Maybe you've ever seen the cool proof that "Tetris is NP-complete". I loved the paper and it was very entertaining. But it involved a much broader and general Tetris problem than the one found in Nintendo Gameboys, because the width and the height of the pit in the reduction was larger than all the console based tetris games I've ever seen.
My understanding is that Gameboy tetris, given the sequence of all future blocks as input and an empty pit starting state, is actually easy to solve computationally.
Similarly, I have to believe that the market as we know it contains some constraints, and all the historical data will abide by those constraints. To show the market problem is NP-hard, you would need all 3-SAT reductions to lead to a valid market problem. Going back to Tetris, IIRC, a large number of the reductions would lead to Tetris games that could not exist on Gameboy Tetris, because you would need a block-pit that is far taller than the game allows.
I think I'm following now. You're saying that the author is assuming a model of economies that is more complex than an actual economy. That could be the first time ever that I've heard such a thing about any model, let alone of an economy. :-)
The only assumption that I see him making is the weak form of the Efficient Market Hypothesis.
I'm curious...how do you feel about that hypothesis, anyway? I've thought the EMH was a pretty strange and obviously false hypothesis ever since I first heard of it in the 80s (in college).
Just look at this statement from the Wikipedia page on the subject: It is the assumption "...that prices on traded assets already reflect all available information, and instantly change to reflect new information." This is a flimsy foundation to build on, because it's assuming the instantaneous propagation of information between economic actors. By what mechanism? Quantum entanglement? Crazy action at a distance?
I realize it was probably first intended in the same way that one uses a point-mass in physics ("we know it can't exist, but it makes the math easier") but I don't think it's quite as harmless as that.
Anyway, I'm happy to see the author taking such a clever swing at it.
My understanding is that Gameboy tetris, given the sequence of all future blocks as input and an empty pit starting state, is actually easy to solve computationally.
Similarly, I have to believe that the market as we know it contains some constraints, and all the historical data will abide by those constraints. To show the market problem is NP-hard, you would need all 3-SAT reductions to lead to a valid market problem. Going back to Tetris, IIRC, a large number of the reductions would lead to Tetris games that could not exist on Gameboy Tetris, because you would need a block-pit that is far taller than the game allows.