First, there is a mathematical limit to the predictive accuracy based on some complex factors; the entire set of market data is incomplete in a mathematical sense (or not perfectly modelable as a matter of algorithmic tractability), so perfect prediction should never be expected. Second, if you had two agents with perfectly symmetric capabilities in this regard, they would take equal shares of the market from other players but would be incapable of beating the other -- a stalemate. They would also be able to detect that another agent of similar capacity was playing the market without explicit knowledge of this fact. Third, theory generally shows that minor asymmetries (as one would expect to find in real life) decide decisively in favor of one or the other in a given domain over time. Fourth, everybody who plays in the market becomes a part of that system. Having to compete directly with other machines of similar intelligence makes modeling the system much more difficult because of the complex and relatively unpredictable (as required by math) consequences of the behavior of the other systems. They can manipulate "stupider" systems (like humans or lesser machines) with ease.
There are a lot of complex caveats here. Implementing tractable algorithms requires complex and clever trade-offs that impact efficacy in subtle but important ways.
Didn't we see something like this a few years ago with the automatic hedging programs?
No. The state-of-the-art for hedge funds ranges from limited and narrow to downright crude, mathematically speaking. That one can compute the mathematical limit of prediction of some dataset and create a model of said dataset that can make predictions that converge on that limit in terms of accuracy has been known for fifteen years. The problem is that the algorithm to create an "optimal universal predictor" is well-known to be intractable for anything but the simplest toy systems. And it turns out that the problem of engineering highly efficient approximations of this algorithm is very non-trivial, which is why it took a decade for researchers to start to figure out the nature of a clever general algorithm that can approach the predictive behavior and capability suggested by the math.
The hedge funds are very aware of these maths. They are most eager to get their hands on this technology because they understand the implications. And one (or more) of them may end up getting it.
The ability of mutiple entities to predict the future will diminish the effectiveness of all similar systems, because, in a competetive marketplace, all will be attempting to predict each other's behavior.
Yes, you would end up with an extremely efficient market with very thin margins, as the market would end up highly optimized in an information theoretic sense. But there is a first mover advantage here. You can expand the predictive accuracy of your system by buying bigger hardware and more mature model. Wash, rinse, repeat. As long as the first guy aggressively reinvests in his bootstrap, no one is likely to catch him. By the time anyone notices, competing could already be extremely prohibitive in terms of the resources required to catch up.
It is a very interesting thing, both in terms of theory and the practical ramifications. A deployed implementation in full bootstrap mode would in a very real sense be Archimede's lever; you hope that relatively nice folks win that race.
I don't have the mathematical background to argue this at your level, but I think there is something missing from your analysis. I think that something is novelty.
There are all kinds of words and phrases labeling what I am trying to get at, but I think "emergent properties" might suffice.
We cannot predict the future because, contrary to aphorism, there are new things under the sun, things that cannot be anticipated from the properties of known things.