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Markets are competitive if and only if P != NP
- xxpor 3mo agoThe actual paper's title is "Markets are competitive if and only if P != NP" Seems that HN's auto-headline rewriting in this case has made a critical error :) >Artificial intelligence, by expanding firms' computational capabilities, is pushing markets from the competitive regime toward the collusive regime, explaining the empirical emergence of algorithmic collusion without explicit coordination. I have to dig more into the paper but I don't see how this follows, except in the most straightforward way. Basically, if everyone uses the same methods to derive price, of course there will be "collusion", or in other words, everyone will have the same price. But this doesn't seem like a result of compute per se, but simply better communication networks and information flows. You could have gotten the same result in medieval England by having everyone post their selling prices on the town square board. Again, I haven't dug into the paper yet, but it seems like what really matters for firms is "compute"/$ (if the "compute" is an LLM or an assistant that has to go walk the 10 minutes down to the square makes little difference) Edit: Isn't another implication of this, that increased compute -> collusion imply that increased compute -> communism becomes feasible? I think this goes to my point above though, the primary problem preventing fully automated luxury communism isn't compute per se, but actually observing the information flows to make it possible. Capitalism famously solves this information problem through the pricing mechanism. So in effect, he's arguing that extra compute makes information gathering more efficient, and at the limit you get perfect information. Which, yeah, I guess so. Assuming everything can be perfectly measured, even theoretically.
- btown 3mo agoHN is competitive if and only if != != =
- derektank 3mo agoYeah, the most obvious recent example of this is RealPage’s YieldStar product. It advised property managers on what they should set their rental rates to, and allegedly established a cartel in which RealPage’s customers coordinated in pricing their units. YieldStar was technically an “AI” product, but I don’t really think the computational abilities were what enabled the collusion. RealPage’s employees (according to the DoJ[0]) would actively monitor whether companies were following their pricing recommendations and call up companies that defected. And the software itself used dark patterns to make it easier to simply follow the YieldStar pricing suggestions, rather than set a lower rental rate and be more competitive. The algorithmic pricing I think did allow people to launder their own judgement and simple “trust the process” in a way that in the past would have required knowing complicity with the cartel, but I don’t think it required substantial compute capacity. (This isn’t a comment on the paper by the way, which I glanced at but did not have the background knowledge to fully comprehend) [0] See the section labeled “RealPage Uses Multiple Mechanisms To Increase Compliance With Price Recommendations” https://www.federalregister.gov/documents/2026/01/21/2026-01009/united-states-of-america-et-al-v-realpage-inc-et-al-proposed-final-judgment-and-competitive-impact https://www.federalregister.gov/documents/2026/01/21/2026-01...
- lokar 3mo agoI’m not sure the use of a common algorithm was the most damming part of that. They also pooled otherwise proprietary information and penalized landlords who failed to follow the “recommendations” You could imagine the exact same scheme without the use of a computer.
- MrGilbert 3mo agoI think "cartel" might be the word to look for.
- tsimionescu 3mo agoI think the common algorithm / the computer were the fig leaf, not the enabler, yes. The point is that they tried to launder obvious cartel practices as a simple computer recommendation system.
- consensus1 3mo agoI was always skeptical of the algorithmic cartel argument in that case. Turns out it was just a regular cartel all along.
- nok22kon 3mo agoor maybe compute allows simulating a lot of possible cooperation strategies, and arriving at the one maximizing profits for the colluding parties
- rosegroove 3mo ago[dead]
- bombcar 3mo agoHN materially changed the title to something surprising!
- nostrademons 3mo agoThe paper seems to be based on an invalid assumption. From the abstract: > If P != NP, the collusion detection problem is computationally infeasible for markets satisfying a natural instance-hardness condition on their demand structure, rendering punishment threats non-credible and collusion unstable. ...and then from the paper: > Stigler (1964) famously argued that the “chief difficulty” of collusion is detecting “secret price-cutting.” The thing is that Stigler's insight is far from proven, and indeed, the primary difficulty in collusion is often not the detection of defection. Firms know they're being undercut all the time. The problem is that very often, there is nothing they can do about it. Markets are specifically structured as firm-to-firm transactions, where competing firms have no leverage over what your firm can do or what sort of transactions you can conduct, and as long as this condition holds it doesn't matter if you know that a competitor is fucking you over, you can't do anything about it. I'd argue that the increase in collusion and anticompetitive behavior lately is because these conditions increasingly don't hold. When you intersperse another party in the transaction, eg. a regulatory agency, permitting body, or exclusive distribution deal, you introduce a leverage point for incumbents to punish competitors who choose to undercut them.
- jt2190 3mo agoWhy can’t my firm react if we find out we’re being undercut by a competitor? Or are you saying that we “know” only in a theoretical, “we can’t prove we’re not being undercut” sort of way, but without “proof” we can’t take action?
- nostrademons 3mo agoYou absolutely can react, but in general, in a functioning competitive market, you can not alter your competitors' actions. Examples of the former: cutting prices yourself; increasing product quality; differentiating yourself; spending more on advertising to get the word out about your product. Examples of the latter: crafting exclusive deals with your distributors to prevent your competitors from getting shelf space; politically influencing regulatory bodies to declare your competitors' existence illegal; making direct agreements with the leadership of opposing firms to not drop prices or hike wages; assassinating, extorting, or kidnapping rival business leaders. Basically it comes down to "control yourself, because you cannot control others". In a functioning market, you have no control over what rival firms offer. Your only legal reaction to competition is to improve your own offering until it is the best it can be. In pathological markets where the assumption is (as in the paper) that you can punish rivals for not colluding, you actively make your competitor's offering worse. Those pathological markets exist today, but if you're analyzing markets economically, your root assumption should not be that pathology is normal and only the lack of information keeps it in check, it should be that information is abundant and it is the lack of ability that keeps it in check.
- pwdisswordfishq 3mo agoThe actual paper’s title is “Markets are competitive if and only if P ≠ NP” It’s 2026, people, you don't have to use crude ASCII approximations of mathematical symbols any more.
- xxpor 3mo agoUnless and until desktop OSes make typing symbols not on the keyboard as easy as iOS or Android, I can't be bothered.
- adrianmonk 3mo agoIt's pretty easy on Linux with the compose key. To get "≠", you just hit compose, then "/", then "=". That's actually the same number of keystrokes as "!=" (since "!" requires the shift key). For whatever reason, the OS documentation lacks a list of allowed compose key sequences. But they are intuitive enough that you can find many of them through experimentation. For example: Musical sharp ("♯"): compose + "#" + "#". Interrobang ("‽"): compose + "!" + "?". Letter "ñ" as in "jalapeño": compose + "n" + "~". Copyright ("ⓒ"): compose + "(" + c + ")".
- classified 3mo agoThe "compose" key was a new rabbit hole for me. Very handy.
- VVertigo 3mo agoAt least in Debian (Trixie), I have a list in: /usr/share/X11/locale/en_US.UTF-8/Compose
- adrianmonk 3mo ago[Replying to myself...] Oops, I got one wrong. Copyright("©"): compose + "c" + "o". The one I had is bigger: Ⓒ vs. ©.
- tavavex 3mo ago> Seems that HN's auto-headline rewriting in this case has made a critical error :) I'm eagerly awaiting the day someone proves that P != NP and HN edits the title of the announcement post in this exact same way.
- fc417fc802 3mo ago> I don't see how this follows, except in the most straightforward way. A more capable actor can anticipate the actions of other participants to a greater degree. Imagine that all sellers are such actors. Consider that collusion happens (and is bad) because it enables sellers to extract much higher prices than the market would otherwise set. When all sellers are such "hyper rational" actors they can act cooperatively to maximize their profits without the need to explicitly coordinate in secret. The same end result without the illegal step sure feels like an end run around the spirit of the law. > Edit: Isn't another implication of this, that increased compute -> collusion imply that increased compute -> communism becomes feasible? That depends on what you think the problem that communism faced was. AI increases our ability to centrally plan but it probably doesn't do much in and of itself to combat various forms of corruption. Human greed is an invariant; by glorifying and directly making use of it capitalism is hardened against a number of otherwise pathological behaviors.
- classified 3mo ago> Seems that HN's auto-headline rewriting in this case has made a critical error :) Software trying to be smart always runs that risk.
- kibwen 3mo agoKeeping in mind the mistake in the HN title (should be "P != NP"), the interesting part of the abstract is this: > Combined with Maymin (2011), who proved that market efficiency requires P = NP, this yields a fundamental impossibility: markets can be informationally efficient or competitive, but not both. (Note that Maymin is the author of both papers.)
- argv_empty 3mo agoExcept Maymin 2011 fails to even establish that his narrow definition of "markets are efficient" (specifically, finding a profitable technical analysis) is actually in NP.
- marcosdumay 3mo agoYet neither paper seems to eliminate the case of markets being neither. So both titles are incorrect.
- iwontberude 3mo agoYeah using time complexity for computers to describe markets is simultaneously awesome and stupid.
- marcosdumay 3mo agoThe idea that markets are an optimizing algorithm is kinda old already, and well established. Both papers seem to be jokes about it, based on complete caricatures of competitiveness and efficiency. It's kinda like a recent paper that was posted here proving "general intelligence" impossible while ignoring that humans exist.
- cs702 3mo agoVery interesting. The author claims to have proved that markets can be informationally efficient or competitive, but not both. The implications for policy and regulation are significant. The author looks credible: https://philipmaymin.com/about-philip https://philipmaymin.com/about-philip Thank you for sharing this on HN. -- To the mods: The title needs to be edited to replace the equal sign with not-equal.
- cwmoore 3mo agoSo it pulls exclamation marks. . .angle brackets maybe? “=“ <> “!=“
- kleiba2 3mo agoUTF8 to the rescue: ≠
- dvh 3mo agoFun fact, pascal uses <> for inequality
- dgellow 3mo agoSql too
- adrianmonk 3mo agoSo does BASIC. It might even be the first, although it's hard to be sure. BASIC[1] came out in 1964, and Pascal[2] came out in 1970. --- [1] https://en.wikipedia.org/wiki/Dartmouth_BASIC https://en.wikipedia.org/wiki/Dartmouth_BASIC [2] https://en.wikipedia.org/wiki/Pascal_(programming_language) https://en.wikipedia.org/wiki/Pascal_(programming_language)
- magicalhippo 3mo agoIt removes a lot of things when posting, but submitter can edit and put them back. Most filters are to avoid sensational titles, AFAIK.
- vlovich123 3mo ago> the collusion detection problem is computationally infeasible for markets satisfying a natural instance-hardness condition on their demand structure, rendering punishment threats non-credible and collusion unstable. And yet we’ve clearly observed stable price fixing cartels. Maybe the word “unstable” means too much or the game theory model used doesn’t describe the real world accurately. When theory is contradicted by the evidence, it would be wise to consider the theory is flawed.
- silentmafia 3mo agoOr, P=NP
- roblabla 3mo agoOr maybe the markets are actually proof that P = NP :^)
- deleted 3mo ago[deleted]
- narnarpapadaddy 3mo agoGame theory here is applied to two fundamental market theorems. It’s a way to analyze the validity of those assumptions, rather than to build a new model. Empirical evidence to the contrary is expected given mutually inconsistent premises, which is what the author’s results predict. The author has simply used game theory math to disprove economist math.
- nok22kon 3mo agowhere do nuclear weapons fit in? do they make markets more/less efficient/competitive?
- lstodd 3mo agoWhere do conventional weapons fit it? Nuclear has been in maintenance mode for so long that there are doubts about if anyone could right now detonate one without shitting their pants on account if it would even go off.
- api 3mo agoIf markets were perfectly efficient, entrepreneurship would not exist. An entrepreneur is, at this level, someone who looks for an arbitrage opportunity in correcting a market inefficiency, usually of the form "there is a market for X, X could be provided, but X is not currently provided."
- xxpor 3mo agoSeems like t is a very critical variable then. For example, you could imagine a particular market is "perfectly" efficient at the moment (however you want to define the boundaries of a particular market), and there is no opportunity. But then a completely unrelated company or university makes a fundemental advancement in materials science that fundamentally changes the landscape. An exogenous shock in other words. In a certain sense I guess this is why every anti-trust suit fundamentally comes down to defining the market bubble more than anything else.
- AaronAPU 3mo agoThat seems to stretch the meaning of market inefficiency. Is the lack of unlimited free energy an inefficiency in a market? Because an entrepreneur who achieves that is going to do pretty well. I’d say that would be creating value not optimizing market efficiency.
- edot 3mo agoYeah, and arbitrage. Arbitrage is exploiting the difference in prices of the same asset between two markets. Arbitrage is also risk-free or darn close to it. Entrepreneurship is anything but. Arbitrage is not "gee this product doesn't exist, I'll start a company and invent it and manufacture it and sell it" ...
- SoftTalker 3mo agoHow would creating unlimited free energy allow an entrepreneur to do pretty well? It it's free, there's no money to be made.
- deleted 3mo ago
- silentmafia 3mo agoA 2010 entry by the same author: Markets are efficient if and only if P = NP https://arxiv.org/abs/1002.2284 https://arxiv.org/abs/1002.2284 :)
- p-e-w 3mo agoAssuming the original result is correct, isn’t the linked paper simply a corollary?
- deleted 3mo ago[deleted]
- philipwhiuk 3mo agoThe newer paper expands on the work of the former.
- Dibby053 3mo agoSo markets can only be (perfectly) efficient or competitive, not both at the same time. Largely theoretical but it tracks common sense!
- ffsm8 3mo agoThe title on this HN submission is just wrong. Click on the link and find out.
- MostlyStable 3mo agoI don't have the mathematical chops to really analyze this on my own. Is this a bigger deal than the fact that real world markets already violate all the theoretical assumptions (e.g. unimpeded access to new entrants, perfect information, etc.etc), and so, in practice are never perfectly competitive or efficient?
- d4ng 3mo agoDefi does a pretty good job regarding unimpeded access in comparison to the more traditional venues. This isn’t just about getting money into the system, but also what instruments you have access to. The term ‘perfect information’ is a bit of a mirage, and has been shown to be impossible in physics (uncertainty principle). What really matters is information advantage: Does your inexact expected value function consistently beat others’ calculations in the market. Here, the true value - value really is just a word and is dependent on people - is irrelevant.
- moomin 3mo agoI don’t think anyone in the business thinks that the markets are 100% efficient, just that they are sufficiently efficient that beating them is a genuinely hard job requiring heavy, expensive analysis.
- danans 3mo ago> just that they are sufficiently efficient that beating them is a genuinely hard job requiring heavy, expensive analysis No expensive analysis is needed. Beating them just requires (1) having disproportionate capital to others, and (2) having disproportionate control (and therefore know in advance) whatever the markets are pricing. It helps that there are enough believers (in the religious/cult sense) that markets are 100% efficient, that they will deny that any of that is happening - even while they lose their shirts to those who are doing the market manipulation.
- FailMore 3mo agoWould anyone mind explaining what P and NP are?
- VMG 3mo agowell obviously N=1
- super_mario 3mo agoWikipedia is a good source on this P complexity class https://en.wikipedia.org/wiki/P_(complexity) https://en.wikipedia.org/wiki/P_(complexity) NP complexity class https://en.wikipedia.org/wiki/NP_(complexity) https://en.wikipedia.org/wiki/NP_(complexity) P vs NP question https://en.wikipedia.org/wiki/P_versus_NP_problem https://en.wikipedia.org/wiki/P_versus_NP_problem
- convolvatron 3mo agoin CS we define a complexity class as a set of problems that have the same growth characteristic. that is for a problem size N, how long does it take in the worst case to find the solution for that problem. one such class is the Polynomial class, or P, where the time to solution is some fixed exponent of N (like N^2, or 3). the next big step is NP, which require a polynomial number of nondeterministic steps, whose solution can only be verified in polynomial time. usually solutions to NP problems are exponential in cost with respect to N (like 2^N), but thats not part of their definition. problems in NP are generally identified by mapping them into a well known problem known to be in NP, where the mapping has to occur in polynomial time. its an open question as to whether NP as a class can actually be solved in P time, but most people doubt that that is really the case.
- PandaRider 3mo agoI have taken algorithms courses. This video explains in detail: https://www.youtube.com/watch?v=YX40hbAHx3s https://www.youtube.com/watch?v=YX40hbAHx3s In short, P means Polynomial time (i.e. markets can solve computation problems efficiently) and NP means Non-Deterministic Polynomial time (i.e. markets can verify solutions of computation problems efficiently but solutions are found by luck). If P != NP, it means luck CANNOT be engineered and markets are competitive.
- glimshe 3mo agoMarkets are competitive if and only if P === NP! Now seriously, I wonder if AI collusion/use in investments would add to the market inefficiency and create opportunities for observing investors.
- AlotOfReading 3mo agoThe argument structure is interesting, and reminds me a lot of Solomonoff Induction, but constrained into NP by the assumptions. I'm not sure the front half is enough to support the back half of the paper arguing that the current LLM craze means firms are actually running collusion detection algorithms, even unintentionally.
- philipwhiuk 3mo ago[dead]
- dzink 3mo agoWhen everyone uses AI to study the same indicators and figures out how the prices move with those indicators they all start investing at the same time and the prices move together. AI silently gets everyone on the same page.
- iwontberude 3mo agoIt’s a great excuse for collusion
- Muromec 3mo agoSounds like soviet communist Sci-Fi with a planned economy managed objectively by The Computer.
- nok22kon 3mo agonext stage - a single AI which computes the "correct" price that everyone else agrees on, and instantly reprice all financial instruments without trading them, thus not paying transaction costs
- hgoel 3mo agoI hate to make the worn out AI to RNG comparison, but this kind of simultaneous "collusion" is really like assuming that everyone is using the same RNG seed to make their calls.
- BoardsOfCanada 3mo agoA lot of things are only true if P != NP but says nothing about P being within epsilon of NP.
- jfengel 3mo agoNot quite sure what you're suggesting here; perhaps it's satire? If P!=NP then it is arbitrarily smaller, for the same reason that e^x > Cx^N for any constants C and N, as long as x grows big enough. There is no epsilon in that can overcome that, no matter how big you make it, because x will eventually dominate the equation. There are a lot of cases where pragmatically x remains small enough that it doesn't matter, and a P algorithm will give you an answer more quickly. (For the same reason I only ever write bubble sorts: I would only write my own at all if I knew that the list would never be bigger than 10. Even then it's only when using the library is too much trouble for some reason.) But we care about P and NP when the number can potentially be very, very large.
- IsTom 3mo agoIn case P /= NP the gap doesn't necessarily have to be exponential, just superpolynomial (e.g. n^loglogn).
- BoardsOfCanada 3mo agoNo, it's not satire. The difficulty of finding the optimal solution says nothing about what it takes to come within 99.999% of optimal with 99.999% probability. So I'm not talking about the number of steps needed to prove optimality with a correct P algorithm versus an exponential one. I'm only talking about how this applies to the efficient market hypothesis.
- bobkb 3mo agoThis gave me shivers
- brunoborges 3mo agoIt's time to forbid bots and HFT. Want to buy/sell a stock? Humans need to manually submit in the system.
- ladberg 3mo agoWhy? Don't you prefer getting better prices when you want to go buy a stock?
- fluoridation 3mo agoI prefer a better price delta between buy and sell, which is blind to price hikes across the board.
- ladberg 3mo agoThat's exactly what "better prices" means...
- fluoridation 3mo agoIf I get a better price when I buy then someone else gets a better price when they buy too. (S + k) - (B + k) = S - B.
- stouset 3mo agoThe argument is not that you get better prices, it’s that you get accurate prices. First, this definition has always been circular: what’s the most accurate price? The one the market comes up with. More market, more accuracy! Second, there is never any reconciliation of the costs society is saddled with in order to chase arbitrarily more accurate prices, the most obvious of which is the massive quantity of fat skimmed off by the financial services sector. Third, as an index investor, I more or less couldn’t care less. This hyperfixation on accuracy only really matters to people who are actively trading, which is already a fool’s game.
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- wellbehaved 3mo ago"Third, I propose computational antitrust: the principle that market complexity itself is a competitive safeguard, and that regulators should consider computational difficulty as a design parameter." This "should" is doing a lot of work here. The paper is mainly about a game-theoretic model allegedly corresponding to real markets, but establishing what regulators ought to do requires far more rationale than mere math. It requires a bridge from "is" to "ought." It reminds me of Hume's warning about this kind of non-sequitur: "In every system of morality, which I have hitherto met with, I have always remarked, that the author proceeds for some time in the ordinary ways of reasoning, ... ; when all of a sudden I am surprised to find, that instead of the usual copulations of propositions, is, and is not, I meet with no proposition that is not connected with an ought, or an ought not. This change is imperceptible; but is however, of the last consequence."
- jopsen 3mo agoThis offers little because while P != NP, in most practical cases it doesn't matter. NP problems gets solved with heuristics every day.
- estebarb 3mo agoThis is interesting. Adam Smith said "People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the public, or in some contrivance to raise prices." The annoying part is that, as the same Adam Smith says, regulating industries would end up enforcing such assemblies, reinforcing the problem... after all, industries can share information via the market itself... And proposed solutions end up being controversial: employees ownership, open source, paying taxes over stocks ownership... or just hoping that colluders will be broken by a randomly ocurring incumbent...
- madihaa 3mo agothe same author 14 years ago. Markets are Efficient if and Only if P = NP and now Markets are competitive if and only if P != NP https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1773169&__cf_chl_f_tk=oMMAB0Q1fIxEduT3wpuZKWRCPnYS08Kxg9ahxuyjyjU-1783097029-1.0.1.1-mNgzpPw2ovuJOl2O0x5Vpt__jgLw10udtorUChNg3pU https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1773169&...
- apothegm 3mo agoWhich would in turn imply that markets cannot be simultaneously efficient and competitive.
- deleted 3mo ago[deleted]
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- elendilm 3mo ago[flagged]
- j05ev1f3 3mo agoThis feels like it's pointing in the same direction Hayek was already pointing 80 years ago. This paper says that even if we had enough computing power to solve these problems, Hayek's argument was that we still wouldnt have all the information needed to do those calculations in the first place. That information is spread across millions of people, constantly changing, and often only known locally. So even if the computation became easy, getting all the inputs would still be impossible to achieve
- dreambuffer 3mo agoBut you can just give computers to each of those millions of people and propagate the information, instead of having less reliable humans doing it? That's kind of what's already happening.
- j05ev1f3 3mo agoThe problem isn't transmitting information, it's how the knowledge is created. Some information only exists in peoples head until they act on it. Sometimes they don't even know it themselves until they're forced to make a decision.
- deleted 3mo ago[deleted]
- dreambuffer 3mo agoProblem of course is that a lot of this information is junk even at scale, which is how you get people "deciding" to pollute, destroy their own health, start wars, etc.
- emil-lp 3mo agoThis paper has all the hallmarks of being crackpot with GPT.
- debugnik 3mo agoIt builds on a similar paper from 2011 by the same author, though. They've just found something very specific that they enjoy analyzing.
- dwroberts 3mo agoThese things should not be submitted here unless there is meaningful editorial/peer commentary about it being significant or correct. There are dozens of bogus attempts to prove and disprove this
- abetusk 3mo agoThere's a long history of proving results like this. NP-Completeness is the norm, not the exception. Any system that's complex enough is almost surely NP-Complete. For similar reasons, Turing Machine Equivalence is also the norm, not the exception. These results are interesting but not unexpected. A more interesting question is under what conditions is the problem difficult to find solutions for. Many NP-Complete instance ensembles turn out to effectively have polynomial time solutions (3-SAT w/ uniform clause variable choice, Hamilton Cycles in Erdos-Renyi random graphs), so proving NP-Completeness is not a death knell for approximation.
- _alternator_ 3mo agoRight. Maybe a better and more humble title is "Identifying General Instances of Market Collusion is NP-complete". Not as headline grabbing, but more in line with the actual result.
- seizethecheese 3mo ago> markets can be informationally efficient or competitive, but not both Really interesting conclusion, but I can't help but feel this is overly reductive, as stated. Surely market efficiency is a sliding scale and so is market competitiveness. Okay, so a perfectly competitive market cannot also be a perfectly efficient market. Interesting! But I'm confused about how this may work when efficiency and competitiveness are a sliding scale. Should we think of this as one axis (with a spectrum from efficiency to competitiveness) or as two separate axes that just happen to have an exclusive relationship between their extremes?
- deleted 3mo ago[deleted]
- z3c0 3mo ago> Artificial intelligence, by expanding firms' computational capabilities, is pushing markets from the competitive regime toward the collusive regime, explaining the empirical emergence of algorithmic collusion without explicit coordination. Wow... this is quite fascinating. It has been theorized for a little while that widespread AI could form accidental trusts due to optimization around one-another. This seems to be taking it a step further and arguing that if P!=NP, then markets are certain to trend towards collusive.
- g42gregory 3mo agoCompetitive markets... In Rodney Dangerfield's immortal words: "You must be drinking!" :-)
- Grosvenor 3mo agoMy hypothesis is markets are fractally efficient and fractally competitive. Much like a strange attractor, they swing between states of efficiency and competitiveness. The default regime is instability. Computational capacity is unstable through time, and the problem size itself changes (fractally) through time.
- kscarlet 3mo agoHonestly I think the author misunderstood and misused P != NP. They should have said something like "collusion is NP-hard". P = NP doesn't imply NP-hard problem is efficiently solvable in practice, but the author assumes so. I was expecting some tight convergence analysis that rely exactly on some superpolynomial behavior. No, yet another fallacy about P = NP vs NP can be solved in practice. We have too many of these.
- investmuse 2mo ago[flagged]