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The Game Theory of How Algorithms Can Drive Up Prices

https://www.quantamagazine.org/the-game-theory-of-how-algorithms-can-drive-up-prices-20251022/
90•isaacfrond•3h ago

Comments

steve_gh•3h ago
Very interesting. I looked at stability in learning agents in artificial markets back in the late 90s for my PhD and concluded that at least the systems I worked with weren't stable - they were prone to bubbles and crashes.

Very interesting to see that there is a class of stable systems that force high prices.

Would be interesting to understand if the no swap regret systems studied also give stable results when it is an N player game rather than a 2 player game

kalinkochnev•3h ago
That sounds actually really cool. Do you have a link to any of your papers?
derbOac•2h ago
I had the same question about N-player settings. My intuition is the more players, the more competition and the more chaotic the dynamics, and the harder it would be for any strategy like they describe to emerge. But intuitions can be wrong.

In any event, it would be interesting to know how the dynamics change with increases in the number of players — I wondered if it might provide some kind of rationale for having a certain number of competitors in a market.

Etheryte•2h ago
Intuitively, stability might also be easier to achieve here since there is a human check in the loop, oftentimes someone with considerable experience and knowledge of the current market state.
pixl97•2h ago
I mean we are in the age of digital pricing, even on the shelf. Modern price collusion is more apt to happen with A/B testing if prices at locations to see what the local market will bear.

I've seen Walmart do this in the past. Items that were not on sale could have significant differences in price, where in general the prices in more affluent areas are higher. We're talking 50 to 75 cents on common items, but sporting goods quite often had a different of 3 to 5 dollars.

PaulKeeble•2h ago
You can see this happening all the time on Amazon these days if you use a price tracker. Most items are swapping between two prices that are maintained for periods and little peaks just a little bit lower and higher to test response. Then when you take that and look across different countries stores you can see they are running different pricing and running tests globally while the price is being sustained in others.

Enormous amounts of price testing with a very clear strategy that is easy to see in pricing charts.

lotsofpulp•2h ago
Having a single flat price is/was due to labor prices being high enough in the developed world to ignore potential profits from price discrimination.

When my grandparents went to the market in the developing country they immigrated from, they would bargain for everything, and every customer got a different price.

The developed world was rich enough that grocery stores didn’t need to waste time doing this, and could simply price high enough to earn a consistent profit margin and expect consistent sales. They did engage in price discrimination via coupons. Just not individually, until smartphones and apps came along.

Now that automation can handle a lot of the price discrimination, expect more of it, everywhere.

kaitai•1h ago
It is not only about labor prices being high enough (creating consumers who can buy more). There is a significant religious component to the introduction of fixed pricing. Quakers are often credited with introducing fixed pricing in the Western world, because they felt that charging higher prices to those less able to haggle (or higher prices by age, gender, race) was immoral, dishonest in the eyes of God. They then experienced greater sales because you could send your kid to the store and trust the kid wouldn't get ripped off. It just took a layer of stress off going to the store. John Wanamaker (a Presbyterian?) I think is the one who really started a retail empire on fixed pricing. One of his main selling points was one price for anyone, and a fair return policy.

The behavioral economics here is that many people will pay a consistent (fair) price to not be surprised and not feel ripped off.

Agree that automation will engage in price discrimination whenever possible. When will we see the backlash? I have heard stories of outrage ("when I looked for airline tickets at work they were way cheaper than when I looked on my home laptop!") but we haven't seen a widespread reaction, and the moral aspect seems to be relatively overlooked at this time.

lotsofpulp•2h ago
Labor and land prices in more affluent areas will be higher, so it is expected COGS will be higher.

However, Walmart now displays in store and online for pickup prices on their website. I walked into the Walmart and paid $1.11 more than if I were to have ordered it via the app on my phone or website for pickup.

And Walmart was very upfront about it, and I knowingly paid $1.11 more because their online order and pickup option sometimes makes you wait 20min+ for a Walmart employee to come out and give you what you bought (even after it says your order is ready for pickup).

photonthug•1h ago
> Modern price collusion is more apt to happen with A/B testing if prices at locations to see what the local market will bear.

One of my first thoughts as well. If you're big enough, you collect so much data and run so many experiments all the time that you know exactly what you'd do if/when there's any competitor on the scene. Not only is there no need to talk to them and make backroom deals, but barely any need to even observe them. You priced like they did/would/could at some point already anyway. At a certain scale and if you already know the price that the market can tolerate.. the most relevant hidden information you want to know is how much cash your competitor has access to. That tells you whether you can win the price-war to sell at a loss for long enough to ruin them, buy them, move on to integrating verticals etc.

Game theory is interesting but also a bad model to the extent that it assumes persistent players with changing strategies, whereas average case in late-stage capitalism is more likely to have players eating players, no new players can enter, players changing rules, etc. As a CS nerd I still like a game theoretical approach better than most econ, but at some point we need to give up on tidy formulas and closed-form answers, and go all in on messy simulations.

nomilk•2h ago
The researcher says

> this strange strategy will maximize your profit. “To me, it was a complete surprise”

It doesn't seem like such a surprise that algorithms that use information about rivals to optimising profit tend to price high.

Consider a small town with two gas stations, you own one. You can set the price (high or low) in the morning and can't change it until the next day. Your goal is to optimise profit for the next 1000 days. On day one you price high (hoping your rival will). But your rival prices low and wins lots of business. On day two, you price high again (hoping your rival will have seen your prices and cooperate). If your rival prices high, you both stay high for the most of the next 998 days (there's some incentive to 'cheat' and price low, but that is easily countered by the rival pricing low). If your rival priced low on day 2, you have to start pricing low too. But occasionally you'll price high to try to 'nudge' your rival to price high to avoid low-low. If they eventually understand, you can both price high for the rest of the 1000 days. Critically, even if stuck at the low-low equilibrium, you'll keep trying to 'nudge' high periodically. The frequency with which you try to 'nudge' will depend on the ratio of profit for high-high vs low-low. If you both make extreme profits when pricing high-high, you have more incentive to 'nudge', but if the difference isn't great, you won't nudge as often.

Seems obvious pricing high will be attempted in proportion to the reward relative to pricing low.

The researchers' conclusion seems reasonable:

> it’s very hard for a regulator to come in and say, ‘These prices feel wrong’”

and

> what can regulators do? Roth admits he doesn’t have an answer.

(i.e. in practical terms, there's no way regulators can police what algorithms sellers use - I can't think of exceptions to this, but perhaps there are some special cases)

hrimfaxi•2h ago
> (i.e. in practical terms, there's no way regulators can police what algorithms sellers use - I can't think of exceptions to this, but perhaps there are some special cases)

Regulators can already police the data used as inputs in decision-making in industries like insurance, so policing the algorithms that operate on that data doesn't seem like too much of a reach.

nomilk•1h ago
> Regulators can already police the data used as inputs in decision-making in industries like insurance

How enforceable is policing which data can be used as inputs though?

It's common for insurance companies to price based on age and sex (e.g. teenage boys will typically pay higher car insurance premiums than similar aged girls). Presumably insurers are not allowed to price on a factor such as race. Unlike collusion, overt use of a variable like 'race' in a pricing model could be detected and enforced via a company whistleblower.

But how would a regulator find/prove algorithmic collusion?

In an extreme case, regulators could ban all use of competitors' data in a sellers' pricing models. But that seems extreme and unproductive since it could stop price wars (downward prices), as well as muting good effects of the 'invisible hand' (higher prices attracting more market entrants and greater investment)

hrimfaxi•1h ago
> But how would a regulator find/prove algorithmic collusion?

They don't need to. At least in the US, courts look at the outcome and if the outcome is discriminatory that's the important part. This is under the idea of disparate impact. Beyond that, the realpage cases offer an example of modern day prosecution of algorithmic collusion.

photonthug•34m ago
Seems like an optimistic read on things. This is the kind of common-sense approach you would expect in a world without lawyers, just observing that collusion is bad because the effects are bad, and digging into the details of the causes are completely irrelevant for the public/plaintiff because it's really just on the company to fix the undesirable result.

IANAL but if realpages outcomes were definitive or reasonably generalized results dealing with the core issue, then similar arguments against e.g. Amazon would be a slam dunk. AFAIK, actual case outcome just hinges on details about "nonpublic data" and similar. Not remotely on bad effects for consumers or anything like that. Since printing realpages database in the newspaper would not actually help apartment-hunters, then this just tells landlords and third party markets how to do price-fixing legally next time? Most likely algorithmic pricing, surveillance pricing, etc is still coming to your grocery store after the issue is "settled" for property rental, or at least settled for realpages, in certain jurisdictions, for now.

skeezyjefferson•7m ago
> AFAIK, actual case outcome just hinges on details about "nonpublic data" and similar.

that sounds like insider trading. price fixing would need not involve nonpublic information (beyond the actual conspiracy to fix the prices as it helps to keep that part secret normally)

bfkwlfkjf•1h ago
> what can regulators do?

Regulators could say "you're not allowed to make more than X profit". They already do that with utilities, so it's not a matter of practical impossibility.

cwmma•1h ago
The problem with this is it ends up being a signal in of itself, so when you say, the cap is X you end up having everyone immediately set their profits to X and never budge from there
vladms•12m ago
Regulators could ensure that detailed financial data of companies is public. If everybody understands how much profit and opportunities are in a certain thing that will encourage other people to do the same thing.

I always think that in this day and age financial secrecy benefits mostly the richest people and adds to the informational imbalance (which does not help even the model of free markets).

friendzis•2h ago
> Imagine a town with two widget merchants. Customers prefer cheaper widgets, so the merchants must compete to set the lowest price.

I always found this statement to be rather wishful. Individual lowering of prices makes sense if and only if your competitor is capable of saturating the market. Otherwise, demand elasticity becomes very relevant. Sure, your competitor may take the larger share of the market, but then you can compensate with higher per item profit.

The common wisdom is that in properly functional markets there's enough supply with n-1 market participants, therefore given a market signal of one participant lowering their prices the last one standing without lowering prices gets kicked out of the market, making maintaining prices the losing move. Yet, if the rest of the market does not react to the signal, the one lowering their prices hurts their profits and possibly kicks themselves out of the market. Making price maintenance, and depending on elasticity maybe even jacking of prices, the winning move in the presence of this signal.

Turns out the probability of either move being the winning move is dependent on probability of other market participants colluding/defecting. However, since lowering the prices hurts the profit a rational market participant would conclude that the rest of the market is inclined, even if a little bit, not to lower their prices in reaction given price cutting signal and similarly a bit more inclined to raise the prices given price hike signal.

lotsofpulp•2h ago
> I always found this statement to be rather wishful. Individual lowering of prices makes sense if and only if your competitor is capable of saturating the market.

Like Walmart/Dollar Tree/Costco/Aldi/Target/Kroger/Amazon etc can (and have)?

And on a macro scale, like China can (and has)?

guywithahat•25m ago
If anything it's incredible how competitive the market is. You can go into walmart, in the richest large country on earth by a significant margin, and buy pants for like $20. There are some heavily regulated industries where maybe we don't want this but in general companies competing to drive down prices is how most things work, and it works unbelievably well.
wordpad•2h ago
This feels like a variation of prisoners dilemma.

I think what you say is true for well established markets. In growing markets the incentive to capture market share may well override any profit considerations.

dghlsakjg•1h ago
It is an intentional oversimplification.

Although a good proxy for the situation in the real world is gas stations, as long as you ignore that gas stations tend not to make much, if any, profit on gas sales.

wat10000•1h ago
No need to ignore it. This is exactly why gas stations tend not to make much profit on gas.

In my area, there's one notorious gas station that's a couple miles away from any other commerce but has a reasonably large amount of traffic passing by. Amazingly, its prices are always about 50% higher than everywhere else.

Competition works when it exists. Yes, you also have to factor in supply. That's why the phrase is "supply and demand."

spwa4•1h ago
You want to get an economist to shut up? Point out that we're now in a situation that for nearly any physical good, one producer is able to saturate the market, that nearly every factory is operating below capacity, that individual farms are so big they can easily produce what an entire state needs and in fact operates below capacity for financial reasons. Both factories and farms: A LOT below capacity. Because 1% of a modern factory's capacity is able to saturate a very large local market, and the rest depends on international treaties, not on supply, demand, or even price.

Which means increasing supply for just about anything ... doesn't actually change price, and in fact the issue you're pointing out is not just one of the influences on prices, but almost the only one.

The market is saturated and producers have no incentive to lower prices, for nearly every good. Which means increasing supply ... does not lower prices. Increasing demand does not raise prices ... that's just not how it works anymore.

The only influence on price is international relations, or to put it more bluntly: various kinds of taxes are the only influence on prices (going from import/export tax, vat/sales tax, subsidies, raw material availability (effectively mostly meaning a tax in the form of export restrictions), what loan conditions are for good X, ...), and so economics just doesn't really apply anymore to the vast majority of goods.

The price of widgets from water balloons to air fryers is controlled by government subsidies in particular countries.

The price of houses is controlled by mortgage conditions, which are set in law. Meaning they are different between countries in both ways that matter (so, for example, Freehold vs Leasehold, Australia's Negative Gearing, whether 30 year fixed price is available, immigration policy, whether foreign investment is allowed ...) and in weird ways that don't matter. Supply and demand don't control price.

The price of labor and services is around 80% tax in most of Europe. Measured by taking $100 that the employer pays to have labour done, so including for example France's "patronal" tax, compared to what the employer would receive and not have to pay to the government in his bank account if the employee chose to spend all of his pay on whatever his labor produces. Yes there is still some supply/demand here ... but not much.

The problem is that for nearly everything "taxes" (as in taxes and tax-like regulations) determine who produces, and the tax swings are so large (going from -10%, yes minus, to 80% and more) depending on location and good, and their effect swamps any economic concern in nearly all sectors of the economy.

wat10000•56m ago
Food in developed nations is incredibly cheap as a direct result of the massive productive capacity of modern agriculture. Factory goods are also very cheap. Increasing supply demonstrably drives prices down.

Housing is an area where supply is heavily restricted, partially because land cannot be manufactured, partly because of government regulations controlling what can be built and where. Surprise, housing is very expensive.

spwa4•30m ago
And yet, if you check it out for real, you'll find most food could be a lot cheaper (some countries have regulations for basic foods to be excepted from most regulation and taxes, and there's a large price difference)

Especially meat could be a great deal cheaper if these countries wanted to make that happen.

Food in the west is only cheap in one sense of the word, and even then if you compare how much of the cheapest bread today you can buy for the average monthly pay today versus how much of the cheapest bread in 2000 you could buy for the average monthly pay in 2000 it's almost a factor 2 less.

But yeah, that's still very cheap: nobody's going hungry at the increased prices.

amelius•1h ago
> I always found this statement to be rather wishful.

The principles behind the free market are flawed. Copyright and patents are flawed. We're being played. But somehow the incumbents always get away with "but we have fair rules", when everybody who has ever entered a game of monopoly late knows this is not true.

shafoshaf•1h ago
Not flawed, but very, very complicated. The theory of free markets holds a lot of very well reasoned and tested lessons that can be instructive, depending to which principles you are referring.

Newtonian principles does a really good job for a huge number of use cases, but it isn't the end all.

When it comes to intertwining human taste, a doctrine of equal opportunity combined with private property, and scarce resources, I don't want to throw the baby out with the bathwater.

Retric•58m ago
Free markets as described by Econ 101 don’t apply in any sector where advertising is useful.

Far more complicated theories get much closer to reality, but aren’t nearly as well known outside of economic circles.

nerdponx•22m ago
The irony is that rental markets are probably one of the better markets to apply Econ 101 principles. Yes you have problems with information asymmetry, but for the most part you have a huge number of relatively small buyers and sellers, and prices freely ab and flow based on supply and demand conditions. So if you are going to analyze the effect of algorithmic pricing in the real estate market, starting with the simple free market assumptions actually is not a bad idea at all.

It's also common practice to show the effect of something on an idealized free market, with the idea of being that * even under supposedly ideal conditions*, the something being analyzed is still problematic.

babush•53m ago
Can gravity buy out magnetism?
Fernicia•50m ago
> The principles behind the free market are flawed

Can you go into specifics?

friendzis•39m ago
The so called "free market" (not to be confused with laissez faire) assumes perfect "information symmetry" and perfectly rational market participants, which is, effectively, impossible in this particular reality, and concerns itself mostly with marginal eventual state. It is a model.

E.g. the model "use VC money to subsidize cost until all competitors are bankrupt then hike prices to recoup" is not really reflected in this "free market"

zaphar•1h ago
You shouldn't lower prices as a direct reaction to your competitor. You should lower prices as a reaction to your customers willingness to buy at a given price. It's an indirect reaction but it factors in the actual market.
jellicle•1h ago
> Imagine a town with two widget merchants. Customers prefer cheaper widgets, so the merchants must compete to set the lowest price.

Imagine a town with two widget merchants. The two go out to dinner one night, and next week they both double their prices. Both widget merchants are pleased.

bluGill•10m ago
In the real world there are always things other than price to compete on. Business school will tell you constantly that best quality is where you want to compete in almost all cases. Quality has many different options and so you can compete with something that is different from someone else by enough that if someone prefers your quality you are the only option.
betimsl•2h ago
Who wrote the algorithm?
alyxya•2h ago
It's possible algorithms simply drive up prices because price isn't the main factor some people use in deciding what to buy. Algorithms are probably able to learn that raising the price outweighs the decrease in the number of people buying something, and if every algorithm does the same, then prices will continue to rise.
js8•1h ago
How is this new compared to https://www.paecon.net/PAEReview/issue53/KeenStandish53.pdf ? (See the section "perfect competitors are not profit maximizers".)
oxqbldpxo•1h ago
Is this applicable to the stock market? Maybe this is why valuations are completely devoid of any intrinsic value.
AlGoreRhythm•1h ago
The author cites the common CEPR paper [0], but missed its most interesting finding. It found that the algorithms definitively did show signs of collusive behaviour, but that their chosen equilibrium price point was far below the Nash equilibrium. That is, the researchers expected these algorithms to maximally extort the consumers, but they only modestly extorted the economy's consumers.

[0] - https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3304991

fellowniusmonk•1h ago
This was the Greystar situation that already happened with apartment rentals.

Are people not aware of this?

A switch to value based pricing for essentials (water,shelter,transport,utilities, etc.)is an extremely easy way to destroy disposable income and even make some areas impossible to live in for the existing members.

Austin, Texas in 2021 saw several of my friends who were renters see a 1 year price increase that more than doubled their rent, I had friends who we're doctors who we're forced to move out of one bedroom apartments, even if it wasn't the plan, it's still a great way to displace people like local musicians so hack comedian can move in.

hrimfaxi•57m ago
> Austin, Texas in 2021 saw several of my friends who were renters see a 1 year price increase that more than doubled their rent, I had friends who we're doctors who we're forced to move out of one bedroom apartments, even if it wasn't the plan, it's still a great way to displace people like local musicians so hack comedian can move in.

Hack comedians are moving in while doctors are priced out? What are you even talking about?

fellowniusmonk•34m ago
That's not what was said.

There were different professional cohorts of people displaced as prices went up around the entire city, this is not a hard concept.

This massive cultural displacement is part of what drove Austin to permit more new construction than any other city in the states.

Fortunately musicians are still the single largest cohesive voting block in Austin.

>it's still a great way to displace people like local musicians so hack comedian can move in.

babush•44m ago
"Algorithmic collusion"... If using an algorithm leads to collusion, then choosing to use the algorithm should be considered regular collusion.
IlikeKitties•39m ago
The Problem is that "using the algorithm" doesn't require you to use a computer. You can do this with pen and paper and it still works. You just have to ensure your competitor is aware of how the algorithm works, which is impossible to make illegal.
babush•23m ago
I never mentioned a computer.
walterbell•14m ago
https://news.ycombinator.com/item?id=45611361

  On October 6, 2025, California Governor Gavin Newsom signed AB325, a law targeting the use and distribution of certain algorithmic pricing tools. This law is part of a larger legislative trend to try to reign in algorithmic pricing.. California’s bill targets pricing algorithms in all markets and will take effect in 2026. However, a violation of the new law requires a conspiracy or price coercion, so as a practical matter, it may not extend the range of violations already encompassed by the Cartwright Act.