[xxpor]

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.

[derektank]

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]

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.

[tsimionescu]

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.

[MrGilbert]

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

[consensus1]

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

[btown]

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

[pwdisswordfishq]

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.

[xxpor]

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

[adrianmonk]

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 + ")".

[classified]

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

[VVertigo]

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

[adrianmonk]

[Replying to myself...]

Oops, I got one wrong.

Copyright("©"): compose + "c" + "o".

The one I had is bigger: Ⓒ vs. ©.

[nostrademons]

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]

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?

[nostrademons]

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.

[tavavex]

> 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.

[classified]

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

Software trying to be smart always runs that risk.

[bombcar]

HN materially changed the title to something surprising!

[nok22kon]

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

[fc417fc802]

> 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.