in market prices. After all you'll likely have neural networks which are effectively being retrained daily, no telling what kind of patterns the system might settle on because of the tight coupling you describe.
