The Schelling point game: meet a stranger without a word

A Schelling point, also called a focal point, is the answer people converge on when they must coordinate and cannot talk: not the best answer on paper, but the one that stands out, because each expects the others to expect it. The idea is Thomas C. Schelling's, in The Strategy of Conflict (Harvard University Press, 1960). It answers a puzzle of the coordination game, in which everyone gains by choosing the same as the others, whichever choice that is. Such a game has a Nash equilibrium for every way of matching, so its payoffs alone cannot say which one people will pick. Schelling found that people pick one anyway, far more often than chance would.

In this lesson each student is paired with a stranger: someone in the room they cannot identify or talk to, the same stranger for both rounds. Both must meet somewhere in the city at noon, at one of six places: the Station clock, the Museum steps, the Park fountain, the Tower top, the Market hall or the Ferry pier. If both pick the same place, they meet and each scores 5 points; if not, each scores nothing. Picking blind, a pair would meet 1 time in 6, so the screen gives the class that yardstick: about 1 person in 6.

Your class plays it as “Meet me at noon”. Everyone picks on their phone while the screen shows how many have answered, never where. Then the big screen deals the picks onto two boards side by side: six bins of where the room waited, and a six-by-six of who found whom, each square counting its people. It underlines the best answers and rings all six matching squares as equilibria, identically, because nothing in the payoffs picks a place. A room usually picks one anyway, and the longest bin and the tallest ringed stack show which. The foot counts how many found each other, in people, two for each pair that met.

Then the same pairs try again, having seen where the room waited. Nothing else changes: the same six places and the same 5 points. A place everyone has seen others choose is a focal point of its own, so the second round tests whether a precedent helps strangers meet. Its bins and its six-by-six deal again on boards of their own. Round 1's count is not on that screen, so say both in the debrief, for example: “In round 1, 10 of us found each other; this time, 20.”

A note for the teacher: only completed pairs count. With an odd number of students one is left without a partner, and a pair where someone sent no answer has no result; neither counts as meeting or as missing, and each such phone says why. No place is better than another on paper, so which one stands out is the lesson.

Counts only: the screen never names a student, a seat or a pair. Each phone shows its own result, the place it chose and the place its stranger chose, never whose it was, and once the round has closed, the count of where the room waited. Try the screen-and-phone preview: the phone is yours, and fictional classmates choose through the same runtime as the lesson; they are illustrative, not observations of a real class.