Markets become increasingly inefficient

Here's a summary of some popular economic reasoning: Market Efficiency is a good thing. Efficiency makes things possible. Markets are efficient because the more people involved in a market the harder it is to beat the other people in the market. Efficient markets mean that you can't do better than a market at getting the people with the needs exchanging with the people with the supplies - it's a mutually beneficial relationship. Everyone benefits in a market, but no one benefits unfairly because they are just naturally efficient.

Here's a mathematician's point of view on this reasoning: Markets are efficient if and only if P = NP.  "Specifically, markets become increasingly inefficient as the time series lengthens or becomes more frequent."

Um... so?

Basically, Philip argues that if markets are such great problem solving machines, he's got a whole bunch of unsolved math problems that he could use the market to solve. In other words, the math behind "market efficiency" is mathematically implausible.

Now, I could go on to explain how "the knapsack problem" (that's what the P = NP thing refers to) is like a competitive buying decision. Here's an example of the problem: "I pay $x to go into a bank vault and pick up small jewelry boxes, each worth a different amount $y and put them in my knapsack. I can keep them if I choose the most valuable combination that fits in my knapsack. $x is known ahead of time, and so is the N - number of jewelry boxes, and $y is at least N * $x, and my "knapsack" is big enough to hold M boxes where M*M is at least N and no larger than N+1.  And, I have N minutes to make my decision, before I have to leave."  If the efficient market hypothesis is valid, this would always be a good deal. But that's a trick question because while it initially seems like a good deal once you add enough jewelry boxes it starts becoming a really hard problem. (It's also a trick question because you would eventually die of old age rather than being able to take full advantage of your allotted time.)

Isn't that a stretch?

I mean, markets are not really like that. You don't have to be "best" to be competitive, you just have to be "better". I don't have to be faster than the bear, I just have to be faster than you.

Except, that was the point. Or part of it.

In other words, from a mathematicians point of view, these kinds of things make markets inefficient:

• High frequency trading
• Long periods of time
• Lots of competition

Wait, what? 

But it's not really like that, right? I mean, people simplify things and ... Actually, this argument can go on and on. But when we look at how poor people live their lives, we see that markets have not been very great for things like health care (where long term health matters the most), child raising (where the time it takes to raise a child is significantly longer than the financial planing cycles of some of the best and brightest companies), and so on. In other words, it's probably no coincidence that many of the budgeting woes of the U.S federal government are associated with its healthcare program.

But that's not all. Other relevant issues include:

Value is not conserved. If no one buys that cabbage, it will eventually rot. And, on the flip side, some time ago that cabbage did not exist.  (But wait, if people could really create value that did not exist before, somebody would be getting rich off of the idea. So that can't be right?)

Currency. I'm going to save that topic for a future blog post on "value coupling". But my current impression is that the problems with the fed are real, are crucially important, and are radically different from what fans of gold, (or bitcoin) currency have been representing them as. (There are superficial similarities, but superficial similarities are what give us a system where, quoting a doctor I know: "I think that it is very sad that I can deliver a baby, and very little will be spent on his education, he may live in an impoverished home and never learn good communication skills that allow him to work and succeed. But, if he's in a car accident because a drunk driver hits him and he ends up in the ICU, suddenly his life is worth $200,000, or even $2 million." Though, of course, inflation will eventually change those numbers.)

Update: I went on an image search, to find examples of the sort of high frequency trading which my intuition suggests to me are examples of the sorts of market inefficiencies I describe here.  I found:

• http://www.marketoracle.co.uk/Article34534.html
• http://www.metamute.org/editorial/articles/destructive-destruction-ecological-study-high-frequency-trading
• http://www.postmedialab.org/destructive-destruction-ecological-study-high-frequency-trading

I did not find the article I was looking for. I do not know how relevant the reasoning is in these articles. But I do feel that the complexity of the trades illustrated in these articles represent artificially induced market inefficiencies.