How to hack the subway using fare arbitrage

Could you save swapping tickets with another commuter during your journey so that the total you both pay is less? This kind of riskless profit-taking, or arbitrage, is common in capital markets where traders aggressively seek out and exploit these inefficiencies in the market. Could commuters also benefit?

Today we get an answer thanks to the work of Asif Haque, a data scientist at Twitter, who has analysed the possibility of fare arbitrage on the San Francisco metro system, known as BART (Bay Area Rapid Transit). Haque says that not only are opportunities for fare arbitrage possible on BART, they occur on more than 13 per cent of all pair-wise combinations of journeys offering considerable potential for savings.

Spotting fare-arbitrage opportunities is relatively straightforward in principle. Armed with an up-to-date fare guide, it’s simple to find out whether a particular pair of trips allows for arbitrage.

People what are you waiting for?  This sounds almost as good as arbitrage using the Forever Stamp:

Haque says that 60,334 of these pairs or 13.5 per cent, have an arbitrage opportunity of at least 5 cents. And 4,666 of these pairs of trips could save commuters at least $1. Haque has generously posted the full list of these 4,666 fares here.

There is further discussion, with examples, here.  For the pointer I thank Tom Fowler.


I take BART daily, and have considered the problem before. Ignoring ethical concerns, there are possibilities for considerable profit here -- imagine I come up from Millbrae (as I do in the evenings), and come into the city, and someone else comes from Daly City and goes down to San Bruno. If we could swap tickets mid-trip, we could profit to the tune of about $3 each per trip, and I could profit at $3 per trip, that's more than a thousand dollars a year.

But it's logistically impossible. You don't "meet" people traveling other directions from you, they're on different trains. Even if you take the (much more limited) profit opportunities that Haque talks about, where both of you are going the same direction, how do you locate the other passenger? Obviously BART is not going to stand for you putting out a sign in their trains or stations advertising your desire to lower their fares (they do not even want you to buy partially-consumed BART tickets that other people want to sell off).

Added to this, passengers who ride BART frequently are almost invariably on Clipper cards, so there is no physical ticket to swap, &c.

Obviously for us and for Haque, this is an academic exercise, but I did wonder for a while whether presumably more cost-conscious people with criminal backgrounds might be trying this.

Surely there's a startup out there which will create an app for the purpose of broking the swaps?

Grindr for subway tickets. Ticketr, I guess.

Riding the D.C. Metro, it's cheaper if you're making more than one trip in a day to purchase an all-day unlimited pass.

So some of us may have developed the habit of giving away their still-good all-day passes to people walking into the station as we exit our last stop for the day... not naming any names, of course... :)

I was thinking the same thing (being a BART rider) but it turns out that's not what they're talking about. Rather, they're talking about people going the same direction, and the bizareness that occurs when prices don't increase linearly and consistently with distance.

It looks (from the examples) like prices increase *sub*-linearly, which why you can save on fares by turning trip-pairs into ones with the longest unbroken trip: it costs less to go from A to C than A to B plus B to C. So if you have someone go from A to B*, and someone else from B to C, then it's cheaper to break it into A to C and B to B*.

I haven't thought about arbitrage, but I have noticed this and it annoyed me: when planning a trip, I figured, "hey, they must charge more the farther you travel". So, when I was about the same distance from two stops, take the one nearest my final destination, right? Wrong. Any starting point from the downtown stops yields the same fare.


Finally, just a nitpick, but this is wrong from the article: "the San Francisco metro system, known as BART (Bay Area Rapid Transit) ". Uh, no:

1) There is no "San Francisco metro system", but a bunch of overlapping transit systems that touch San Francisco.

2) If you asked people about "the" SF metro system, they would assume you're talking about SF Muni, the dominant one that's SF-specific, and is different from BART, despite a little overlap.

3) BART is not the San Francisco-anything system; it covers -- wait for it -- the Bay Area. Not all of it, but a lot more than SF; south to Millbrae, or south to Fremont across the bay, far east to Pleasanton or Bay Point, and up north through Berkeley to Richmond.

This post is shit, since it's not clear at all WTF they are talking about.

Basically the first idea is that if one is traveling A->C and the other B->D, then they can instead buy A->D and B->C and then meet at C, swap tickets and perform a transfer so they are both better off.

The second idea is that if one is travelling A1->B1 and the other B2->A2, then they can buy A1->A2 and B2->B1 and swap tickets, effectively traveling for free on the AB route.

The first idea simply exploits the fee structure, while the second is a full exploit of the system allowing nearly free travel but requires to be able to meet while traveling in opposite directions.

Obviously both exploits are fixed by tying tickets to ID, and the second only is fixed by running trains in the center and requiring reticketing to switch sides of the station.

In principle, I think this is perversely exploiting the economy of scale that BART offers customers: 20 miles is cheaper than two 10 miles.

Instead of two medium length trips buying one huge & one tiny ticket is cheaper. Tiny being the overlapping segment of your two mediums.

Two small problems - it's almost certainly against the conditions of carriage to exchange tickets, and is probably fraudulent too.

.....but OTOH probably impossible to police against practically.

After all, crime is a large industry. Don't they deserve thir own economists specializing in the practical problems of crime, analyzing rational and irrational strategies, arbitrage opportunities, etc.? Heck, they should have their own Journal of Criminal Economics, which should be an open access journal, of course, because you certainly can't expect the subscription model to work. And there should be chairs of criminal economics, at universities which accept anonymous Bitcoin endowments.

I really feel like this should be a thing. It feels to me like gov't law is becoming less and less relevant. I basically smoke weed, download illegal bittorrents, trade unregulated crypto, look at secret NSA docs, might have sex with a prostitute one day just to add another crime, etc., etc., and this is all socially acceptable and some of it's normal, some of it's uncommon but not particularly deviant... It should be studied with a view to facts, not to eradication or moralizing. I would donate some BTC for more of this.

"This sounds almost as good as arbitrage using the Forever Stamp"

Which also doesn't sound like much of an opportunity. The market for $0.49 stamps in the period after the increase will be lousy, since any organization that buys stamps in numbers large enough to matter (and is price sensitive) will have had the foresight to stock up beforehand. And price insensitive organizations won't bother to look for bargains after the increase.

This makes me think of the Barro-Gordon model of inflation. The USPS has an incentive to make people *think* that forever stamps are forever, and then renege.

Wow. Savings of a dollar.

This is a far cry from the days when you could book two round trip flights (from A to B and B to A, both over Saturday night) and save hundreds of dollars per trip. This amounted to thousands of dollars annually since I made the trip almost weekly.

A former boss of mine did that. He was in LA, and came up to SF (almost) every Wednesday. His tickets were (LAX-SFO Feb 3 am, SFO-LAX Feb 10 pm), then (LAX-SFO Feb 10am, SFO-LAX Feb 17pm), etc. Even though the flight from LAX to SFO and back wasn't that expensive, especially when you ordered well in advance, it did save the company enough money to make it worth someone's time to set that up.

Even now, I've often seen a London-DC flight selling for ~$1500 whereas a Istanbul-London-DC flight sells for only $700.

Too bad there's no way of getting them to allow you to board at London.

I have seen this type of thing from time to time, too, and I don't really understand it. What is the benefit to the airline of having you sit in the seat from Istanbul-London? Even if they have a 0% chance of selling that leg on its own, their overall cost is slightly lower if they just have the seat empty.

Isn't it just price discrimination? London-DC travelers have more purchasing power.

The market for flights from Istanbul to DC is different from the market for flights from London to DC. With the London-DC flight the only serious competition is between other London-DC flights, while on the Istanbul itinerary, the competition is not only a nonstop flight from Istanbul, but also with flights that connect through Paris, Frankfurt, Amsterdam, or Zurich (among others). Very few people are going to fly London-Frankfurt-DC to save a few buck, more people would be willing to take a connection on an Istanbul itinerary.

Interestingly, this price differential doesn't seem common on the reverse flight i.e. DC-LON. It's the same purchaser demographic so my guess is only because it's harder to prevent a passenger from hopping off midway (esp. if travelling sans check in bags).

Are they arbitrage opportunities if they don't take into account the transaction costs of making the exchange (e.g. finding the people with whom to swap tickets, the awkwardness of actually asking someone to swap tickets)? It is important to always look at the cost side as well as the benefit side before labeling something an arbitrage opportunity.

I suspect Coase would have used this as an example of transaction costs being greater than the efficiencies from market transactions

Yep. Nailed it.

I laughed out loud at the forever stamps line.

If you really want to 'hack' a subway, move to LA. They don't ever check tickets on most lines and if they do, you can generally flash any old ticket and walk by.

Once true, but no longer. No more paper tickets, just TAP cards, which must be used to enter turnstyles. When checks do occur, they scan the TAP cards for actual use.

Time is a cost. This is not arbitrage.

Same criticism can be made of many classic financial arbitrages. Particularly in many small and illiquid instruments you can find (pretty close to) pure arbitrage opportunities all over the place. The thing is that most of these arbitrages don't yield much money relative to the effort they take. Which is of course why they continue to exist.

Free lunch economists have taken over. No longer do economists seek to build better futures, but they instead seek to profit from pillage and plunder. Hell with rules and fair exchange; let's just cheat and let the fools pay the bills.

You're preaching to the wrong choir if you're looking for folks trying to create a brighter future. This crowd will push a toddler down the stairs to make a buck.

Exactly right.

'if you’re looking for folks trying to create a brighter future'

So that 'small steps toward a much better world' is just PR?

p_a trying to get the Biggest Douche title back from Ray Lopez

What, you think our host is not sincere, or do you think that some commenters here are completely oblivious to the motto in the title?

A third alternative, of course, is both - but then, I'm fairly sure you never worked for GMU's PR department or a privately funded center affiliated with GMU, so you wouldn't be able to know just how correct that last alternative would be.

I don't work for anybody, I'm David Koch

Free lunch economists have taken over. No longer do economists seek to build better futures, but they instead seek to profit from pillage and plunder. Hell with rules and fair exchange; let's just cheat and let the fools pay for our .lunch.

All mourn the fall of San Francisco, "plundered" by marauding economists who figured out a way to reduce subway revenue by 0.7%. The smoldering ruins of the once great city layed to waste by "free lunch economists" armed with their fare guides, as devastating as Genghis Khan's Golden Horde.

You're also ignoring that as more arbitrage occurs, price differentials drop. This creates price smoothing. Of course this price smoothing will not occur in the official market if the subway administration does not change the fare structure. It will occur in the secondary market, and the individuals involved will stand to benefit from the exchange.

Right On, Mulp.

I was dismayed by the lack of social conscience on this thread, until I got to your post. The subway is a heavily subsidized social good and somebody will have to pay to make up for the cheaters. So many people on this thread seem happy to screw the subway they benefit from if they can save themselves 70 cents.

Professsor Cowen, I was an econ grad student at GMU for five years in the 80s, and I don't think I ever heard a prof or even a student discuss economics in such a selfish and socially destructive way. These people do not have the character to work for me and I would not hire them.

Could the subway just introduce a fare policy where such arbitrage wasn't possible? Or would that hurt revenue?Perhaps this is merely stupidity of the fare planners?

OOPS! After carefully reading all the posts, I see that some of them are sarcastic and pretty clever. My apologies to them, but not to the cheaters.

As economists I think we all can agree with the logic of that. However, I was a citizen advisor to DC Metro for a while, and setting fares is a long and highly politicized process with the final decision done by committee in the late hours with last-minute compromises. Once the fare schedule is finally agreed upon, nobody wants to reopen the process to deal with a small glitch.

And you were worried about the cheaters? How about the system you are describing which cannot possibly create efficient rules?

Then, the system deserves the travelers it gets.

The fare arbitrage is 100%. Just go to your destination and swap with someone who wants to go where you came in. You both pay$0. Or you can stick two tickets in the entry slot each way the first time you travel, and be set for life without having to deal with anyone else. Public transit still wouldn't be worth it, however.

During the 1990s your second plan would have worked on the DC Metro, although it is a little more complicated than you described. I hope Metro has eliminated most of this by having the computer check time stamps. I could have saved a bundle on my daily commute from Vienna to Federal Triangle, but this is defacto stealing. (At our office we had a desperately poor working mother who was using this trick, but she was special case.)

Why not just jump the turnstile instead? It requires less effort, saves you the whole fare instead of just part of it, and is legally and ethically equivalent.


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