The Game Theory of How Algorithms Can Drive Up Prices
67 comments
·October 23, 2025friendzis
eitau_1
I find double-action[0] a really useful mental model of market.
[0] https://en.wikipedia.org/wiki/Double_auction#Game-theoretic_...
zaphar
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.
positron26
This is still so oversimplified. There's always bellwether products customers buy a lot and get used to. They use those to decide if you are cheap or expensive. Costco hotdogs are about satisfaction. If I can get one good deal or even a great deal that I find every time, I'm much more likely to be satisfied.
BizarroLand
I was just thinking about this. Costco either loses money on or just barely breaks even on their hotdogs, but they keep selling them at $1.50. It's a part of their brand.
It would be smarter for them to raise the price of their membership another $10/yr to offset the losses than it would to raise the price of their hot dogs another $0.50 to make them profitable.
sharemywin
if you've ever shopped at Giant Eagle instead of Kroger you'll understand the flaw in the logic.
higher prices usually equals better service, less busy shopping. get in and get out.
so if your time is worth more than your money you aren't sensitive to price at the widget scale. most widgets are bundled with some kind of service.
I bought some printing and it was super cheap but no service not an email not a phone number nothing. not ordering from their again.
bluGill
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.
ozim
That’s the fun part of observing influencers.
Let’s say there is a dozen of them playing Minecraft, one could say they are in the same market competing with each other.
But what happens really is some folks like dude with long hair, others like the other guy that screams every time he wins.
Same with training videos, I bought course from a guy that is kind of monotonous and I don’t care but my GF cannot stand watching the guy for longer than 10 minutes.
Bakeries seem like closest one would be best, but somehow I’d rather go 10 mins further because I don’t like the feeling of the first one. Even though quality or price they don’t differ.
amelius
> 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
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.
walkabout
It’s also the case that market-ideals tend to become miserable to experience in practice if you approach them too closely.
Usually the discussion of that kind of thing revolves around the near-elimination of profit via (hypothetical) too-perfect competition among producers and too-perfect information for consumers, but with the rise of automated mass-scale spying and automated finer-grained price discrimination (plus enormous consolidation of markets due to near-abandonment of anti-trust enforcement in the ‘70s), we’re kinda seeing the real deal play out the other direction: approaching-maximum extraction of profit from every transaction.
Which sucks, to put it mildly. You do not want markets that function “too well” in any direction.
Retric
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.
babush
Can gravity buy out magnetism?
indoordin0saur
> Copyright and patents are flawed... the incumbents always get away with "but we have fair rules"
You're right, but I'd add that important thing here is that this is not a free market.
Fernicia
> The principles behind the free market are flawed
Can you go into specifics?
friendzis
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"
dghlsakjg
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
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."
wordpad
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.
photochemsyn
Imagine a town with two landlords who own all rental properties. Yes consumers prefer cheaper rentals, but all the landlords have to do is write an app that they can use to set prices as high as they can while not having too many units empty. If the homeless population in the town increases, that's an externality - especially if the landlords themselves don't live in the town.
indoordin0saur
This works if landlords don't have significantly more units than are demanded by the population AND it is both very expensive for new units to be built and new competitors to enter the market. If enough supply comes on the market and the best move for the landlord with the additional supply would be to lower prices. Tenants then all move into the better value units and the expensive landlord is left with either empty buildings or is forced to lower his price.
nomilk
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)
sharemywin
that doesn't even consider the buying the competitor across the street and paying lobbyist to have congress ignore you for the benefit of the consumer because with the combined stores you can gain market efficiencies. of course ignore the price gouging that actually happens.
vladms
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).
hrimfaxi
> (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
> 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
> 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.
MangoToupe
> (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)
One obvious answer would be to introduce a publicly-owned, zero-margin competitor not constrained by this algorithm, thus reintroducing an incentive to drive down costs or drive up quality.
bfkwlfkjf
> 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
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
AlGoreRhythm
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
alyxya
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.
babush
"Algorithmic collusion"... If using an algorithm leads to collusion, then choosing to use the algorithm should be considered regular collusion.
IlikeKitties
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
I never mentioned a computer.
walterbell
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.js8
How is this new compared to https://www.paecon.net/PAEReview/issue53/KeenStandish53.pdf ? (See the section "perfect competitors are not profit maximizers".)
oxqbldpxo
Is this applicable to the stock market? Maybe this is why valuations are completely devoid of any intrinsic value.
LatteLazy
I never understand why people don’t pay more attention to “n” in these cases: number of other players.
If there are 2 suppliers in a market, they will collude without algos or private meetings: I can be pretty sure you will not cut your price if I don’t cut mine. The issue there is that there are only 2 suppliers, so trust is very easy.
If there are 100 other suppliers, I know ONE of them will cut their price. So I best cut mine first.
What I am trying to say here is that, algos or not, n is the major driver here imho.
That’s kind of interesting since the US has been very relaxed about falling values of n as long as prices seem ok.
pixl97
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
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
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
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.
photonthug
> 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.
lotsofpulp
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).
steve_gh
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
derbOac
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
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.
kalinkochnev
That sounds actually really cool. Do you have a link to any of your papers?
parineum
"Algorithm" has got to be the least useful word in English today.
It isn't the software that's responsible driving up prices, it's the information.
> Yet a widely cited 2019 paper (opens a new tab) showed that algorithms could learn to collude tacitly, even when they weren’t programmed to do so. A team of researchers pitted two copies of a simple learning algorithm against each other in a simulated market, then let them explore different strategies for increasing their profits. Over time, each algorithm learned through trial and error to retaliate when the other cut prices — dropping its own price by some huge, disproportionate amount. The end result was high prices, backed up by mutual threat of a price war.
This is nonsense. Those "algorithms" were programed to do that. I also notice they didn't add a third copy of the algorithm or a fourth. The summary of this research is that they built a novel algorithm (not one used in practice) and put it in a simulation. How this is representative of any real world scenario escapes me. They proved that software written to optimize profits optimizes profits. Shocking.
The researchers quoted in the article are, essentially, defining collusion as knowing what competitors prices are.
> 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.