This paper just gets me every time I see it.<p>It really doesn’t claim or do much that isn’t already quite obvious (it also has the other problem of going on completely unrelated tangents.)<p>First, it does this funny thing where it “proves” that EMH (or market efficiency) is NP-hard, by building gadgets based on options and then using them to “embed” 3-SAT. This is fine except (a) we often don’t care about an exact solution (so we need approximation-hardness that isn’t shown) and (b) I can come up with millions of other obvious things like this! Here’s a silly one one: I give a derivative whose price is $1 if a solution (that is known to exist) to an NP-hard problem is found by a given time. This will “show the NP hardness of EMH” because obviously the derivative price should be 1 (the problem has a solution, by construction) and so anyone should “obviously” price it at $1.<p>This is like saying “life is NP-hard.” Like, yeah, of course it is. That doesn’t mean we aren’t pretty good at doing the right thing and rationality (like EMH) is a good, if imperfect tool to analyze behavior. Taking it to its extreme then everything breaks, because the model is wrong. We don’t throw up our hands and quit because making real-life decisions is a sampling-hard, query-hard, and NP-hard problem (if all data is known), but a basic model of rationality would say that humans can “perfectly” solve it. (Which is obviously crazy, but we obviously don’t throw the assumption of rationality of agents out the window because of this.)<p>Otoh, I am definitely of the opinion that some economists hold EMH as a “magical” axiom, but that’s a different story.
The report, while a fun thought exercise for any aspiring academic, is not a novel insight, and is obviously untrue for most definitions of market efficiency.<p>If we are going to play the academic one-upmanship game, a more general result that "best" or "multiple" N-player Nash Equilibria for N > 2 is already NP-hard. The implication of an efficient market would be if every player had a polynomial-time algorithm to solve the NP-hard problem, ergo P=NP.<p>[1] <a href="https://people.csail.mit.edu/costis/simplified.pdf" rel="nofollow">https://people.csail.mit.edu/costis/simplified.pdf</a><p>[2] <a href="https://www.quantamagazine.org/in-game-theory-no-clear-path-to-equilibrium-20170718/" rel="nofollow">https://www.quantamagazine.org/in-game-theory-no-clear-path-...</a><p>[3] <a href="https://arxiv.org/abs/1104.3760#:~:text=Unlike%20general%20Nash%20equilibrium%2C%20which,as%20finding%20a%20planted%20clique" rel="nofollow">https://arxiv.org/abs/1104.3760#:~:text=Unlike%20general%20N...</a>.
If curious see also<p>2018 <a href="https://news.ycombinator.com/item?id=17202950" rel="nofollow">https://news.ycombinator.com/item?id=17202950</a><p>2012 <a href="https://news.ycombinator.com/item?id=4589264" rel="nofollow">https://news.ycombinator.com/item?id=4589264</a><p>2011 <a href="https://news.ycombinator.com/item?id=2895474" rel="nofollow">https://news.ycombinator.com/item?id=2895474</a><p>Discussed at the time: <a href="https://news.ycombinator.com/item?id=1144548" rel="nofollow">https://news.ycombinator.com/item?id=1144548</a><p>and <a href="https://news.ycombinator.com/item?id=1124782" rel="nofollow">https://news.ycombinator.com/item?id=1124782</a> (a bit)
Markets are obviously not efficient. The proof is trivial. Have you ever made a mistake? Congrats, that’s your proof. The market is a collection of people making decisions. People are capable of mistakes. People en masses are still people, and just as fallible, if not more. Thus, markets can and constantly do misprice things/inefficiently allocate capital.<p>These real events are incompatible with perfectly efficient markets:<p>* tulips<p>* Bitcoin<p>* google (billion dollar startups)<p>* crashes<p>* theranos<p>* salem witch hunts<p>that’s not to say markets are perfectly inefficient either. But they’re clearly fallible and imperfect. They clearly misinterpret available information all the time, even though they easily could’ve interpreted it correctly. Markets are full of emotion driven irrational actors, not Bayesian robotic egoless predictors, even though we like to pretend we’re the latter sometimes.
How much does this matter given that in the vast majority of cases, we don't care about exact/perfect solutions to problems that might be NP complete in the general case, but usually have heuristic methods that work well enough for most practical purposes?
The only if is clear but the if side seems to be assuming that P=NP entails not just proving the existence of polynomial time solution algorithms but also constructing said algorithms?
... you can't prove mathematical theory with social science 'theories'. The latter is not even well defined.. ln(x) \approx x (for interest rate)? common...
P==PN on analog photonic machines. A light prism calculates Fourier in O(1) (given a prism is not aware of Big O). Using Fourier, one can factorize a number in O(1), and then solve NP in P.