I thought I'd read about this problem years ago, but cannot find the answer online. There is a more well-known dining philosophers problem that is vaguely similar.
https://en.wikipedia.org/wiki/Dining_philosophers
Here is my problem: three metaphysicians go out to dinner. When it is time to pay the bill, they settle the bill as follows:
(1) one of them will pay the entire bill
(2) the other two will not know who paid the bill
(3) all three have a random generator of some sort (coin, dice)
(4) they can communicate with each other and have a plan beforehand, but they are not allowed to exchange physical objects
(4) is necessary because an easy solution for this problem would be to have two black tokens and one white token in a bag and each metaphysician draw one in secret.
Another way to think about this problem is playing werewolf in a group of three. One person needs to be the werewolf, two people are the villagers, but the villagers need to not know who the werewolf is. There is no physical contact; they can only exchange verbal information. However, two of the three can exchange information without the third person hearing it.