Since you and the other player are cooperating, rather than thinking of the “Schelling point number,” think of the Schelling point strategy that you expect each other to implement to try to win.
If I’m avoiding my ex, I might go to a bar that I like more than her, while she goes to a bar that she likes more than me. In the case of the list of numbers, I might pick a number that I think is more significant to me than to the other player.
This assumes that the two players have information that distinguishes them. But not only is that how it is in real life, it’s also easy to show that it’s necessary for any kind of nontrivial answer: if the two players are identical copies of the same physical system, and they don’t have access to any source of randomness like an internet connection or a Geiger counter, then they’re going to give the same answer.
Since you and the other player are cooperating, rather than thinking of the “Schelling point number,” think of the Schelling point strategy that you expect each other to implement to try to win.
If I’m avoiding my ex, I might go to a bar that I like more than her, while she goes to a bar that she likes more than me. In the case of the list of numbers, I might pick a number that I think is more significant to me than to the other player.
This assumes that the two players have information that distinguishes them. But not only is that how it is in real life, it’s also easy to show that it’s necessary for any kind of nontrivial answer: if the two players are identical copies of the same physical system, and they don’t have access to any source of randomness like an internet connection or a Geiger counter, then they’re going to give the same answer.