If two people are trying to meet in New York City, and they forgot to pick a spot, and both of their phones are dead, so they both just go and stand under the clock in Grand Central Station, hoping that the other will expect them to do that, guessing that if they were going to pick a spot to do this, it would be that one, then what you have is a Schelling point.
This is a pretty contrived circumstance, and I usually hear Schelling points talked of as if they are neat but only relevant in those rare cases when communication is impossible. For instance, Wikipedia says ‘In game theory, a focal point (or Schelling point) is a solution that people tend to choose by default in the absence of communication.’
As I was falling asleep last night, somewhere after imagining a kind of house made from genetically engineered trees that just grew into pleasing rounded house shapes roofed with massive leaves, it occurred to me that actually Schelling points are perfectly applicable and even very interesting in cases with communication. It’s just that when there is some combination of a relatively small amount of communication and clear norms about how to respond to communication, then communication often provides a particularly salient Schelling point, so there is not much of a question of what to do, and Schelling points don’t seem relevant.
When many things are being said, or there are other salient Schelling points, or it isn’t clear that everyone’s motives are trustworthy, or probably in other cases, there is no longer a determinate Schelling point necessarily.
- Ten thousand oppressed people have to decide when to launch a revolution against a tyrant. If a small number try to revolt alone, they are probably captured by the oppressors and useless to the revolution. So all ten thousand would like to coordinate to fight at once. They can communicate perfectly freely with one another. However there are constantly suggestions that it happen tonight from the youngest and least strategic members of the group, so if such a suggestion is made, everyone has to guess whether this is the one that everyone is going to get behind. Even if Alice is wise and makes such a suggestion, and Bob knows her to be wise, if Bob doesn’t think everyone will be sure enough that everyone will be sure enough, then he won’t want to go out tonight.
Charles and Dick are in a fight, and both would strongly like to not be in a fight, however would not like to stop fighting before their opponent, because then they might get punched extra. They also don’t really want to fight beyond when their opponent is fighting, because if they punch him extra, he will hold a grudge. So ideally they would stop at the same time. But there is another Nash equilibrium at both continuing to fight (i.e. if both were going to fight more, neither would want to stop earlier). So they have to try to coordinate on one of the Nash equilibria. Charles says that he is going to stop now, but that doesn’t inform Dick much, because of course Charles wants Dick to think Charles is stopping, since then he too will stop. But Charles always wants Dick to stop sooner, regardless of his own plans. So the communication is hopeless in normal terms, and at least not automatically a Schelling point.
Here is the table of payoffs for one punch:
stop punch stop 5, 5 -5, 3 punch 3, -5 4, 4
- Ellen and Frederick are meeting in New York City, and their phones are working fine, and Ellen texts ‘I’ll meet you outside the station in ten?’ and Fred texts ‘yeah’. But Ellen is somewhat tempted to go in and wait under the clock because she and Fred met there once before under highly romantic circumstances, and she is interested in going back there, as it were, but from their current platonic situation, it would be weird to just ask him to meet under the clock again, or to immediately proposition him. She figures that if he feels the same way, and their coordination game is on point, he will actually wait for her under the clock, then come outside if she doesn’t show up. And if he’s not there, well, she tried, and will be a minute late outside. Frederick also figures he might be able to risk-free learn if she feels the same way, and waits inside.
You might argue that these are not all ‘communication’ in some strict sense of genuine information in fact being cheap to convey. Fair enough probably, but in that strict sense, limits to communication are more common.
You might argue that these are still all very contrived examples. Which is fair, but I suspect it stems at least partly from how hard it is to come up with examples, especially if they are examples of a game theoretic situation you recently thought of being manifest.
I assume this is not an original point, but don’t know who it is unoriginal because of. If you liked this post, you might like The Strategy of Conflict, which for all I know literally has this point in it, but at least has a lot more good discussion of Schelling points, including introducing the concept.