Friday, December 11, 2009

A Cold Game

An interesting strategic situation arose yesterday. A local bookstore is running a promotion in which it gives away iPhones, which they scatter at different local businesses. It gives clues about the location of the phones, and whoever finds them first wins. I have an old Nokia and I'm exasperated with its spontaneous vibrations, small screen, and inability to access the internet. I thought this iPhone promotion would be a good way to update cheaply.
The phone to be given away yesterday was at a store on campus called the Safe Sex Store. The store opens at noon, and whoever was the first person to enter and ask the person at the register for the prize would win. All throughout the morning, I debated my strategy and consulted with one of my professors. His first response was that I should "just go buy one yourself!", but after an explanation of my budget constraint, this is what we came up with.
  • The first person to arrive should never leave. As tempting as it may be to go across the street and enjoy a hot coffee in the -4 windchill temperatures, the chance that someone else comes and takes the top spot is too great to risk. Leaving the position of control would be a bad choice: if you get there first you should be there for the long haul.
  • The second arriver should stay and wait behind the first arriver. There is a nontrivial probability that the first arriver chickens out and leaves, gets distracted and leaves his spot open, or that the store owner will randomly select the winner from all those who are waiting. Of course, if the latter is the best possibility, the second arriver should probably leave the line as it gets longer, then show up at the very end. A line with ten people creates an expected value (assuming random selection) of only $20, an amount that most would not want to wait for. The second arriver could also attempt to pay the first arriver for his rights to the first spot.
  • A third arriver should not stay in line at all and only appear a little before noon in hopes that random selection will take place.
And what happened? I arrived at the store at 10:30, a time which I though would be more than sufficient. To my dismay, I was the second arriver. The first arriver was ridiculously bundled up and looked like he would not be deterred from his prize. Although there was probably a nontrivial probability of random selection, I did not choose to stick around: after one thirty mile-per-hour gust of wind, I was out of there.

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