Get the organizer to tell you who the other person is.

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.

1. You must assume that the other person wants to win.
2. Like you, the other person needs to assume that you want to win.
3. The two of you will need to cooperate in some way even absent explicit communication.
4. Each must assume that the other player has some knowledge of NYC.
5. The time to meet is in some way limited, so appearing at the same place simultaneously is important.
6. If you wander and the other stays in one place, it might help.
7. 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.

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Hang out in the Villages Sumter Landing office while open and then at Sumter Landing. Have taped your token to an orange baseball cap while doing this.

I'd turn the token into a pinwheel, with each spoke of the pinwheel decorated with the words "PRIZE TOKEN!" in different colors. I'd affix the pinwheel to a rainbow hat, wear a dayglo yellow tee-shirt with the words PRIZE TOKEN STARBUCK's ON THE HOUR painted on it in violet, and ride a unicycle around Sumter Landing Town Square. And then, five minutes before the hour, I'd cycle over to Starbucks and just stand there looking like an abject moron until the designated time had passed, or the other person appeared, whichever came first.

Alternately, I would sell the token for 10% of the prize value. Since I get to make up that value, we'll call the total value 2 million bucks, split two ways. So I'd walk away with 200,000, and not have to actually do anything at all after that.