Research paper: Markets are efficient if and only if P=NP https://arxiv.org/abs/1002.2284

Can this be used to prove P != NP ?

I am incredibly skeptical of the "iff" statement. How the hell could it be possible that

P=NP -> Markets are efficient.

Because if P=NP the vast array of the majority of known "hard" problem becomes trivial to solve, not just market information. That's the reason P=NP is considered so consequential to society in many ways if it does happen to be true and implementable.

But what about the "P=NP but nobody knows how to do it yet" case.

Which implies that the markets, up to today, aren't efficient. Because nobody knows how to do it yet.

So then it appears it is possible that P = NP and markets are not efficient, so it is not true that "Markets are efficient if and only if P=NP" because P = NP !-> Markets are efficient

For the markets to be efficient today they must calculate P=NP to achieve the solution. Nobody has done that yet. Markets today are inefficient as nobody has implemented P=NP to do the required calculation. Markets in the future could be efficient, but today's ones are not as we have to gauge market value the traditional way with incomplete information and guesstimation and modelling.

But the scientific consensus so far is heavily biased towards the presumption that P!=NP.

I think I understand the sketch of the proof and pretty familiar with the P=NP debate. Perhaps my point is pedantic, and I've also looked at the paper and seen that it doesn't try to prove an "iff" claim, but:

To prove an "iff" you have to prove that Markets are efficient -> P = NP and P=NP -> Markets are efficient . I buy the first claim entirely, but not the second.

Let's assume P really does = NP, but as you've said "nobody has done that yet." Then, markets today must be inefficient, but that is T -> F which is impossible if P=NP -> Markets are efficient □

In lay words, how can it be true that `markets are efficient if and only if P=NP`, if it is possible that `P=NP but markets aren't efficient`.

I think we're on the same page, just different paragraphs. I think I get the gist of your line of reasoning.

Let me try an analogy for the if True case. Gravity (P=NP) exists, and always has. But we didn't understand it a few hundreds of years ago. Before we understood it, we didn't have interplanetary rockets (Efficient Markets). But we do now, and they were never outright impossible before our understanding of delta-v and other aspects. But before we had that understanding, we just straight up didn't have rockets.

Meanwhile if hypothetically gravity was, perhaps stronger or more pervasive over longer distances (P!=NP), it could have stopped interplanetary travel altogether and we would have never have achieved it.

We are just in an equivalent time period to that time in the 1600s before we understood, one way or another, what was ahead of us. If markets can be efficient in the future, they could always have been now and in the past. We just didn't have the tools to figure it out.

Analogy seems roughly right, if it was a statement like "P=NP -> Markets could possibly be efficient" then I'd buy it.

But I think what's more interesting is that

"Markets (present-day) are efficient -> P=NP" could plausibly be true, suggesting that the contrapositive is true: "P!=NP -> Markets (present-day) aren't efficient." Given current state of thought around plausibility of P=NP, that seems pretty powerful nonetheless.

With the slightly stronger statement "Nobody currently possess a polynomial time algorithm to solve a problem in NP -> Markets (present-day) aren't efficient" it starts to become quite likely markets aren't fully efficient.

This is going to be great fodder for some debates, thank you very much.

I’m reminded of some research I tried to get published a while back. One editor comment came back with a suggestion to reject simply with “this appears to contradict the EMH.” No further explanation.

Well, no shit. It said so right in the introduction. I think this is what’s called “theory induced blindness”

The efficient market hypothesis just states the market represents the sum total of all available information.

If everyone thinks stocks will go up, then the efficient market hypothesis would support a bubble.

This is a misunderstanding of the EMH. “Efficient” does not mean “rational” or “always right”. It simply means that, at any time, the difference between actual prices and “rational” prices is random.

It’s important to understand that efficiency is something that markets approximate. The EMH may be more “true” for you than for someone with a dedicated fiber line between the NYSE and the CME.

Here’s Burton Malkiel in more depth about what the EMH actually means: https://www.forbes.com/sites/quora/2014/06/13/what-does-the-...

That actually reinforces my point. For bubbles to occur, the delta between the price and the “rational” price must not be random. In bubbles prices exhibit strong temporal autocorrelation.

Assuming bubbles are real, which is somewhat unprovable. There are careful ways to falsify different formulations of the EMH.

"Bubbles" is not one.

The (strong form) efficient market hypothesis (EMH) doesn't state or require that there be no bubbles. The EMH means that bubbles are extremely hard to predict/see, largely because of the market's feedback loop.

Is there a distinction between an efficient market and a efficient market subject to propagation delays? It would seem that there is a limit to how fast information can be disseminated and the resulting reaction time. The market may always tend towards efficiency at some time scales and not at others.

> Bubbles don't happen in efficient markets.

But how do you know a bubble ahead of time?

Tesla looks like a pretty obvious bubble, but what do I know?

> what do I know?

exactly