alt.hn

7/3/2026 at 3:41:44 PM

Markets are competitive if and only if P != NP

 https://arxiv.org/abs/2602.20415

by kscarlet

7/3/2026 at 3:56:31 PM

Very 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

Thank you for sharing this on HN.

--

To the mods: The title needs to be edited to replace the equal sign with not-equal.

by cs702

7/3/2026 at 4:29:37 PM

The implications are not significant..? the real world is messy enough that this will not ever apply.

by ajkjk

7/3/2026 at 5:15:32 PM

The fact that free markets don't exist, and that supply and demand is not a natural law that implies efficient markets has never stopped people acting like both are true and stuffing fingers in their ears.

But, both free markets and supply/demand are useful enough concepts to talk loosely about processes to understand the interest that I'll enjoy digging into this.

by throwaway27448

7/3/2026 at 5:20:34 PM

They're not just useful concepts tho, they're how every business operates, and the concepts cover the vast majority of situations.

The behavioral economics/Freakonomics thing was like "Hey, here's this thing that might if you squint real hard fall outside of efficient market theory" and then for a decade people took that to mean that that the base concepts were worthless, which was a severe overcorrection from people that didn't understand economics.

by peder

7/3/2026 at 5:39:23 PM

The vast majority of real world businesses create prices based on cost plus systems, not on supply/demand, which are generally impossible to measure directly. Another good chunk of smaller businesses simply copy the prices of larger businesses, at least in b2c markets. Sure, if their goods are not selling, they might reduce price, but they might try other tactics as well (marketing, targeted discounts, etc).

by tsimionescu

7/3/2026 at 7:00:59 PM

I always thought of supply and demand as more defining a limit that the price approaches as the number of transactions and the size of the market approach infinity, barring structural obstacles or persistent information asymmetry to prevent it than as something that was supposed to happen immediately on any given transaction.

by BobaFloutist

7/3/2026 at 7:37:56 PM

Businesses generally follow the rule "price is set to whatever the market will bear". Which is just an indirect way of setting price by supply and demand.

by bryanlarsen

7/3/2026 at 5:51:37 PM

these "other tactics" are just attempts at increasing demand. Cost plus is how many business set prices but that is entirely separate from what the market decides. If cost plus is not an attractive price, it won't sell, because the demand is not there.

by wrqvrwvq

7/3/2026 at 8:49:12 PM

> If cost plus is not an attractive price, it won't sell, because the demand is not there.

Sure, but that only sets a cap. The market might bear twice the initial price, but few businesses actually take the time in practice to explore things at this level

by tsimionescu

7/3/2026 at 5:47:16 PM

Knowledge accumulation seems to have cyclical patterns where general observations are condensed into "laws", and common wisdom is to treat these as unassailable truths. As exceptions and contradictions are found, the popular wisdom is to entirely dismiss the overwhelming universal conformity with the earlier principles because it sounds smart to common people. A lot of normal people see the basic problems with most methodological maxims but are led to believe that the maxim is truth. It takes a podcaster with a "study" to then "debunk" the "myth" they were yesterday defending as unimpeachable. People are generally not well informed enough to know anything and the podcaster class is the worst imaginable vector for knowledge dissemination or popularization. Just clickbait garbage monkeys with foreign money and vicious antisocial tendencies.

by wrqvrwvq

7/3/2026 at 5:45:09 PM

There are many ways that free and competitive markets can fail other than behavioural economics! Monopoly, informational asymmetry, externalities… All of these are plausibly pervasive.

by dash2

7/3/2026 at 6:30:25 PM

Well yes, market forces as theorized are the very premise we've structured our entire economy around. Or, more bluntly, the desire to purely encapsulate political-economic power in capital. How else could an economic process operate without being attacked by the state? But this is also why our market behaves so irrationally—these concepts have very obvious predictive limits that investors are struggling to grapple with and our politicians (and largely our electorate tbf) have blind faith in

by throwaway27448

7/3/2026 at 5:56:13 PM

Economics is one of the scientific sore spots for liberal ideology. If you are liberal and mostly swim in liberal circles, you probably believe that economics is mostly bunk pseudoscience. Akin to conservatives and climate change

by WarmWash

7/3/2026 at 6:19:26 PM

To be fair, macroeconomics can hardly be called science, though. It is incredibly hard to falsify a lot of the theories given the lack of possibilities for experimentation. It is far closer to philosophy than to any of the even remotely hard sciences.

Nothing to do with ideology, but with the nature of the field. Take epidemiological research in the areas of food and medicine: incredibly hard and expensive to get right and even then with often tenuous results. Now try doing that with ridiculously heterogeneous nations influenced by potentially almost everything on the planet.

It's a small miracle that economists manage to get some useful insights out of the data, but we should definitely be aware of how weakly most of them are supported (don't start talking about "error bars" with economists).

by dinfinity

7/3/2026 at 7:35:52 PM

An argument of the last couple of decades is that videogames have built incredible labs for macroeconomic experimentation. So far mostly what we learn are failure cases (mudflation, being such a big learning from videogames that the term itself is named after a type of them), but we are learning things (some of them exploitative, but that's a different ethical question).

by WorldMaker

7/4/2026 at 5:58:56 PM

You are overstating this. Mudflation does not transfer to the real world well, if at all. Very few skill-capped bits of DLC for real world activities.

These games do not include many of the complexities of the real world and can thus provide few insights that generalize to the real world on a macroeconomic level. They are toy universes. I'm not saying they are useless, far from it, but they are not "incredible labs for macroeconomic experimentation".

Try determining the effect of raising the central bank interest rate within a game of your choice. Or changing the minimum wage. Or the effects of investing in education. Etc.

by dinfinity

7/4/2026 at 7:28:17 PM

They are incredible compared to "no labs at all" and "no way to run experiments" as the above poster lamented.

Mudflation aka hyperinflation aka situations where "the money printer goes brr too fast" have happened in the real world. Sometimes at "extremely" small scale (for macroeconomics) such as company town scrip, but they've happened and affected real people's lives.

But also, if Bitcoin is real then videogame economies are very real. You can trade USD for most in-game currencies. Sometimes directly in game as micro-transactions today ("diamond" or "platinum" middle funging currencies that convert to other game currencies), sometimes on trading platforms that are certainly against game terms of service and possibly illegal in some states, but that doesn't really stop them existing or people living in low wage countries making ends meet by grinding game currencies to sell for "realer" ones.

(Mudflation is also the answer to the why the book I read of "Ready Player One" was better than the one the author wrote because it seemed obvious the economy in the book was a textbook mudflationary one and much of the dystopia outside of its central game could easily be explained by how much of its economy was tied into its in game mudflationary currency. I appreciated that Hank Green's book "A Beautifully Foolish Endeavor" did a better job of doing that on purpose.)

> They are toy universes.

So are most experiments, fundamentally. You model the real world as best you can. You do what you can to eliminate variables. You learn from your experiment and you improve your model. You can't test the entire universe all at once, that's too many variables, you find the interesting toys that seem to look enough like our current understanding of our universe and then you play them until you break them (assert either the null hypothesis or the alternative hypothesis). Repeat until done.

Your examples seem easy to build toy universes for. The Animal Crossing series has decades of "research" in the effects of raising a central bank interest rate. (Look for Tom Nook memes, they alone are a modern study of macroeconomics and teenagers' direct relationships with them.) Many MMOs have "trades" and "crafts" that need to balance a minimum wage to get players interested and/or invested in them versus opportunity costs in other systems in the game. Funding Education is a similar problem explored in various RPG mechanics by sometimes direct analogies such as investments into player attributes and skill levels and skill trees.

And so on and so forth. The boundary between "real" and "virtual" economics seems nearly nonexistent, they are the same thing (and currency always wants to flow between them). In this case the map seems to be the territory. In this case the analogy seems to be the real thing. Because people are involved and people are ultimately irrational, but start to do really interesting economic things the more people you put in the same "place", whether virtual or real. Which is what macroeconomics has always been about.

by WorldMaker

7/3/2026 at 6:24:08 PM

In fact that there's both a liberal and conservative economics ideology, and what could form a scientific discipline in between is unfortunately cornered and sorely lacking visibility.

by stymaar

7/3/2026 at 7:10:37 PM

The distinction between liberal and conservative political labeling in america is entirely cultural. There is precisely zero ideological, ie political-economic, difference. It's just culture wars all the way down while we get pickpocketed together.

by throwaway27448

7/3/2026 at 8:58:53 PM

I see what you mean, but I'd disagree with the idea that there's “precisely zero ideological, ie political-economic, difference”.

That's true that since at least Clinton, the Democrats as a political party have mostly embraced the business-friendly view that is also the conservatives' position on the subject.

But the Democrat's leadership are only a (very) imperfect mirror of their electorate and of the intellectual left, and there is definitely a significant set of left-wing economists (Polanyi, Stiglitz, Piketti to name a few of the most prominent, in chronological order).

You can't look at Cochrane and Piketti and say there's no progressive vs conservatives divide in economics.

by stymaar

7/3/2026 at 9:19:10 PM

I don't think that Piketty himself would say his views are well-represented by either party; but he does posit an ideological divide: http://piketty.pse.ens.fr/files/Piketty2018.pdf

I was being deliberately facetious, I suppose, but because of our campaign finance problems any policy of major economic import has coordinated bipartisan pressure.

by throwaway27448

7/3/2026 at 7:09:40 PM

I think exactly the opposite: adherence to market economics, even to the extent of calling it a science, is what defines a liberal. In this sense conservatives are just angry liberals.

Tbf, most americans just sort of skate along on vibes and don't have many concrete values or material understanding of our society at all, regardless of how they identify.

Cf any argument over rent control: people either want it out of some sort of justice for inhumanely priced rents, or people bought into some kind of idea that it doesn't work because some think tank they put faith in pushed that messaging. Few people actually study the literally thousands of ways that almost every other society manages to house their population more effectively. It's all just vibes.

by throwaway27448

7/3/2026 at 7:28:57 PM

I've been picking up a different feeling that economics is sort of in a pre-calculus moment that conservatives/libertarians and liberals/progressives have sort of been building two different sciences of economics and are missing the "calculus" to reunite them (or at least choose the winner between them).

I mention calculus specifically because it does feel like more of the progressive movements in economics are focused on rate of change rather than point in time. I personally often tend to get into electrical circuit analogies that current/resistance/impedance are more useful than steady state voltage. I find I especially bring these metaphors up a lot when discussing cryptocurrencies (and why I distrust them: inflation/deflation is the wrong axis, in my opinion, some inflation is a useful sign of "impedance" in the circuit, the trick to a healthy economy is not "deflationary" [most of real world history states that the deflationary economies are the worst to live in] but carefully managing the rate of change of inflation).

That progressive science of economics is happening, slowly (this paper seems relevant), but so much of conservative discussions get trapped in (misreads of) Adam Smith still. From a progressive point of view it does seem easy to dismiss conservative views of economics as bunk pseudoscience if they begin and nearly always end with Adam Smith, ignore some of Adam Smith's own warnings (for instance, relevant to above conversation: Adam Smith was also often the first to admit that the "free market" is an ideal/a model and unlikely to ever be a reality because humans are messy and ultimately irrational as individuals), and also ignore centuries worth of work since then, especially a lot of the "pre-calculus" stuff.

by WorldMaker

7/4/2026 at 4:42:00 AM

The vast majority of cash transactions are fired by a computer model so the implication are significant. It goes a long way towards explaining why increasingly financialized countries aren't experiencing noticeable real world improvement while also becoming increasingly extractive.

by casey2

7/4/2026 at 5:34:56 AM

Hmm. I am not so sure about that statement. There are many models at play in the market, not one model. What mechanistic patterns are driving those models that are falsified by this paper and lead to the outcome of increasingly extractive/stagnating economies?

by wuschel

7/4/2026 at 7:25:01 AM

Neoclassical economics is based around the idea that markets are 100% efficient. If they are only 99% efficient the whole thing falls apart, because the standard defense of neoclassicals against exponentially growing defects in the economy is that they never happen in the first place. The moment you permit a 1% defect rate, the cascade starts and it is only a matter of time for things to go wrong.

by imtringued

7/3/2026 at 4:33:53 PM

the abstract itself explains why there is a problem even if the real world is messy; markets are a social construct

by baq

7/4/2026 at 1:24:47 AM

No bro you don't understand bro, supply and demand maths said capitalism is the only way forward bro and give me money now

by mcdeltat

7/3/2026 at 4:00:03 PM

So it pulls exclamation marks. . .angle brackets maybe?

    “=“ <> “!=“

by cwmoore

7/3/2026 at 4:43:01 PM

It removes a lot of things when posting, but submitter can edit and put them back.

Most filters are to avoid sensational titles, AFAIK.

by magicalhippo

7/3/2026 at 4:12:44 PM

For the older among us, that's .ne.

by hughw

7/3/2026 at 5:15:46 PM

You had lower case? In my day...

by kps

7/3/2026 at 4:24:01 PM

assuming the typical "spherical market in a vacuum where the agents are maximally rational non-biological utility maximizers"

by nok22kon

7/3/2026 at 5:18:55 PM

Well, for better or worse, markets are becoming increasingly dominated by "non-biological utility maximizers" - mostly hft bots, but now also llm-based reasoning agents.

by falcor84

7/3/2026 at 5:53:57 PM

Actually there’s a literature on whether llms have the standard cognitive biases, via cultural inheritance….

by dash2

7/3/2026 at 5:45:28 PM

They're not necessarily maximising utility, just the number on the screen.

by HPsquared

7/3/2026 at 6:10:02 PM

The utility monster has decided that numbers are more useful than products usable by humans.

by pixl97

7/3/2026 at 6:55:13 PM

"Ahkchually the paperclip maximizer isn't maximizing [human] utility, just a dumb metric" isn't a particularly useful observation to make in the context of the world being gradually consumed by an army of nanobots.

by fc417fc802

7/4/2026 at 12:59:08 PM

I'm thinking of an earlier time when computers ran on "facts and logic" and you could probably stop the machine by giving it a logical conundrum. Vibes-based systems are a lot more resistant to this, but can still be distracted.

by HPsquared

7/3/2026 at 3:59:06 PM

A 2010 entry by the same author:

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

:)

by silentmafia

7/3/2026 at 5:09:14 PM

In a P=NP world, it still takes only one uninformed participant to make the market inefficient. I don't think the implication is bidirectionally true unless you assume every single player is rational, infinitely smart, and has access to the same set of information.

by dheera

7/3/2026 at 5:20:44 PM

Its game theory so perfect play is assumed. Spherical cows and all that

by samrus

7/3/2026 at 4:15:26 PM

So markets can only be (perfectly) efficient or competitive, not both at the same time. Largely theoretical but it tracks common sense!

by Dibby053

7/3/2026 at 4:26:30 PM

The title on this HN submission is just wrong. Click on the link and find out.

by ffsm8

7/3/2026 at 5:24:11 PM

The title is wrong but you’re also wrong. Read the abstract of the paper. Here’s the relevant section:

> 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.

by seizethecheese

7/3/2026 at 4:35:53 PM

isn't that what they're saying with "not both at the same time"? the papers both have opposite signs, one has != and the other has =

by abejfehr

7/3/2026 at 6:21:58 PM

Without the braces around the perfectly I would have understood it... yeah, I think I was misinterpreting what he meant to say

by ffsm8

7/3/2026 at 4:06:22 PM

Assuming the original result is correct, isn’t the linked paper simply a corollary?

by p-e-w

7/3/2026 at 4:37:50 PM

The newer paper expands on the work of the former.

by philipwhiuk

7/3/2026 at 3:53:30 PM

The 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.

by xxpor

7/3/2026 at 4:20:48 PM

Yeah, 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/2026/01/21/2026-01...

by derektank

7/3/2026 at 4:24:00 PM

I’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.

by lokar

7/3/2026 at 5:48:19 PM

I 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.

by tsimionescu

7/3/2026 at 5:33:08 PM

I think "cartel" might be the word to look for.

by MrGilbert

7/3/2026 at 4:43:25 PM

I was always skeptical of the algorithmic cartel argument in that case. Turns out it was just a regular cartel all along.

by consensus1

7/3/2026 at 3:58:14 PM

HN is competitive if and only if != != =

by btown

7/3/2026 at 5:01:14 PM

The 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.

by pwdisswordfishq

7/3/2026 at 5:21:38 PM

Unless and until desktop OSes make typing symbols not on the keyboard as easy as iOS or Android, I can't be bothered.

by xxpor

7/3/2026 at 6:19:32 PM

It'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 + ")".

by adrianmonk

7/4/2026 at 5:05:43 AM

At least in Debian (Trixie), I have a list in: /usr/share/X11/locale/en_US.UTF-8/Compose

by VVertigo

7/4/2026 at 6:41:40 AM

[Replying to myself...]

Oops, I got one wrong.

Copyright("©"): compose + "c" + "o".

The one I had is bigger: Ⓒ vs. ©.

by adrianmonk

7/4/2026 at 4:56:24 AM

The "compose" key was a new rabbit hole for me. Very handy.

by classified

7/3/2026 at 4:36:44 PM

The 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.

by nostrademons

7/3/2026 at 5:38:28 PM

Why 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?

by jt2190

7/3/2026 at 6:12:00 PM

You 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.

by nostrademons

7/3/2026 at 6:21:41 PM

> 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.

by tavavex

7/3/2026 at 4:33:52 PM

HN materially changed the title to something surprising!

by bombcar

7/3/2026 at 4:21:07 PM

or maybe compute allows simulating a lot of possible cooperation strategies, and arriving at the one maximizing profits for the colluding parties

by nok22kon

7/3/2026 at 4:30:13 PM

[dead]

by rosegroove

7/4/2026 at 4:36:06 AM

> Seems that HN's auto-headline rewriting in this case has made a critical error :)

Software trying to be smart always runs that risk.

by classified

7/3/2026 at 6:38:26 PM

> 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.

by fc417fc802

7/3/2026 at 4:02:03 PM

I 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?

by MostlyStable

7/3/2026 at 4:58:26 PM

Defi 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.

by d4ng

7/3/2026 at 5:35:00 PM

These 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

by dwroberts

7/3/2026 at 4:20:31 PM

A lot of things are only true if P != NP but says nothing about P being within epsilon of NP.

by BoardsOfCanada

7/3/2026 at 4:28:57 PM

Not 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.

by jfengel

7/3/2026 at 5:34:42 PM

No, 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.

by BoardsOfCanada

7/3/2026 at 4:43:49 PM

In case P /= NP the gap doesn't necessarily have to be exponential, just superpolynomial (e.g. n^loglogn).

by IsTom

7/3/2026 at 4:17:13 PM

The 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.

by AlotOfReading

7/3/2026 at 4:43:54 PM

This offers little because while P != NP, in most practical cases it doesn't matter.

NP problems gets solved with heuristics every day.

by jopsen

7/3/2026 at 4:56:16 PM

> while P != NP

You don't know that!

by makeset

7/3/2026 at 5:21:49 PM

In a minute you'll be tellin' folks that those quantum fangdoodles aren't going to revolutionise their stock pickin'!

You do realise that you'll never work in this town again? \s :)

by sgt101

7/3/2026 at 5:23:40 PM

This 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

by j05ev1f3

7/3/2026 at 5:44:52 PM

But 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.

by dreambuffer

7/3/2026 at 6:19:40 PM

The 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.

by j05ev1f3

7/3/2026 at 11:13:04 PM

Problem 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.

by dreambuffer

7/3/2026 at 4:54:33 PM

the 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&...

by madihaa

7/3/2026 at 4:56:26 PM

Which would in turn imply that markets cannot be simultaneously efficient and competitive.

by apothegm

7/3/2026 at 5:37:12 PM

There'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.

by abetusk

7/3/2026 at 5:40:53 PM

Right. 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.

by _alternator_

7/3/2026 at 5:41:00 PM

> 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?

by seizethecheese

7/3/2026 at 4:19:12 PM

When 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.

by dzink

7/3/2026 at 4:26:14 PM

next 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

by nok22kon

7/3/2026 at 5:12:08 PM

I 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.

by hgoel

7/3/2026 at 4:24:13 PM

Sounds like soviet communist Sci-Fi with a planned economy managed objectively by The Computer.

by Muromec

7/3/2026 at 4:24:37 PM

It’s a great excuse for collusion

by iwontberude

7/3/2026 at 4:07:59 PM

I 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.

by moomin

7/3/2026 at 5:48:20 PM

> 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.

by danans

7/3/2026 at 4:08:40 PM

Markets 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.

by glimshe

7/3/2026 at 4:22:58 PM

NP factorial sounds like NP-ultra-hard.

by astrodust

7/3/2026 at 5:29:47 PM

NP! should be something like NP^NP, which is well known to be Σ^2_P. Slightly larger, but still inside PH.

by emil-lp

7/3/2026 at 11:34:32 PM

My 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.

by Grosvenor

7/3/2026 at 4:45:59 PM

This 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...

by estebarb

7/3/2026 at 5:30:35 PM

This paper has all the hallmarks of being crackpot with GPT.

by emil-lp

7/3/2026 at 5:37:43 PM

It builds on a similar paper from 2011 by the same author, though. They've just found something very specific that they enjoy analyzing.

by debugnik

7/3/2026 at 9:57:53 PM

Competitive markets... In Rodney Dangerfield's immortal words: "You must be drinking!" :-)

by g42gregory

7/4/2026 at 5:01:44 AM

Honestly 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.

by kscarlet

7/3/2026 at 4:00:45 PM

If 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."

by api

7/3/2026 at 4:07:54 PM

That 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.

by AaronAPU

7/3/2026 at 4:36:35 PM

Yeah, 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" ...

by edot

7/3/2026 at 4:49:06 PM

How would creating unlimited free energy allow an entrepreneur to do pretty well? It it's free, there's no money to be made.

by SoftTalker

7/3/2026 at 4:06:18 PM

Seems 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.

by xxpor

7/3/2026 at 5:19:03 PM

In perfectly efficient markets, arbitrage gets paid exactly as much as it costs to discover and execute the arbitrage. Entrepreneurs would still exist, they would just be ambivalent between finding new arbitrage opportunities and seeking market-rate employment for their skills in finding arbitrage.

by ThrustVectoring

7/3/2026 at 4:38:20 PM

Ok so the market is perfect... but I exist and have labor to provide. Am I not naturally an "inefficiency" by not participating in the market? Therefore by participating alone, I have a new wrinkle to work from?

by jayd16

7/3/2026 at 4:08:39 PM

Would anyone mind explaining what P and NP are?

by FailMore

7/3/2026 at 5:23:20 PM

It's a vast generalization of the cost to verify a problem/solution.

- P means polynomial - NP means nondeterministic polynomial

Roughly polynomial (P) represents the upper bound of the cost to verify, and the polynomial characterization says that given a problem with a certain input (e.g. the input can be the number of training examples in ML training set or the number of constraints/conditions in a general problem— e.g. all the places you want to visit on your next trip, given many "wants" in a group)

When the cost is polynomial relative to the input size it means it can only be finitely larger than the input - that's a characteristic of the polynomial which is just a finite sum of powers of x (the input).

When the cost is nondeterministic polynomial, one way to think about it in what is called a nondeterministic Turing machine. The nondeterministic part refers to the "states" that the machines can transition to from any current state. When the transition can happen to more than one state, we say it's non-deterministic— and can imagine it's determined by some probability.

The general assumption is that polynomial (P) is easier than nondeterministic polnomial (NP). This isn't necessarily the case as there can be arbitrarily large finite numbers (making P solutions intractible)

The P vs NP problem is one of the main open problems and generally considered a crank magnet and general confusion. For a good (likely the best) resource see https://scottaaronson.blog/

by random3

7/4/2026 at 12:02:50 PM

Sorry, what's the significance of finiteness? The upper bound on an NFA is exponential steps of state transition splitting, thus P ⊆ NP ⊆ EXP, the class of exponential time algorithms.

by calf

7/3/2026 at 4:21:21 PM

I have taken algorithms courses.

This video explains in detail: 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.

by PandaRider

7/3/2026 at 4:40:29 PM

P and NP are classes of computational problems.

A problem in P can be solved in polynomial time - the computation required grows relatively slowly as the input size increases. Like sorting a list of numbers.

A problem in NP requires exponential time or greater, but a proposed solution can be verified quickly. For example, checking a completed Sudoku puzzle.

It is believed but unproven that all problems in NP are NOT in P.

by dpweb

7/3/2026 at 5:15:58 PM

A problem in NP can have a (positive) solution verified in polynomial time. That's it. Requiring more than polynomial time to solve isn't part of the definition, and in fact it's an open question whether any problems in NP require more than polynomial time to solve.

Every single problem in P is in NP. What is believed but unproven is that some problems in NP are not in P.

by calfuris

7/3/2026 at 4:53:50 PM

I have never really understood this, from the time it was first introduced to me in my undergraduate education nearly 40 years ago. It seems to boil down to saying "all unsolvable problems are not in the set of solvable problems" which seems like a tautology. I don't get why "P != NP" is considered so profound.

I feel like I have not yet found the proper explanation. Or I'm just too dense to get it.

by SoftTalker

7/3/2026 at 5:12:42 PM

Not sure you're wanting an explanation, but it comes down more to equivalent algorithms than rigid categories. For example there is a P algo to sort a list of numbers, but not to solve a sudoku (NP). However there is a polynomial algo to check sudoku (spaces ^ 2 if you check every space against every other space for rule violation).

However, the reason all NP algos are part of the same category is because you can solve any problem in NP by switching the problem into another problem in the same category and solving that. For example, you can turn sudoku into a graph coloring problem, which is also NP. You can turn sorting (P) into something like balancing a tree, which is also P.

The major question is "is there any algorithm that would allow us to change some NP problems into P problems, solve it, then use it for the original problem". E.g. could we take graph coloring and turn it into sorting a list of numbers?

So basically, if there is any way to bridge the two, then it might mean every NP problem is actually solvable by a P algorithm, under some transformation. This would be immense because it would completely change the way we solve those algorithms and greatly reduce compute costs.

While this seems far-fetched, realize that there are some problems that seem extremely expensive if done the naiive way, but are actually solvable in P. For example, you _could_ write an exponential sorting algo (try every element in every position), but clever people found a way to make it efficient (P). So its possible we just need the right algo to completely change the landscape of computing.

However, as you say, its almost self-evidently true that P != NP, but has never been proven so (to do so, we need to prove that no such algorithm can exist). But clearly, solving an exponentially complex problem using a O(log n) algo would be remarkable.

To take a concrete example, currently the best algos to exhaustively check a board game like chess or go are exponential (NP). Its easy to verify the winner, but its exponential to enumerate every possible move (e.g. 80^turns states). If we found a polynomial way to solve this (even by converting to something simplified), then it would mean we could exhaustively search chess polynomial to the number of moves (e.g. turns^100). This changes it from "cannot be done in the lifespan of universe" to "its possible with a powerful computer in measurable time". We already use heuristics and estimates to explore the exponential space in efficient time, so if we had a polynomial algo chess, markets, optimization, and other NP problems would be extremely efficient to solve.

by program_whiz

7/3/2026 at 5:02:47 PM

NP contains P. You're thinking of NP-hard problems.

by bjourne

7/3/2026 at 4:14:53 PM

well obviously N=1

by VMG

7/3/2026 at 4:17:29 PM

in 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.

by convolvatron

7/3/2026 at 4:35:01 PM

It's time to forbid bots and HFT.

Want to buy/sell a stock?

Humans need to manually submit in the system.

by brunoborges

7/3/2026 at 4:38:25 PM

Why? Don't you prefer getting better prices when you want to go buy a stock?

by ladberg

7/3/2026 at 4:41:47 PM

I prefer a better price delta between buy and sell, which is blind to price hikes across the board.

by fluoridation

7/3/2026 at 4:43:23 PM

That's exactly what "better prices" means...

by ladberg

7/3/2026 at 4:51:13 PM

If 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.

by fluoridation

7/3/2026 at 4:47:10 PM

The 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.

by stouset

7/3/2026 at 6:03:56 PM

> First, this definition has always been circular: what’s the most accurate price? The one the market comes up with. More market, more accuracy!

Market makers and HFT don't determine price: price is usually purely determined by the net inflows and outflows as decided by humans. MMs just smooth it out over time so everyone gets good pricing at the time and in the size they want it.

> Second, there is never any reconciliation of the costs society is saddled with in order to chase arbitrarily more accurate prices

By definition market makers are earning a fraction of the price improvement they provide, ergo the costs to society have to be less that the benefits for better pricing for the companies to stay in business!

> Third, as an index investor, I more or less couldn’t care less

As an index investor you should absolutely care! How do you think you are able to buy into the fund at a reasonable price? And then how do you think the fund is able to rebalance without transaction costs destroying performance long-term?

by ladberg

7/4/2026 at 12:00:49 AM

> By definition market makers are earning a fraction of the price improvement they provide

By definition, they’re making in aggregate essentially whatever the difference was between the “misprice” and the “true price”, assuming sufficient belief in both of these things. One of the parties in the hypothetically mispriced trade is bearing the loss. Their cut had to come from somewhere.

> As an index investor you should absolutely care! How do you think you are able to buy into the fund at a reasonable price?

You are relying on an interpretation of “reasonable” to intuitively mean “cheap” when in reality it means “accurate” in this context.

As an index investor, as long as it is accurate enough I don’t care. Any mispricing of assets up and down will come out in the wash.

Index funds existed well before HFTs were endemic. I have seen zero evidence that HFTs have caused index funds to net more of the gains from their underlying indexes.

by stouset

7/3/2026 at 7:47:18 PM

> price is usually purely determined by the net inflows and outflows as decided by humans.

"as decided by humans", more than 90% of trades are led by bots, so no, price is not being determined by humans.

In fact, we have seen time and again how some weird companies get a huge inflow of purchases simply because of bots misinterpreting news articles.

by brunoborges

7/3/2026 at 7:57:14 PM

It feels like you're intentionally omitting parts of what I said to make a point, and that I have no hope of correcting your world view, so just gonna clarify for any onlookers then stop arguing further.

> > price is usually purely determined by the net inflows and outflows as decided by humans.

> "as decided by humans", more than 90% of trades are led by bots, so no, price is not being determined by humans.

You skipped past the "MMs just smooth it out over time so everyone gets good pricing at the time and in the size they want it" right afterwards which exactly explains why most trading is between bots! Person A wants to buy 10 shares of Y at time T1, Person B wants to sell 20 shares of Y at time T2, Person C wants to buy 10 shares of Y at time T3. Those are all at different times, therefore bots have to take the other side of each trade, then trade with each other to smooth out prices in between each point.

> In fact, we have seen time and again how some weird companies get a huge inflow of purchases simply because of bots misinterpreting news articles.

I actually clearly see this happening more with humans than with bots. Can you think of a single example attributed to bots? A bot that can misinterpret a news article and lose money is fixed and/or disabled forever. There is no shortage of dumb humans willing to lose money due to a lack of literacy.

by ladberg

7/3/2026 at 4:41:39 PM

"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."

by wellbehaved

7/3/2026 at 3:55:38 PM

Keeping 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.)

by kibwen

7/3/2026 at 4:14:03 PM

Yet neither paper seems to eliminate the case of markets being neither. So both titles are incorrect.

by marcosdumay

7/3/2026 at 4:26:41 PM

Yeah using time complexity for computers to describe markets is simultaneously awesome and stupid.

by iwontberude

7/3/2026 at 4:42:32 PM

The 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.

by marcosdumay

7/3/2026 at 4:05:08 PM

Except Maymin 2011 fails to even establish that his narrow definition of "markets are efficient" (specifically, finding a profitable technical analysis) is actually in NP.

by argv_empty

7/3/2026 at 6:01:02 PM

> 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.

by z3c0

7/3/2026 at 3:58:07 PM

> 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.

by vlovich123

7/3/2026 at 4:18:06 PM

I suspect this is a standard mathematical “it is computationally impossible to do this in the general case despite it being entirely feasible in many cases”.

by moomin

7/3/2026 at 4:10:46 PM

Game 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.

by narnarpapadaddy

7/4/2026 at 3:58:37 AM

Simple resolution: the market isn’t maximally efficient at all information discovery but it is optimally efficient as far as is practical. The economist math still works.

by vlovich123

7/4/2026 at 4:25:48 PM

I buy that markets are like a traveling salesman problem. “Impossible” in the general case, but good enough could algorithms exist. Where’s the economist formulation of that algorithm? What are the policy implications that fall out of that?

I admit I’m not particularly well versed in this space, but I’ve never come across that formulation, only the “pure” one the original researcher says is internally inconsistent. I don’t necessarily buy “it’s close enough it doesn’t matter” given what I perceive as many notable exceptions.

by narnarpapadaddy

7/3/2026 at 4:28:15 PM

where do nuclear weapons fit in? do they make markets more/less efficient/competitive?

by nok22kon

7/3/2026 at 5:07:09 PM

Way above my pay grade. I’m not an expert in game theory, economics, warfare, or nuclear proliferation. :)

by narnarpapadaddy

7/3/2026 at 4:50:06 PM

Where 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.

by lstodd

7/3/2026 at 4:01:30 PM

Or maybe the markets are actually proof that P = NP :^)

by roblabla

7/3/2026 at 4:01:21 PM

Or, P=NP

by silentmafia

7/3/2026 at 5:18:12 PM

[flagged]

by elendilm

7/3/2026 at 4:36:57 PM

[dead]

by philipwhiuk

7/3/2026 at 4:29:30 PM

This gave me shivers

by bobkb