Markets are competitive if and only if P != NP

https://arxiv.org/abs/2602.20415

by kscarlet • 19 days ago

231 164 19 days ago

arxiv.org

xxpor3• 19 days ago

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.

btown• 19 days ago

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

derektank• 19 days ago

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...

lokar• 19 days ago

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.

consensus1• 19 days ago

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

nok22kon4• 19 days ago

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

bombcar• 19 days ago

HN materially changed the title to something surprising!

nostrademons2• 19 days ago

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.

jt2190• 19 days ago

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?

pwdisswordfishq• 19 days ago

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.

xxpor3• 19 days ago

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

tavavex• 19 days 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.

fc417fc8022• 19 days 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.

classified2• 19 days 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• 19 days ago

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.)

argv_empty• 19 days ago

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.

marcosdumay2• 19 days ago

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

iwontberude2• 19 days ago

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

cs702• 19 days ago

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.

cwmoore• 19 days ago

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

    “=“ <> “!=“

kleiba2• 19 days ago

UTF8 to the rescue: ≠

magicalhippo• 19 days ago

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

Most filters are to avoid sensational titles, AFAIK.

hughw• 19 days ago

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

kps• 19 days ago

You had lower case? In my day...

nok22kon4• 19 days ago

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

falcor84• 19 days ago

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.

ajkjk• 19 days ago

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

baq• 19 days ago

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

throwaway274485• 19 days ago

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.

mcdeltat• 19 days ago

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

casey2• 19 days ago

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.

imtringued• 19 days ago

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.

vlovich1232• 19 days 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.

silentmafia2• 19 days ago

Or, P=NP

roblabla• 19 days ago

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

narnarpapadaddy3• 19 days ago

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.

nok22kon4• 19 days ago

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

vlovich1232• 19 days ago

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.

moomin2• 19 days ago

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”.

silentmafia2• 19 days ago

A 2010 entry by the same author:

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

p-e-w• 19 days ago

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

philipwhiuk• 19 days ago

The newer paper expands on the work of the former.

Dibby053• 19 days ago

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

ffsm82• 19 days ago

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

dheera• 19 days ago

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.

samrus• 19 days ago

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

api• 19 days ago

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."

xxpor3• 19 days ago

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.

AaronAPU• 19 days ago

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.

edot• 19 days ago

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" ...

SoftTalker2• 19 days ago

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

jayd16• 19 days ago

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?

ThrustVectoring• 19 days ago

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.

MostlyStable• 19 days ago

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?

d4ng• 19 days ago

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.

moomin2• 19 days ago

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.

danans• 19 days 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• 19 days ago

Would anyone mind explaining what P and NP are?

VMG• 19 days ago

well obviously N=1

super_mario• 19 days ago

Wikipedia is a good source on this

P complexity class

https://en.wikipedia.org/wiki/P_(complexity)

NP complexity class

https://en.wikipedia.org/wiki/NP_(complexity)

P vs NP question

https://en.wikipedia.org/wiki/P_versus_NP_problem

convolvatron• 19 days ago

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.

PandaRider• 19 days ago

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.

dpweb• 19 days ago

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.

SoftTalker2• 19 days ago

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.

bjourne• 19 days ago

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

calfuris• 19 days ago

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.

random32• 19 days ago

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/

calf• 19 days ago

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.

glimshe• 19 days ago

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.

astrodust• 19 days ago

NP factorial sounds like NP-ultra-hard.

emil-lp2• 19 days ago

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

AlotOfReading• 19 days ago

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.

dzink• 19 days ago

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.

Muromec• 19 days ago

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

iwontberude2• 19 days ago

It’s a great excuse for collusion

nok22kon4• 19 days ago

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

hgoel• 19 days ago

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.

BoardsOfCanada2• 19 days ago

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

jfengel• 19 days ago

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.

IsTom• 19 days ago

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

BoardsOfCanada2• 19 days ago

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.

bobkb• 19 days ago

This gave me shivers

brunoborges2• 19 days ago

It's time to forbid bots and HFT.

Want to buy/sell a stock?

Humans need to manually submit in the system.

ladberg4• 19 days ago

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

fluoridation2• 19 days ago

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

stouset2• 19 days ago

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.

wellbehaved• 19 days 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• 19 days ago

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

NP problems gets solved with heuristics every day.

makeset• 19 days ago

while P != NP

You don't know that!

sgt101• 19 days ago

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 :)

estebarb• 19 days ago

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...

madihaa• 19 days ago

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&...

apothegm• 19 days ago

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

j05ev1f32• 19 days ago

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

dreambuffer2• 19 days ago

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.

j05ev1f32• 19 days ago

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.

emil-lp2• 19 days ago

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

debugnik• 19 days ago

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

dwroberts• 19 days ago

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

abetusk• 19 days ago

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.

_alternator_• 19 days ago

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.

seizethecheese2• 19 days 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?

z3c0• 19 days 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• 19 days ago

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

Grosvenor• 19 days ago

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.

kscarlet• 19 days ago

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.

Markets are competitive if and only if P != NP

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