Hotelling’s Game, or Why Gas Stations Have Competitors Nearby (2008)(mindyourdecisions.com)
mindyourdecisions.com
Hotelling’s Game, or Why Gas Stations Have Competitors Nearby (2008)
https://mindyourdecisions.com/blog/2008/03/25/game-theory-tuesdays-hotelling%e2%80%99s-game-or-why-gas-stations-have-competitors-nearby/
64 comments
This is actually a common misunderstanding. The example of ice-cream vendors on a beach or, in this case, gas stations, are toy examples.
The model is not really about location. It is about product differentiation in SOME dimension. By extension, it is also about the number of market participants with differentiated products. Distance or location stands for this differentiation of products.
This is typical of econ models. They are not trying to be realistic, but show a certain mechanism.
By the way, the model can be extended with different pricing mechanisms and many actors (for example on a circle, not a line, to show that generally too many firms enter a market than can be supported).
As for your points:
1) Pricing depends on demand and maket configuration. Usually, one would work with what is called the "inverse demand", where the company has basically solved price as a function of the the amount of goods it WANTS to sell, given other market participants. Note how pricing is implicit in this. While these functions are of course usually assumed to be well behaved, you could do what you want here. So it doesn't miss pricing, it just abstracts from it
In particular, that you can jack up prices depending on location is _explicitly_ in this model.
2) Note how the locations depend on the distribution of demand along the "line". Your intuition depends on this as well. If demand is concentrated somewhere in the middle, you will get a different result...
The model is not really about location. It is about product differentiation in SOME dimension. By extension, it is also about the number of market participants with differentiated products. Distance or location stands for this differentiation of products.
This is typical of econ models. They are not trying to be realistic, but show a certain mechanism.
By the way, the model can be extended with different pricing mechanisms and many actors (for example on a circle, not a line, to show that generally too many firms enter a market than can be supported).
As for your points:
1) Pricing depends on demand and maket configuration. Usually, one would work with what is called the "inverse demand", where the company has basically solved price as a function of the the amount of goods it WANTS to sell, given other market participants. Note how pricing is implicit in this. While these functions are of course usually assumed to be well behaved, you could do what you want here. So it doesn't miss pricing, it just abstracts from it
In particular, that you can jack up prices depending on location is _explicitly_ in this model.
2) Note how the locations depend on the distribution of demand along the "line". Your intuition depends on this as well. If demand is concentrated somewhere in the middle, you will get a different result...
By the way, think about what would happen if you could differentiate in two dimensions? You'd be on a plane or a circle on which a demand distribution exists... etc.
That's the idea.
That's the idea.
The assumption in the example is that the product being sold is a commodity, which cannot be differentiated significantly in terms of pricing or quality.
It limits its applicability, but it doesn't mean the model is incorrect.
https://en.wikipedia.org/wiki/Location_model
https://saylordotorg.github.io/text_introduction-to-economic...
"In Hotelling’s Location Model, firms do not exercise variations in product characteristics; firms compete and price their products in only one dimension, geographic location. Therefore, traditional usage of this model should be used for consumers who perceive products to be perfect substitutes or as a foundation for modern location models."
It limits its applicability, but it doesn't mean the model is incorrect.
https://en.wikipedia.org/wiki/Location_model
https://saylordotorg.github.io/text_introduction-to-economic...
"In Hotelling’s Location Model, firms do not exercise variations in product characteristics; firms compete and price their products in only one dimension, geographic location. Therefore, traditional usage of this model should be used for consumers who perceive products to be perfect substitutes or as a foundation for modern location models."
Customers will naturally migrate to where there is more options, similar to the network effect. See: mall food courts, food trucks, strip malls, etc. So it's possible that the two clustered stands end up splitting a >50% share of the market.
What I'd also like to know is why a cluster of gas stations ends up with different prices. If you have a competitor next door advertising gas at, say, $3.95 per gallon, why would you put up a giant sign saying yours cost $4.05?
Even more baffling, as a customer, why would you go to the more expensive pumps? Sure, loyalty discounts might account for a certain number of decisions, but that can't be the only answer. I've often wanted to go up to someone pumping gas at a higher price when there's a cheaper station right next door, and just ask them how they decided to pay more.
Even more baffling, as a customer, why would you go to the more expensive pumps? Sure, loyalty discounts might account for a certain number of decisions, but that can't be the only answer. I've often wanted to go up to someone pumping gas at a higher price when there's a cheaper station right next door, and just ask them how they decided to pay more.
Back when prices spiked in 2008, I asked a gas station owner about that, he said that the contract he signed with the oil company provider essentially gave them the right to set his prices- and they processed his credit card transactions so they could enforce the deal. If he charged more than they wanted him to, his next set of tankers were priced even higher than everyone else's. If he charged less, they would keep the price for his next set of tankers the same and make him eat the difference. So he pretty much always charged the prices that they told him to. Their prices were set "by a computer" in ways that he didn't understand at all, but he carried them out, because that's what the contract said.
I never look at the price before I go to the pump. If there are multiple stations available then I probably made the choice based on which was easier to get to (side of the street / which direction I'm going) or which looked like it will have cleaner restrooms if I need to pee. I'm not super wealthy or anything, but none of the vehicles I drive take a ton of gas so a difference of 10¢ per gallon just isn't really worth thinking about.
I've seen differences up to $0.30. Pay me $4 to make a left turn? Sign me up.
Driving in Florida, I'll gladly pay $4 to _skip_ a left turn... :)
I fill up once every 4-5 weeks. I'd gladly pay $4 for a cleaner, well lit, easier to access and less busy gas station. I'm balancing all these things in the 5-10 seconds I have when I'm trying to choose between gas stations.
Gas is priced using software, just like hotel rooms or airline tickets. Here's a white paper download, it may explain the factors:
https://www.kalibrate.com/achieve-fuel-pricing-mastery-lp
> In our latest free e-book, you'll find out: What data you need to capture to make better decisions, How to properly gather the right information, Why competitor pricing matters
https://www.kalibrate.com/achieve-fuel-pricing-mastery-lp
> In our latest free e-book, you'll find out: What data you need to capture to make better decisions, How to properly gather the right information, Why competitor pricing matters
Right turn vs left turn.
Brand loyalty; that one time your uncle went to the other place and then two days later needed an engine rebuild, lalala.
Brand loyalty; that one time your uncle went to the other place and then two days later needed an engine rebuild, lalala.
Cleaner restrooms, better cover from sun/rain at the pumps, more likely to have a bottle of sunscreen that hasn't been on the shelf for three years, more likely to have the kind of chips the kids have been screaming about for the last fifty miles.
If I'm able to see the price for multiple stations at the same time and I'm able to adjust my driving to get to any particular one, I'll go for the cheapest one. Typically I tend to optimize for easiest/safest to get to > amenities > price.
For the gas stations available where I live, I have a general idea of which one is going to be cheapest and just go there. The <$2 I could have saved by going out of my way to go for the _currently_ cheapest is not worth the effort to me, especially given how crazy people drive here (Florida).
For the gas stations available where I live, I have a general idea of which one is going to be cheapest and just go there. The <$2 I could have saved by going out of my way to go for the _currently_ cheapest is not worth the effort to me, especially given how crazy people drive here (Florida).
I regularly go to a gas station that I know has better windshield washing fluid and squeegees, even though it's a bit more expensive than the other nearby option.
Besides the obvious issues of branding and gas quality (some brands overtly cut gasoline with ethanol), some states have rules limiting how frequently stations can change prices. If you can only change price once a week and the competitor can only change once a week, the prices can deviate on underlying volatility even if both stations use the same supplier etc
> some brands overtly cut gasoline with ethanol
I think this is actually mandated most everywhere in the USA. Not that I like it. Just saying, that I wish I could choose a station that didn't do that.
I think this is actually mandated most everywhere in the USA. Not that I like it. Just saying, that I wish I could choose a station that didn't do that.
In NY, 99% of gas stations sell gas with ethanol in the standard amount, but there are a few which (claim to) sell non-ethanol gas, so it must not be a legal requirement. However, I haven't tested it, so I'm not sure. I did monitor my gas mileage, and some tanks were way higher than others, so I wonder if the "non-ethanol" gas sometimes has ethanol and sometimes doesn't.
My understanding is the rule is one price change per day. A regulation from the 70's (guess?) to stave off price gouging. Same principle applies.
Same principle? What do price change rules have to do with mandating including ethanol? I don’t get it.
Edited to add: Perhaps the ethanol requirement was to decrease the use of actual gas in order to keep prices at the pump from rising as quickly as oil prices were? I don’t know the history. I just know that ethanol is terrible for small engines and terrible for mileage.
Edited to add: Perhaps the ethanol requirement was to decrease the use of actual gas in order to keep prices at the pump from rising as quickly as oil prices were? I don’t know the history. I just know that ethanol is terrible for small engines and terrible for mileage.
Whoops replied to the wrong comment. Was meant to be in reply to "how frequently stations can change prices"
As someone who has gotten a tank of sand & water before, I tend to prefer the less sketchy station, even if it costs more.
It's a couple cents difference most of the time in my experience, not worth driving in a different direction or such for that.
This baffles me every time in Germany. Price differences for normal gas are around, let's say for the sake of simplicity, 4 cent between different stations. Sometimes it's even lower. But people will drive further or go out of their way so save those 4 cent per litre. If you fill up an 80 litre tank, that's 3,20 Euro at all. Really not worth driving 10 km extra on my way back from work, especially including the time it takes longer and so on.
> What I'd also like to know is why a cluster of gas stations ends up with different prices.
Same reason there are different buy/sell positions on the stock market. People have all kinds of different strategies and portfolios and the price at any given time represents a snapshot of these fluctuating values. Not everyone buys gas for the same price at the same time, not everyone is shooting for the same margin, some may use gas as a loss leader to encourage purchase of overpriced goods in the accompanying store, etc.
Same reason there are different buy/sell positions on the stock market. People have all kinds of different strategies and portfolios and the price at any given time represents a snapshot of these fluctuating values. Not everyone buys gas for the same price at the same time, not everyone is shooting for the same margin, some may use gas as a loss leader to encourage purchase of overpriced goods in the accompanying store, etc.
Little things that make no economic sense like can I pay at the pump, how fast is the credit card processing if I go inside (they’ve gotten slower since chip credit cards are required), does the place have Apple Pay.
For instance my default is always choose a QuikTrip. No matter what part of town I’m in, the place is clean and friendly, they don’t act as if everyone who comes in is a potential robber, and they take Apple Pay.
For instance my default is always choose a QuikTrip. No matter what part of town I’m in, the place is clean and friendly, they don’t act as if everyone who comes in is a potential robber, and they take Apple Pay.
I have no idea. Usually I remember which one typically has the lower price and stick with that one unless there’s a temporary convenience factor, then I might go to the other one.
Honestly I would probably go to the one with the cooler sign that's my favourite colour and not look at the prices.
More or less, the distributors are all paying about the same when they load the gas onto the truck from the plant. The difference in cost comes from the additive mix. Some gas brands qualify as "top tier detergent gasoline," which some cars brands will recommend using.
It's very interesting seeing an article on HN about this. Before my current job, I worked as a data scientist at one of the largest travel centers in the U.S., and we analyzed this problem almost nonstop with regard to both gas and diesel prices. A good pricing strategy is quite complex, and you'd be surprised at the number of factors that goes into it.
Can you talk more about a good pricing strategy for gas and diesel prices, some factors involved, or things you learned?
I don't drive a car nor buy hot-dogs but what struck me as a convincing and important example is how all news-stations play the same news. And not only that but they also much broadcast at the same time.
A discussion from 2011: https://news.ycombinator.com/item?id=2814864.
This is a powerful example but for some reason it never dives into what happens when the 3rd stand appears :D
> If voters pick the candidate closer to their views, and voters are spread out across the spectrum, then both candidates would converge to the middle. It’s no surprise that politicians seek the “average vote.” It also suggests why it’s so hard to tell the difference between candidates during the campaign trail.
Needs a (2008)...
Needs a (2008)...
> Needs a (2008)...
Maybe the differences in the 2016 election were more of style than substance.
Both candidates pointed the finger at powerful (but opposing) foreign-policy enemies (China and Russia). Both made statements in line with interventionist foreign policies. Both lacked any substantial policies to change course on deficit-financed spending. Both said little to nothing about the appropriateness of domestic surveillance. Neither had anything remarkable to say about promoting freedom of the press.
Of course there were some visible policy differences. For example: who to tax and who to let into the country.
And then there were the abundant stylistic difference.
Getting back to the game/analogy presented in the article's video, maybe the differences we saw were more about what color to paint your hot-dog stand and what resemblance if any your logo bears to those used by boogeymen from the past. It had less to do with the quality of the ingredients or prices.
Maybe the differences in the 2016 election were more of style than substance.
Both candidates pointed the finger at powerful (but opposing) foreign-policy enemies (China and Russia). Both made statements in line with interventionist foreign policies. Both lacked any substantial policies to change course on deficit-financed spending. Both said little to nothing about the appropriateness of domestic surveillance. Neither had anything remarkable to say about promoting freedom of the press.
Of course there were some visible policy differences. For example: who to tax and who to let into the country.
And then there were the abundant stylistic difference.
Getting back to the game/analogy presented in the article's video, maybe the differences we saw were more about what color to paint your hot-dog stand and what resemblance if any your logo bears to those used by boogeymen from the past. It had less to do with the quality of the ingredients or prices.
The fact that you think issues immigration (and healthcare, etc.) are dwarfed in importance by the stylistic differences between the candidates says more about your utter callousness and the sheltered bubble you live in than the absence of substantive differences between the candidates.
One candidate wanted to repeal the ACA and replace it with something else TBD, the other wanted to keep it. Unfortunately, the ACA is not going to solve this country's health care problems. So a candidate's position on it largely doesn't matter.
(Ironically, the current administration struck the penalty for not carrying health insurance, reducing health care costs for some of the poorest)
Compare this approach to Sanders, who wanted to extend Medicare to everyone. That is a clearly different policy approach.
Going back to the hot dog stand analogy, Sanders wasn't only far from the middle of the beach. He was on top of a cliff on the opposite end of the island.
That's what a policy difference looks like to me.
I'm not saying that health care and immigration don't matter. I'm saying the party nominees of 2016 were like two hot dog stands located within spitting distance of each other on the beach.
(Ironically, the current administration struck the penalty for not carrying health insurance, reducing health care costs for some of the poorest)
Compare this approach to Sanders, who wanted to extend Medicare to everyone. That is a clearly different policy approach.
Going back to the hot dog stand analogy, Sanders wasn't only far from the middle of the beach. He was on top of a cliff on the opposite end of the island.
That's what a policy difference looks like to me.
I'm not saying that health care and immigration don't matter. I'm saying the party nominees of 2016 were like two hot dog stands located within spitting distance of each other on the beach.
It's incredible how the political landscape has forever changed in the last years.
Fewer people having more voting power via their states having disproportionate voting power changes the game.
It hasn’t changed, politicians are just less subtle about expressing their views. They don’t bother about trying to use dog whistle politics like showing the “welfare queen” or “Willie Horton” ads.
This is also not a Republican or Democratic thing. While yes, the Republicans have Trump, the Clintons also championed the get tough on crime “Three strikes you’re out” laws to protect the good citizens against evil non violent “inner city” criminals.
This is also not a Republican or Democratic thing. While yes, the Republicans have Trump, the Clintons also championed the get tough on crime “Three strikes you’re out” laws to protect the good citizens against evil non violent “inner city” criminals.
What happens in the repeated game? Seems more applicable to the current problem.
How often do gas stations move locations?
How often do gas stations franchise and expand locations within a similar region?
This makes sense, but it's very unfortunate. In Utah there are quite a few small communities that have no services at all so you have to drive maybe 20 to 30 minutes for the closest anything. Needless to say this sucks. In the rare event that a small town has only one station it is virtually guaranteed to have extremely high prices (with one exception that I know of). It's one of the reasons why even tho I prefer a more rural place to live, I opt to live closer to the big city instead. We are getting to a point where the opportunities and conveniences of the big city are making small town life much more difficult (in contrast) and expensive. You have to forgo many conveniences. Perhaps things will change in the future, but that is definitely not the current trend.
Another factor: commercial use and potential hazard zoning. Cities may disallow gas stations in large areas.
Indeed, I'd say in the case of gas stations in particular, zoning could be the primary cause of such clustering.
Another way of thinking about it; when you've been on the highway and see gas, and pull off the highway, and there's a sign "1 gas station left" and "3 gas stations right", you almost always go right. You probably try to go to the first station, but if you pass it, you go to the second station. Each one tries to be the "first" station there, but only one can be first, and the real estate costs for gas-stationed zoned properties probably go up for the closest one.
Explains why political primaries tend to skew so far left or right, and yet when the final election comes, the candidates race towards the middle while framing their opponents as extremists.
The Gas Station's game doesn't seem to correlate well with the game suggested with the Hot Dog stand analogy.
Setting up gas stations is expensive and requires a lot of infrastructure setup and time, once set up people just can't move it around in a city. Now if I were setting a new gas station I would place it in a location where I win greater market share and is disadvantaged to the competitor. Due to the resource constraints, the competitor has to just stay where they were. Gas station locations don't lie in efficient markets where the equilibrium is achieved by being close to each other.
Reminds me of my own observation in the US ( 2001 ) : car dealers concentrate.
Anyone going to dealerships in 2019 is already losing. I made that mistake recently with my wife's car. We went into dealer and I talked to manager. We knew exact model and color we wanted and told him we were there to see it in person and then would get quotes from area dealers... Because he was nice I told him to just give me his absolute best price then and we'd consider it... it was few grand more than I knew I could get so I went the email/quote route. 2 weeks later he won the pricing quote and was 6 grand lower than what he said was his lowest in the showroom. Only shop via email. Ever.
Reminds me when I bought my second car. I wanted to test drive 2 different cars at a couple dealerships. I called ahead to the first one and asked if the model I wanted was available. They said yes, and asked what I wanted to pay for it. I totally low-balled them because I didn't care at this point. When I got there they gave me the price I offered. Never test drove the second car...
This is something I appreciate. Car dealerships are an eyesore, so it's nice when they group together somewhere.
That case seems like it'd be driven by different factors -- car dealerships need lots of space to store all those cars, so they gravitate towards locations where land is cheap; they want to be close to a highway exit, to make taking delivery of new cars easier; there may be local law/zoning issues that limit where businesses that do things like car maintenance on-site can be located; etc.
When I shop for a new car, I go to "auto row" where the dealers are clustered, then it's easy to comparison shop. If I go to a dealer with nobody near, then it's harder. The dealers know this when siting their business.
This article is writing as if this is a growth business, we are a century in and it is more a game of musical chairs, so it is a question of where the survivors are located, not where new entrants start.
There used to be petrol stations everywhere, it was the hot new product to sell once upon a time and every garage would want to have a forecourt. The infrastructure needed then wasn't that much more sophisticated than that needed for a lemonade stand. You could just put the sign up and profit from the passing trade very much on a know-the-customer-personally basis. No upsells were needed, it was an easy way to print money.
Then the market got saturated. Much like mobile phone shops, suddenly small towns had half a dozen of them.
Then this business got picked off by the supermarkets in European markets. They sold own brand petrol at first at a better price than the established brands. The brand did not matter as it is a commodity product. They did not have to make money off it as they were luring customers in for their big shop.
After this round of musical chairs only supermarkets, convenience stores and motorway service stations survived.
I think it has been a cruel business and it is quite sad that something so valuable has no return in it for the end retailer.
There used to be petrol stations everywhere, it was the hot new product to sell once upon a time and every garage would want to have a forecourt. The infrastructure needed then wasn't that much more sophisticated than that needed for a lemonade stand. You could just put the sign up and profit from the passing trade very much on a know-the-customer-personally basis. No upsells were needed, it was an easy way to print money.
Then the market got saturated. Much like mobile phone shops, suddenly small towns had half a dozen of them.
Then this business got picked off by the supermarkets in European markets. They sold own brand petrol at first at a better price than the established brands. The brand did not matter as it is a commodity product. They did not have to make money off it as they were luring customers in for their big shop.
After this round of musical chairs only supermarkets, convenience stores and motorway service stations survived.
I think it has been a cruel business and it is quite sad that something so valuable has no return in it for the end retailer.
In Ireland, I remember the petrol being sold on the street in front of newsstands. It makes clear the reason for having the gas cap on the left side in Japanese and British cars, because people would just parallel park and fill up. I imagine those locations are rare now both for flow-of-traffic and environmental reasons.
In the US gas stations used to be very full service. For the price of a tank (and tip) you would get your radiator and tires topped off, windshield cleaned, etc. There were probably a few old groceries that had a couple pumps but the full service stations quickly became popular. That ended with the oil crisis and stagflation, and self service became the norm, except in a few holdout states like New Jersey, where full service was the law.
The sad result you mention (which is good for consumers, perhaps bad for the environment) is that commodity pricing and loss-leader mentality has made gas worth selling at a small loss to get people to buy high-margin items in the store. QT has cheap gas and expensive sodas.
In the US gas stations used to be very full service. For the price of a tank (and tip) you would get your radiator and tires topped off, windshield cleaned, etc. There were probably a few old groceries that had a couple pumps but the full service stations quickly became popular. That ended with the oil crisis and stagflation, and self service became the norm, except in a few holdout states like New Jersey, where full service was the law.
The sad result you mention (which is good for consumers, perhaps bad for the environment) is that commodity pricing and loss-leader mentality has made gas worth selling at a small loss to get people to buy high-margin items in the store. QT has cheap gas and expensive sodas.
"every garage would want to have a forecourt"
In American this would be every... mechanic? would want... a gas pump out front?
In American this would be every... mechanic? would want... a gas pump out front?
As an American, "garage" is still perfectly valid nomenclature
Zoning is a giant factor in clustering of gas stations in populated areas, link below an example.
https://www.apnews.com/7bf2dceaacfc48178535dfc56d5cdbf3
https://www.apnews.com/7bf2dceaacfc48178535dfc56d5cdbf3
In economics, this is called clustering. Malls and shopping streets are a good example, but also the NYC Diamond District, Las Vegas, and Silicon Valley.
1) It misses pricing. If I am next to another gas station or hot dog stand, I have competitive pressure; my best strategy is to price just below the competitor. If I am isolated, I can jack up prices by however much people are willing to spend to not go further.
2) It also assumes just two players on a beach. With more players and a longer beach, you end up with everyone spread out. With three players, the two outer players will continue to move in towards the center player. If the center player ever has less than 1/4 of the beach, they'll want to move to just outside one of the other two players, who will then want to move to the center.