Thomas Schelling first asked a question like this at Yale in 1960. In his version, the meeting was to take place in NYC. He asked it in a class where students most likely felt strongly about coming up with intelligent answers.
Key points.
- You must assume that the other person wants to win.
- Like you, the other person needs to assume that you want to win.
- The two of you will need to cooperate in some way even absent explicit communication.
- Each must assume that the other player has some knowledge of NYC.
- The time to meet is in some way limited, so appearing at the same place simultaneously is important.
- If you wander and the other stays in one place, it might help.
- But, you have no way to know whether the other person will wander, too.
Apparently, at that time, the winning strategy was to go to the Information Desk at Grand Central Station. Schelling described the location as a "focal point". Today, he might have chosen "iconic".
I did not go to Yale. I was only in grade school at that time. But I was curious what the "iconic" location in The Villages might be.
@Neli57 and @ElDiableJoe seem like they were the only participants with much chance of winning. One chose a band to select a square. Probably if that band were not playing he would have chosen the band that he felt was most popular on that night. Perhaps those two would have met!
This idea arose from the study of strategic conflict and games that involve cooperation.