8 ms·

Hotelling’s Game, or Why Gas Stations Have Competitors Nearby

128 points by madiator 15y ago

VladRussian 15y ago
zoning.
- jamesbritt 15y ago
  Good point. I don't doubt that some form of what was described plays a role, but it's interesting that such a obvious (in retrospect ;) ) point was apparently not considered. So now I'm wondering why this is only obvious once mentioned, and to what degree this sort of market/real-world ignorance features in various decisions about stating a business. You often don't know what you don't know, so how does one avoid these sorts of blinders? One answer: try stuff where you can fail fast and (hopefully) cheap.
  - cagey 15y ago
    plays a role Try "is 100% responsible for"; if (in CA, USA) I decided to defy or ignore the zoning bureaucracy and open a gas station (or any "bricks and mortar" business within city limits), I think the 'crats would apply "corrective measures" (up to and including jail time) within days (if not hours or minutes). Although in practice, they'd notice long before that I was missing the multitudinous appropriate permits, and bring my efforts to a crashing halt. As to why this most obvious explanation was missed: maybe the authors have thus far in their lives avoided contact with such bureaucracies?
    - randallsquared 15y ago
      You copied the part of gparent's post that referred to game theory, not zoning.
- neutronicus 15y ago
  That, and highway off-ramps.
  - mc32 15y ago
    Yeah. I think when you see three corners of a 4-way intersection with gas stations it obviously involves zoning as mentioned and traffic volume enough to sustain the three service stations. Where you have lots of volume in multiple directions, there is enough to sustain multiple stations --they in turn eliminate U-turns and crossing traffic in multi-lane roads/highways. I don't often see consecutive stations on the same side of the highway/road --tho I do occasionally (19th ave in SF, for example).
- 9999 15y ago
  I'm surprised your brief rebuttal is not floating higher, as I think it is a far superior explanation for the phenomenon. In rural areas where zoning laws do not account for clustering of services like gas stations and fast food restaurants, there are many other factors that can confound a game theory based solution to this sort of question (availability of utilities like communications, electricity and water for example).
  - wisty 15y ago
    In China, shops try to open up near competitors. Most cities have an "electric bike street", where all the shops in an area are electric bike shops (or restaurants / convenience stores). Customers like choice, and hate to go to a place where they can't compare prices. That might be zoning (I can imagine Chinese authorities saying "OK, that street can sell product X), but I think it's also a long standing tradition. Here, shops hate to be near competitors, and it's not unknown for them to lobby the local council over zoning infringements that their competitors are making. This is despite their competitors pulling in a lot of business. After all, shops will pay many times the rent to be in a mall, proximately because that's where the customers are, but ultimately because that's where the competition is. OK, a small hamburger joint needs to worry if McDonalds sets up next door. But if another small hamburger joint sets up nearby, it will increase traffic. The "competition" isn't the guy next door. It's the guy next door, the food strip in the mall, and home-cooked food; and only the guy next door is pulling in foot-traffic to your area. But guess who most business owners will try to put out of business?
- SoftwareMaven 15y ago
  Except you can (and often have to) petition to get zoning changed. Zoning plays a role, but it is not 100%. I would also bet (but I have no evidence; I'd love to be proven wrong here) that in areas without rigid zoning, you will see the same behavior.
asifjamil 15y ago
you would just hope that the competition between two adjacent gas stations would drive the cost of gas down!
- pyre 15y ago
  I've heard of 'price wars' between gas stations across from each other.
  - madiator 15y ago
    like who has the highest price wins?
  - vacri 15y ago
    I remember seeing one attendant using binoculars to check out the prices of the station down the road from them. I also remember a radio station's competition where the petrol station that sold fuel at the lowest price won the competition. In the final hours of the competition, there were two or three stations selling petrol at 1c/litre... and they lost to the station that was paying customers 1c/litre...
    - StavrosK 15y ago
      What was the prize?
      - vacri 15y ago
        It was about 10 years ago, I can't really remember. Something like $10-20k? Maybe 50? It wasn't outrageous, but it was enough to get a lot of petrol stations competing for it.
- icegreentea 15y ago
  Gas of price has relatively little to do with the business actually operating the gas station [1]. You'll see that on average, you have something like 20 cents going to "Distribution Costs, Marketing Costs, and Profits" at 4 dollars a gallon. You're not going to be able to squeeze much out of that. Unfortunately, I can't get a source to it, but from what I remember, the margins on gas are already so thin that most profit at gas stations come from the random other stuff they sell. I mean think about it... 20 cents (maybe) for a gallon of gas, or like 80 cents (or more) for a can of pop. Also, a side effect of the razor thin margins, as well as the relatively fixed consumption pattern means that while price at the pump tracks crude prices going up almost instantly, on the way down, every single gas station wants to be able to enjoy their extra margins for as long as possible, so they reduce their prices slower. And this clustering phenomenon just encourages that even more, since the moment you undercut your competitor, they'll know in like 5 minutes or something and match you, and now both of you just missed out a bunch of extra cash. Edit: silly me, linky here: [1] http://energyalmanac.ca.gov/gasoline/margins/index.php http://energyalmanac.ca.gov/gasoline/margins/index.php
smeatish 15y ago
OK, now add a third hot dog stand. What's the nash equilibrium now? With 3 hot dog stands, they have an incentive to spread out - if you're in the middle of the other two, then you move to the outer side of one of the other two to capture everyone on that side of the beach. This repeats - there is no stable equilibrium.
- eric-hu 15y ago
  Assuming the 3 hot dog stands start out with spacing to allow for equal coverage, their positions are -2/3, 0, 2/3. Everyone gets 2/3, 1/3rd on each side. The two on the outside have an incentive to move towards 0 because they can take more market share without losing any. The one in the middle does not want to move to either outside area until moving means he can have more market share than what he currently has. If the rightmost player decided to move inward from 2/3 to 0.5, he'd have 0.75 market share (out of 2). The middle player would have 1/3 + 1/4 = 7/12 or 0.58. It still wouldn't be in his interest to become the rightmost player, as his upper market share limit would be 0.5 (a little less). However, there's already an incentive to move to the right player's location, causing the locations to be (-2/3, 0.5, 0.5). The left player gets 1/3 + (2/3 + 0.5)/2 = 1/3 + 1/3 + 1/4 = 11/12 or 0.91. The remainder, 1.09, is split equally among the other two to 0.545 each. Only the left player has incentive to move at this point, since each of the right players stand to lose the right-side market by moving inward, or losing half the left-side market by moving outward. The leftmost player has incentive to move inward now, and can do so until he takes enough market share from the other two that one of them can move to him and gain more. If they all did this and ended up at 0, they'd again have an equal 2/3rds. However, anyone can move slightly to one side or the other and increase his market share to nearly 1. Looks like you're right. I would say there's "equilibrium behavior", though--the 3 players will oscillate between the boundaries [-2/3, 2/3], with someone frequently taking the same position as another.
  - saurik 15y ago
    > If the rightmost player decided to move inward from 2/3 to 0.5, he'd have 0.75 market share (out of 2). This move would not have been made by theoretically optimal players: if he had moved from 2/3 to 0+ instead he would have had 1 market share (out of 2). > Only the left player has incentive to move at this point, since each of the right players stand to lose the right-side market by moving inward, or losing half the left-side market by moving outward. The middle player actually has an incentive to move to the center of the board for the same reason that the original player in the two player case had an incentive to choose the middle of the board (despite having monopoly). > If they all did this and ended up at 0, they'd again have an equal 2/3rds. However, anyone can move slightly to one side or the other and increase his market share to nearly 1. In this configuration the two players on the outside would actually each have ~1, leaving the player in the middle ~0. If we call these positions using formats like 0-, 0, and 0+, the 0 player will move to 0++, causing either the 0- player to move to 0 and the 0+ player to move to 0--. Now we have 0--, 0, and 0++. Now, the 0++ player will move to 0+, and the 0 player will move to 0++, leaving the 0-- player to move to 0-. The 0+ player will move to 0--, the 0++ player will move to 0, and the 0- player will move to 0+. "Finally", the 0-- player will move to 0-. I am pretty certain that this algorithm does not terminate.
aresant 15y ago
Game theory is a well worn chapter in the internal "best-practices" conversion voodoo guide. EG - The OPTIMAL variant for conversion rate is actually at least TWO variants. This isn't perfectly in line with the gas-station example (variants aren't dissipated, they're stacked) but it follows the same logic. Damn hard to test and balance with off the shelf tools, but if you're at scale this is a truth.
- andrenotgiant 15y ago
  Game Theory + MVT? That is tantalizingly interesting, you can't just leave us hanging! I would love to hear, (or be directed to) a more detailed explanation of this!
  - aresant 15y ago
    Awesome - it's one of my favorite "discoveries". The day true mathematicians enter the CRO field the rest of us are toast. I will 100% write up a blog post on this some day - hit me up via my user name contact details and I'll point you in right direction in the meantime.
latch 15y ago
Anyone else think of the Price is Right when he's explaining the optimal position?
chaz 15y ago
NPR Planet Money did a similar story a little while ago: "Why Clusters Of Like Businesses Thrive." http://www.npr.org/templates/story/story.php?storyId=121304873 http://www.npr.org/templates/story/story.php?storyId=1213048...
icefox 15y ago
Sidenote: One has to wonder why doesn't gas buddy make their map interface better. They must realize that no matter where you look the prices overlap.
flomo 15y ago
As the story goes, McDonalds had a very sophisticated system for finding locations. They were constantly doing geographical analysis, looking at development plans, and so on. Meanwhile Burger King did not. Burger King would look where they were opening a McDonalds and try to place a store nearby. Eventually Burger King figured out that the McDonalds' locations were generally more prominent and easily accessible than their own. For example, a McDonalds might be convenient to rush hour traffic, while the nearby Burger King was on the wrong side of the freeway or required a U turn to access. They may have also realized that, when given the choice, more people prefer McDonalds. Their copycat approach was hurting sales. Eventually, Burger King built up their own location-finding capabilities and started locating stores in places where McDonalds was not.
- jacques_chester 15y ago
  A simple rule of thumb for fast food, petrol stations and other "drive by" businesses is that they will position themselves on the side of the road dominated by "homeward" traffic. Most folk in the morning are anxious to get to work on time. But on the way home, you can catch them on an impulse. It's not an ironclad rule, but look around and you'll see what I mean.
  - nowarninglabel 15y ago
    Having worked closely with a Mcdonald's franchisee for some time, I'm pretty sure your observations are merely anecdotal. If you look at Mcdonald's revenues by average franchise, and adjust for number of hours served, breakfast & dinner revenues are roughly equal (in the simplest case just measuring rush hour breakfast revenues of 7-9am with rush hour dinner revenues of 5:30-7:30pm).
    - jacques_chester 15y ago
      I'm willing to be wrong on this. It's based on my observations in a few different cities I've lived in.
      - 15y ago
jacques_chester 15y ago
The application of Hotelling's Law to public choice theory breaks down in voluntary voting scenarios because the full spectrum of voters is no longer present. It does work, roughly, when voting is made compulsory. Australia, where voting is compulsory, has quite a quite pedestrian, quite retail sort of politics. There's sloganeering and accusations of skullduggery, but most of the pitch is usually quite unrhetorical in its format. Policy debates are closely aligned on the median voter, and both major parties work tirelessly to position themselves in that centrist position. The USA, where voting is voluntary, has a mix of soaring rhetoric and absolutely maximised negativity. The difference is that in Australia, you're looking at the people who are "on the beach". In the USA, the goal is to deter the other guy's customers from turning up at all, while ensuring that yours do. Hence the mix of beauty and bile. Edit: removed surplus apostrophe. The unutterable shame.
- orky56 15y ago
  Let's say the US population breaks down to 50% Democrat and 50% Republican. If I am a D candidate, I want the Ds to show up and the Rs to stay at home and same if I were R. If I defend the Ds too much, the Rs take it offensively and vice versa. Assuming they both use equivalent tactics to harm the other while improving their own popularity, how does that not lead to a Nash equilibrium? BOTH populations are riled enough to support their chosen candidate (and prevent the other from winning) or be apathetic enough to stay at home (and let the other candidate win). With voting, candidates cannot be satisfied with just 50% of those who voted i.e. become a commodity and split it. They need to use the fact that belittling someone has a more visible reaction that just praising themselves. The balancing act that BOTH candidates need to play leads to the Nash equilibrium. But really the fact is that the population is not 50/50 and there are regional/demographic differences which just makes candidates' strategies that much more complicated.
  - jacques_chester 15y ago
    > Rs take it offensively This is incomplete. Negative advertising a) motivates the already-motivated, but more importantly it demotivates the less motivated. Essentially, your goal as the Democrat is to make the Republican moderate say "a pox on both their houses!" And yes, it's more complicated than a simple straight line and a fifty-fifty split. We're talking about median positions floating in hyperdimensional issue spaces (the most interesting times in politics are the catastrophic jumps from one local minima to another). But the simplified model has surprising explanatory power. Edit: I didn't properly address your argument which, if I read it correctly, is that perfectly symmetrical strategies will cancel out in a perfectly symmetrical race. That's true, as far as it goes. But the implementation varies, the candidates vary, the electorates vary (especially in the USA where you have gerrymandering -- over here electorates are carved out by an independent commission). Nevertheless, the beauty-and-bile strategy fits the circumstances better than beauty or bile by itself. It's a minimum viable strategy.
vacri 15y ago
Game theory makes the mistake of assuming its the only variable. Another reason for clustering is the congregations of similar stores attract more business. Think of a shopping centre. Now take one of the clothes stores and stick it on a suburban street. It's generally going to do less well by itself because you have to know about it before you go - you have to decide to go to that shop, rather than just show up and see what's on offer, as it were. Perhaps a better example: I'm about to go to Vietnam. Hoi An is "the city with all the tailors". Everyone says "spend a couple of days in Hoi An and get lots of clothes made up". Now, there are tailors all throughout Vietnam of course, but they cluster in Hoi An - and tourists specifically wait until they get there to purchase clothes.
- saurik 15y ago
  While your explanation is generally interesting, and while I'm also not claiming that game theory is the only (or even the primary) variable in this situation, I feel the need to point out that one does not go from gas station to gas station and find that they came home with 30 gallons of gas after an accidental "shopping spree" at the gas mall.
  - vacri 15y ago
    While that is true, if you have equidistant from you two locations, one with one station, and one with four, then all other things being equal, you're going to go to the location with four stations - more price competition, less likelihood of queueing and the like.
    - saurik 15y ago
      Unfortunately, it could easily be the case that the mentioned price competition outweighs the value of increased traffic due to decreased queuing, given how incredibly small the margin on gas stations is (from what I've heard from friends that have managed them).
- ipince 15y ago
  I don't think "game theory makes the mistake of assuming its the only variable". Just like economics, we are simply modeling reality in some (limited) way and gaining some insight and conclusions from analyzing that model. The fault is for someone to apply those conclusions to reality without considering the assumptions made in the model.
impendia 15y ago
The map looks cool but is misleading. There are many more gas stations in San Francisco than that (and the prices are more variable).
Eliezer 15y ago
I've yet to see a Lucky next to a Safeway. Why are supermarkets different from gas stations?
- Simucal 15y ago
  Right next to my house (Ofallon, MO) there are two grocery stores within 200ft of each other. This is just ancedotal but any time I've thought about this topic I've always thought about it in relation to those grocery stores.
  - sesqu 15y ago
    I do some of my shopping in the corner store, and some in the nearby business cluster that has, among others, 4 supermarkets. I'd guess real estate, loyalty programs and product offerings outweigh proximity, in the case of foodstuffs.
goodside 15y ago
The conclusion here has an unfounded moral lesson: "The model suggests why competitors always seem to locate so close to each other and compete on real estate. Think about big burger chains, supermarkets, and video stores. You will almost always see them clustered even though it would be nicer if they spread out." How do you know it would be nicer if they spread out? You'd waste money (and carbon emissions) shipping resources to remote businesses that aren't profitable, or at least not as profitable as they could be if they were closer and easier to ship to. As a reductio ad absurdum, you can't build and maintain a gas station in Antarctica just so that it would "nicer" if someone happened to be there on vacation with their snowmobile. The reason there's no gas stations in Antarctica is the same reason there's so few in Wyoming. It's also the reason they're all clustered around high-traffic areas immediately outside of major cities. If you can't calculate from empirically established methods a "socially optimal equilibrium" that doesn't directly imply that we should be building gas stations in Antarctica, you don't know that the current distribution is suboptimal. More generally, there's a lesson for policymakers here: you shouldn't endeavor to destroy established equilibria that you don't understand. Otherwise, kudos to the author for a pretty neat example and visualization. People who do stuff like this are awesome.
- showerst 15y ago
  My reading of this is that the 'socially' optimal equilibrium (that is to say, the equilibrium for customers) is to build stations in a way that minimizes people's effort to get to them (assuming an even distribution, it would be at .3~ and .6~ on that line he uses), whereas the equilibrium for station owners in light of competition is to cluster roughly in the middle. Social optimality in this case is all about population density (finding the minimum of the function that represents the total effort of everyone involved, _assuming station owner profits are constant_ which is a big assumption), and has nothing to do with forcing stations into Wyoming (unless a few million people suddenly move to Cheyenne). I could be reading this totally wrong though, you can define social equilibrium an infinite number of ways depending on what you're trying to maximize, and what you simplify to 'ceteris paribus'
  - deleted 15y ago
    [deleted]

128 points by madiator 15y ago

VladRussian 15y ago

zoning.

jamesbritt 15y ago
Good point. I don't doubt that some form of what was described plays a role, but it's interesting that such a obvious (in retrospect ;) ) point was apparently not considered. So now I'm wondering why this is only obvious once mentioned, and to what degree this sort of market/real-world ignorance features in various decisions about stating a business. You often don't know what you don't know, so how does one avoid these sorts of blinders? One answer: try stuff where you can fail fast and (hopefully) cheap.
- cagey 15y ago
  plays a role Try "is 100% responsible for"; if (in CA, USA) I decided to defy or ignore the zoning bureaucracy and open a gas station (or any "bricks and mortar" business within city limits), I think the 'crats would apply "corrective measures" (up to and including jail time) within days (if not hours or minutes). Although in practice, they'd notice long before that I was missing the multitudinous appropriate permits, and bring my efforts to a crashing halt. As to why this most obvious explanation was missed: maybe the authors have thus far in their lives avoided contact with such bureaucracies?
  - randallsquared 15y ago
    You copied the part of gparent's post that referred to game theory, not zoning.
neutronicus 15y ago
That, and highway off-ramps.
- mc32 15y ago
  Yeah. I think when you see three corners of a 4-way intersection with gas stations it obviously involves zoning as mentioned and traffic volume enough to sustain the three service stations. Where you have lots of volume in multiple directions, there is enough to sustain multiple stations --they in turn eliminate U-turns and crossing traffic in multi-lane roads/highways. I don't often see consecutive stations on the same side of the highway/road --tho I do occasionally (19th ave in SF, for example).
9999 15y ago
I'm surprised your brief rebuttal is not floating higher, as I think it is a far superior explanation for the phenomenon. In rural areas where zoning laws do not account for clustering of services like gas stations and fast food restaurants, there are many other factors that can confound a game theory based solution to this sort of question (availability of utilities like communications, electricity and water for example).
- wisty 15y ago
  In China, shops try to open up near competitors. Most cities have an "electric bike street", where all the shops in an area are electric bike shops (or restaurants / convenience stores). Customers like choice, and hate to go to a place where they can't compare prices. That might be zoning (I can imagine Chinese authorities saying "OK, that street can sell product X), but I think it's also a long standing tradition. Here, shops hate to be near competitors, and it's not unknown for them to lobby the local council over zoning infringements that their competitors are making. This is despite their competitors pulling in a lot of business. After all, shops will pay many times the rent to be in a mall, proximately because that's where the customers are, but ultimately because that's where the competition is. OK, a small hamburger joint needs to worry if McDonalds sets up next door. But if another small hamburger joint sets up nearby, it will increase traffic. The "competition" isn't the guy next door. It's the guy next door, the food strip in the mall, and home-cooked food; and only the guy next door is pulling in foot-traffic to your area. But guess who most business owners will try to put out of business?
SoftwareMaven 15y ago
Except you can (and often have to) petition to get zoning changed. Zoning plays a role, but it is not 100%. I would also bet (but I have no evidence; I'd love to be proven wrong here) that in areas without rigid zoning, you will see the same behavior.

asifjamil 15y ago

you would just hope that the competition between two adjacent gas stations would drive the cost of gas down!

pyre 15y ago
I've heard of 'price wars' between gas stations across from each other.
- madiator 15y ago
  like who has the highest price wins?
- vacri 15y ago
  I remember seeing one attendant using binoculars to check out the prices of the station down the road from them. I also remember a radio station's competition where the petrol station that sold fuel at the lowest price won the competition. In the final hours of the competition, there were two or three stations selling petrol at 1c/litre... and they lost to the station that was paying customers 1c/litre...
  - StavrosK 15y ago
    What was the prize?
    - vacri 15y ago
      It was about 10 years ago, I can't really remember. Something like $10-20k? Maybe 50? It wasn't outrageous, but it was enough to get a lot of petrol stations competing for it.
icegreentea 15y ago
Gas of price has relatively little to do with the business actually operating the gas station [1]. You'll see that on average, you have something like 20 cents going to "Distribution Costs, Marketing Costs, and Profits" at 4 dollars a gallon. You're not going to be able to squeeze much out of that. Unfortunately, I can't get a source to it, but from what I remember, the margins on gas are already so thin that most profit at gas stations come from the random other stuff they sell. I mean think about it... 20 cents (maybe) for a gallon of gas, or like 80 cents (or more) for a can of pop. Also, a side effect of the razor thin margins, as well as the relatively fixed consumption pattern means that while price at the pump tracks crude prices going up almost instantly, on the way down, every single gas station wants to be able to enjoy their extra margins for as long as possible, so they reduce their prices slower. And this clustering phenomenon just encourages that even more, since the moment you undercut your competitor, they'll know in like 5 minutes or something and match you, and now both of you just missed out a bunch of extra cash. Edit: silly me, linky here: [1] http://energyalmanac.ca.gov/gasoline/margins/index.php http://energyalmanac.ca.gov/gasoline/margins/index.php

smeatish 15y ago

OK, now add a third hot dog stand. What's the nash equilibrium now? With 3 hot dog stands, they have an incentive to spread out - if you're in the middle of the other two, then you move to the outer side of one of the other two to capture everyone on that side of the beach. This repeats - there is no stable equilibrium.

eric-hu 15y ago
Assuming the 3 hot dog stands start out with spacing to allow for equal coverage, their positions are -2/3, 0, 2/3. Everyone gets 2/3, 1/3rd on each side. The two on the outside have an incentive to move towards 0 because they can take more market share without losing any. The one in the middle does not want to move to either outside area until moving means he can have more market share than what he currently has. If the rightmost player decided to move inward from 2/3 to 0.5, he'd have 0.75 market share (out of 2). The middle player would have 1/3 + 1/4 = 7/12 or 0.58. It still wouldn't be in his interest to become the rightmost player, as his upper market share limit would be 0.5 (a little less). However, there's already an incentive to move to the right player's location, causing the locations to be (-2/3, 0.5, 0.5). The left player gets 1/3 + (2/3 + 0.5)/2 = 1/3 + 1/3 + 1/4 = 11/12 or 0.91. The remainder, 1.09, is split equally among the other two to 0.545 each. Only the left player has incentive to move at this point, since each of the right players stand to lose the right-side market by moving inward, or losing half the left-side market by moving outward. The leftmost player has incentive to move inward now, and can do so until he takes enough market share from the other two that one of them can move to him and gain more. If they all did this and ended up at 0, they'd again have an equal 2/3rds. However, anyone can move slightly to one side or the other and increase his market share to nearly 1. Looks like you're right. I would say there's "equilibrium behavior", though--the 3 players will oscillate between the boundaries [-2/3, 2/3], with someone frequently taking the same position as another.
- saurik 15y ago
  > If the rightmost player decided to move inward from 2/3 to 0.5, he'd have 0.75 market share (out of 2). This move would not have been made by theoretically optimal players: if he had moved from 2/3 to 0+ instead he would have had 1 market share (out of 2). > Only the left player has incentive to move at this point, since each of the right players stand to lose the right-side market by moving inward, or losing half the left-side market by moving outward. The middle player actually has an incentive to move to the center of the board for the same reason that the original player in the two player case had an incentive to choose the middle of the board (despite having monopoly). > If they all did this and ended up at 0, they'd again have an equal 2/3rds. However, anyone can move slightly to one side or the other and increase his market share to nearly 1. In this configuration the two players on the outside would actually each have ~1, leaving the player in the middle ~0. If we call these positions using formats like 0-, 0, and 0+, the 0 player will move to 0++, causing either the 0- player to move to 0 and the 0+ player to move to 0--. Now we have 0--, 0, and 0++. Now, the 0++ player will move to 0+, and the 0 player will move to 0++, leaving the 0-- player to move to 0-. The 0+ player will move to 0--, the 0++ player will move to 0, and the 0- player will move to 0+. "Finally", the 0-- player will move to 0-. I am pretty certain that this algorithm does not terminate.

aresant 15y ago

Game theory is a well worn chapter in the internal "best-practices" conversion voodoo guide. EG - The OPTIMAL variant for conversion rate is actually at least TWO variants. This isn't perfectly in line with the gas-station example (variants aren't dissipated, they're stacked) but it follows the same logic. Damn hard to test and balance with off the shelf tools, but if you're at scale this is a truth.

andrenotgiant 15y ago
Game Theory + MVT? That is tantalizingly interesting, you can't just leave us hanging! I would love to hear, (or be directed to) a more detailed explanation of this!
- aresant 15y ago
  Awesome - it's one of my favorite "discoveries". The day true mathematicians enter the CRO field the rest of us are toast. I will 100% write up a blog post on this some day - hit me up via my user name contact details and I'll point you in right direction in the meantime.

latch 15y ago

Anyone else think of the Price is Right when he's explaining the optimal position?

chaz 15y ago

NPR Planet Money did a similar story a little while ago: "Why Clusters Of Like Businesses Thrive." http://www.npr.org/templates/story/story.php?storyId=121304873 http://www.npr.org/templates/story/story.php?storyId=1213048...

icefox 15y ago

Sidenote: One has to wonder why doesn't gas buddy make their map interface better. They must realize that no matter where you look the prices overlap.

flomo 15y ago

As the story goes, McDonalds had a very sophisticated system for finding locations. They were constantly doing geographical analysis, looking at development plans, and so on. Meanwhile Burger King did not. Burger King would look where they were opening a McDonalds and try to place a store nearby. Eventually Burger King figured out that the McDonalds' locations were generally more prominent and easily accessible than their own. For example, a McDonalds might be convenient to rush hour traffic, while the nearby Burger King was on the wrong side of the freeway or required a U turn to access. They may have also realized that, when given the choice, more people prefer McDonalds. Their copycat approach was hurting sales. Eventually, Burger King built up their own location-finding capabilities and started locating stores in places where McDonalds was not.

jacques_chester 15y ago
A simple rule of thumb for fast food, petrol stations and other "drive by" businesses is that they will position themselves on the side of the road dominated by "homeward" traffic. Most folk in the morning are anxious to get to work on time. But on the way home, you can catch them on an impulse. It's not an ironclad rule, but look around and you'll see what I mean.
- nowarninglabel 15y ago
  Having worked closely with a Mcdonald's franchisee for some time, I'm pretty sure your observations are merely anecdotal. If you look at Mcdonald's revenues by average franchise, and adjust for number of hours served, breakfast & dinner revenues are roughly equal (in the simplest case just measuring rush hour breakfast revenues of 7-9am with rush hour dinner revenues of 5:30-7:30pm).
  - jacques_chester 15y ago
    I'm willing to be wrong on this. It's based on my observations in a few different cities I've lived in.
    - 15y ago

jacques_chester 15y ago

The application of Hotelling's Law to public choice theory breaks down in voluntary voting scenarios because the full spectrum of voters is no longer present. It does work, roughly, when voting is made compulsory. Australia, where voting is compulsory, has quite a quite pedestrian, quite retail sort of politics. There's sloganeering and accusations of skullduggery, but most of the pitch is usually quite unrhetorical in its format. Policy debates are closely aligned on the median voter, and both major parties work tirelessly to position themselves in that centrist position. The USA, where voting is voluntary, has a mix of soaring rhetoric and absolutely maximised negativity. The difference is that in Australia, you're looking at the people who are "on the beach". In the USA, the goal is to deter the other guy's customers from turning up at all, while ensuring that yours do. Hence the mix of beauty and bile. Edit: removed surplus apostrophe. The unutterable shame.

orky56 15y ago
Let's say the US population breaks down to 50% Democrat and 50% Republican. If I am a D candidate, I want the Ds to show up and the Rs to stay at home and same if I were R. If I defend the Ds too much, the Rs take it offensively and vice versa. Assuming they both use equivalent tactics to harm the other while improving their own popularity, how does that not lead to a Nash equilibrium? BOTH populations are riled enough to support their chosen candidate (and prevent the other from winning) or be apathetic enough to stay at home (and let the other candidate win). With voting, candidates cannot be satisfied with just 50% of those who voted i.e. become a commodity and split it. They need to use the fact that belittling someone has a more visible reaction that just praising themselves. The balancing act that BOTH candidates need to play leads to the Nash equilibrium. But really the fact is that the population is not 50/50 and there are regional/demographic differences which just makes candidates' strategies that much more complicated.
- jacques_chester 15y ago
  > Rs take it offensively This is incomplete. Negative advertising a) motivates the already-motivated, but more importantly it demotivates the less motivated. Essentially, your goal as the Democrat is to make the Republican moderate say "a pox on both their houses!" And yes, it's more complicated than a simple straight line and a fifty-fifty split. We're talking about median positions floating in hyperdimensional issue spaces (the most interesting times in politics are the catastrophic jumps from one local minima to another). But the simplified model has surprising explanatory power. Edit: I didn't properly address your argument which, if I read it correctly, is that perfectly symmetrical strategies will cancel out in a perfectly symmetrical race. That's true, as far as it goes. But the implementation varies, the candidates vary, the electorates vary (especially in the USA where you have gerrymandering -- over here electorates are carved out by an independent commission). Nevertheless, the beauty-and-bile strategy fits the circumstances better than beauty or bile by itself. It's a minimum viable strategy.

vacri 15y ago

Game theory makes the mistake of assuming its the only variable. Another reason for clustering is the congregations of similar stores attract more business. Think of a shopping centre. Now take one of the clothes stores and stick it on a suburban street. It's generally going to do less well by itself because you have to know about it before you go - you have to decide to go to that shop, rather than just show up and see what's on offer, as it were. Perhaps a better example: I'm about to go to Vietnam. Hoi An is "the city with all the tailors". Everyone says "spend a couple of days in Hoi An and get lots of clothes made up". Now, there are tailors all throughout Vietnam of course, but they cluster in Hoi An - and tourists specifically wait until they get there to purchase clothes.

saurik 15y ago
While your explanation is generally interesting, and while I'm also not claiming that game theory is the only (or even the primary) variable in this situation, I feel the need to point out that one does not go from gas station to gas station and find that they came home with 30 gallons of gas after an accidental "shopping spree" at the gas mall.
- vacri 15y ago
  While that is true, if you have equidistant from you two locations, one with one station, and one with four, then all other things being equal, you're going to go to the location with four stations - more price competition, less likelihood of queueing and the like.
  - saurik 15y ago
    Unfortunately, it could easily be the case that the mentioned price competition outweighs the value of increased traffic due to decreased queuing, given how incredibly small the margin on gas stations is (from what I've heard from friends that have managed them).
ipince 15y ago
I don't think "game theory makes the mistake of assuming its the only variable". Just like economics, we are simply modeling reality in some (limited) way and gaining some insight and conclusions from analyzing that model. The fault is for someone to apply those conclusions to reality without considering the assumptions made in the model.

impendia 15y ago

The map looks cool but is misleading. There are many more gas stations in San Francisco than that (and the prices are more variable).

Eliezer 15y ago

I've yet to see a Lucky next to a Safeway. Why are supermarkets different from gas stations?

Simucal 15y ago
Right next to my house (Ofallon, MO) there are two grocery stores within 200ft of each other. This is just ancedotal but any time I've thought about this topic I've always thought about it in relation to those grocery stores.
- sesqu 15y ago
  I do some of my shopping in the corner store, and some in the nearby business cluster that has, among others, 4 supermarkets. I'd guess real estate, loyalty programs and product offerings outweigh proximity, in the case of foodstuffs.

goodside 15y ago

The conclusion here has an unfounded moral lesson: "The model suggests why competitors always seem to locate so close to each other and compete on real estate. Think about big burger chains, supermarkets, and video stores. You will almost always see them clustered even though it would be nicer if they spread out." How do you know it would be nicer if they spread out? You'd waste money (and carbon emissions) shipping resources to remote businesses that aren't profitable, or at least not as profitable as they could be if they were closer and easier to ship to. As a reductio ad absurdum, you can't build and maintain a gas station in Antarctica just so that it would "nicer" if someone happened to be there on vacation with their snowmobile. The reason there's no gas stations in Antarctica is the same reason there's so few in Wyoming. It's also the reason they're all clustered around high-traffic areas immediately outside of major cities. If you can't calculate from empirically established methods a "socially optimal equilibrium" that doesn't directly imply that we should be building gas stations in Antarctica, you don't know that the current distribution is suboptimal. More generally, there's a lesson for policymakers here: you shouldn't endeavor to destroy established equilibria that you don't understand. Otherwise, kudos to the author for a pretty neat example and visualization. People who do stuff like this are awesome.

showerst 15y ago
My reading of this is that the 'socially' optimal equilibrium (that is to say, the equilibrium for customers) is to build stations in a way that minimizes people's effort to get to them (assuming an even distribution, it would be at .3~ and .6~ on that line he uses), whereas the equilibrium for station owners in light of competition is to cluster roughly in the middle. Social optimality in this case is all about population density (finding the minimum of the function that represents the total effort of everyone involved, _assuming station owner profits are constant_ which is a big assumption), and has nothing to do with forcing stations into Wyoming (unless a few million people suddenly move to Cheyenne). I could be reading this totally wrong though, you can define social equilibrium an infinite number of ways depending on what you're trying to maximize, and what you simplify to 'ceteris paribus'
- deleted 15y ago
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