My colleague and I who were traveling together from Poland had an experience on Sunday that should serve as an excellent discussion point on game theory. Okay, here's the setup: He and I were able to communicate on the flight in to Detroit and, since we had a VERY short time for a connecting flight, agreed that we would not wait for each other if one of us got their baggage early. We agreed that whoever got their bags would head straight to the gate of the connecting flight and see if there is any chance of getting on.
When we landed (we got our bags at the same time), we were told by the airline representative that we could not make the flight. Instead, we were booked on a later flight through a different city. So, we just decided to go to the gate for the new flight. On getting through security, I happened to look at some flight monitors and noticed that the earlier flight was delayed slightly and there was a very small chance that we could catch it if we rushed straight to the gate for that flight. I whirled around and could not see my colleague anywhere. He did not have a cell phone, so there was no way of contacting him. What would you do?
Well, I assumed that (a) either he also noticed that the flight was delayed and had headed straight to that gate, (b) he was walking towards the gate for the later flight and would notice that the earlier flight was delayed and rush there, or (c) he would never realize that the earlier flight was delayed and he would be comfortably ensconced at the gate for the later flight waiting for me. What would you do in this situation? If you go to the gate for the later flight looking for him, you will almost certainly miss the earlier flight. Perfect game theory situation where you have to respond in anticipation of how someone else will respond without being able to communicate with them!
I went running to the gate for the earlier flight, hoping he would already be there. In two of the three options he would be there. In the third option, neither one of us would make the earlier flight. It would have been foolish to head to the gate for the later flight and I assumed he would realize this and head straight to the gate for the earlier flight. No such luck. I was able to board the flight and get home earlier, never knowing what happened to my colleague (he managed to get another flight home).
I was surprised to find that he seemed upset that I had not come to the gate for the later flight to get him (given the time limitation, that would have been impossible). Amazingly, he seemed to suggest that he had noticed that the earlier flight was delayed but still chose to go to the gate for the later flight assuming I would come there. My own guess of his response was that if he had noticed the flight was delayed, obviously the previous agreement (which was premised on taking any possible chance of one of us managing to catch the earlier flight) would supercede the later decision to head to the gate for the later flight (since this later decision was based on the assumption that it was impossible to catch the earlier flight).
Obvious breakdown of game theory because of some indeterminate differences in our assumptions on how the other person would act. Strange and interesting ...
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