[em70]

This paper is rubbish. Trading is ultimately a partial information, sequential game with an unknown number of participants whose payoff functions (and utilities) are also unknown. Could the market be closer to being efficient if P=NP? Likely. Does P=NP imply efficiency? Not at all.

[argv_empty]

On top of that, the argument rests on the kind of error you expect to see freshmen making in a discrete math course:

> The basic argument is as follows. For simplicity but without loss of generality, assume there are n past price changes, each of which is either UP (1) or DOWN (0). How many possible trading strategies are there? Suppose we allow a strategy to either be long, short, or neutral to the market. Then the list of all possible strategies includes the strategy which would have been always neutral, the ones that would have been always neutral but for the last day when it would have been either long or short, and so on. In other words, there are three possibilities for each of the n past price changes; there are 3n possible strategies.

There are 2^n possible histories of length n. If a strategy maps each history to one of three positions, there are 3^(2^n) strategies that consider n bits of history.

[kizer]

Why wouldn't it be 3^n? Edit: wait, it's because bitstring -> strategy is a function, right?

[argv_empty]

Yes. Mapping from 2^n bitstrings to 3 market positions.

[kizer]

Thanks.

[danbruc]

Is it even theoretically possible to show that markets are efficient on purely theoretical grounds? As a thought experiment, imagine that all human brains have a weird defect that causes them to always ignore some specific kind of information when making pricing decisions, including when they write software dealing with those decisions, and under all other conceivable circumstances. In that case, it seems to me, it would be impossible to decide on purely theoretical grounds that markets are efficient because it strictly depends on the empirical observation that human brains have this weird defect. I could imagine the other way around to work, i.e. that there could be an obstruction to markets being efficient that can be shown to exist on purely theoretical grounds. But no matter what the answer to the second question is, in no case could you arrive at an »if and only if« result without including the empirical observation that brains do not have this weird defect.

[epr]

The entire premise of this paper is complete nonsense, and serves only to demonstrate the authors complete lack of understanding when it comes to the subject of markets.

"Trading is ultimately a partial information, sequential game with an unknown number of participants whose payoff functions (and utilities) are also unknown."

Markets in general are essentially an infinitely-armed bandit problem where everyone plays whether they know it or not, and resources are allocated over time in a manner not unlike evolution.

[naasking]

You seem to be missing the point. Markets were and possibly still are widely considered weak-form efficient. This is a disproof of that conjecture by showing an inherent contradiction between widely believed properties, ie. P!=NP and markets are weak-form efficient, therefore at least one of them is false.

Edit: "Does P=NP imply efficiency? Not at all." This isn't even a claim of the paper. The paper is claiming the opposite, that market efficiency is true only if P=NP.