On Saturday I took a Greyhound bus to Boston to visit Julia and Moss, who have a new place in Cambridge, Mass. Another objective: to get a day's head start on reuniting with Leonard, who had just spent a week and a half near Boston on business.

I found the one-day trip wonderful and intend on returning; what I saw of Boston I liked (what a civilized bus terminal they have!) and of course Moss and Julia are a powerhouse. And Greyhound has a deal where if you buy your round-trip ticket online, Boston-NYC roundtrip is $30.

However! A ticket from Greyhound using that special fare is not, despite the date and time and bus number printed upon it, a specific boarding pass for that bus. It is a general pass that can get you on any bus on that route, for something like a year after the purchase date. So if you arrive a half hour early for your bus, as the ticket suggests, and there's a bus right there and there's room, you can get on that bus! But that means that the bus is first-come, first-served. Should you arrive on time at 9am and find a huge line in front of you, even if your ticket says 9am and theirs don't, they'll get on before you. If the bus runs out of room, you'll have to take the 10am bus. A fellow behind me in line at the Port Authority was vocally unhappy about this with a Greyhound employee, who didn't sooth him terribly well.

And yet! I recently noticed a sidebar notice on Greyhound's web site, in the middle of the purchase process:

Reserve your seat and preboard the bus for only $5.

Available on select schedules only at select terminals.

Reserve Seating can only be purchased in station at the designated ticket line. Customers must be prepared to board 20 minutes prior to schedule departure. See ticket agent for details.

And indeed the not-terribly-amiable Greyhound employee at Port Authority mentioned this $5 reserved-seat upgrade to the disgruntled passenger, so he and a few others who overheard her took her up on it. I assured the people behind me that, despite how very much it sounded like a scam or entrepreneurialism on the part of the Greyhound agent, it was legit. The new VIPs clustered in a new, separate line; they'd board the next bus before our line did.

But then we wondered: what are the game-theoretic implications of this ticketing system?

1. If the people in line behind me do it, and I don't, I lose out, so I have to do it.
2. By induction, everyone has to buy the upgrade to get on the next bus. If everyone does it, no one benefits (except that Greyhound makes $5n). Prisoner's dilemma?
3. But there is a limit on the number of seats on the bus! So only 60 people can be sold reserved-seat upgrades for the 9am bus, and everyone else has to wait for the next (10am) bus.
4. So I should convince people ahead of me in line to buy the upgrade, so fewer seats are available to the people behind me.
5. But the people in front of me have a lower incentive to buy them....unless they fear those behind them. Time to scaremonger?

I didn't buy an upgrade and I made it onto the next bus anyway. Thoughts?