# The Schelling Point Game: Focal Points in Game Theory, Live Source: https://decka.dev/classroom/game-theory/schelling-point-game Each student is paired with a stranger they cannot talk to, and both must meet somewhere in the city at noon: one of six places, each as good as the others on paper. If both pick the same place, they meet and each scores 5 points. Then the same pairs try again, having seen where the room went. ## What it teaches Students meet the focal point as a room rather than a definition. A pure coordination game with six equally good places has six Nash equilibria in pure strategies, and its payoffs cannot pick one. The class tests on itself whether strangers who cannot talk still find each other more often than blind picks would, and where, and then whether seeing where the room went makes a focal point sharper. ## What is a Schelling point, or focal point, in game theory? 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. ## Classroom debrief If one place drew the most: all six matching squares are ringed the same, so the payoffs do not prefer it. Why did so many of you go there? If two places split the room: what would make one of them the obvious one? If you met about as often as blind picks would, about 1 person in 6: did anyone try to be clever? If more of you met in round 2, say round 1's count aloud first, since round 2's screen does not show it. What did seeing round 1 do? If fewer of you met in round 2: did some of you move away from the crowd, guessing your stranger would? If everybody met at one place: was it the best place, or just the one everyone expected everyone to expect? If someone had no partner or sent no answer, their pair has no result and counts neither as a meeting nor as a miss. Why is that fairer than counting it as a miss? Thomas Schelling put the question to a group of people: where would you meet a stranger in New York, with no way to arrange it? Most chose the information booth at Grand Central Station, and nearly all chose noon (The Strategy of Conflict, 1960). What would our city's answer be, and why? ## Schelling point questions, answered ### What is a Schelling point? A choice people converge on without talking, because it stands out and each of them expects the others to pick it too. Thomas C. Schelling described it in The Strategy of Conflict (1960), and it is also called a focal point. It explains how people coordinate when the rules give them no reason to prefer one answer over another. ### Is a focal point the same as a Nash equilibrium? No. In a coordination game every way of matching is a Nash equilibrium: here, all six places, which is why the board rings all six matching squares the same. A focal point is the equilibrium people actually land on, picked out by something the payoffs do not contain, such as a landmark, a habit or what everyone saw happen last time. ### What is a coordination game? A game in which players gain by choosing the same thing as each other, whichever thing it is. Driving on the left or on the right is one: either works, as long as everyone does the same. This lesson is a pure coordination game: every match pays the same 5 points, so nothing but what stands out can decide where a pair meets. ### What changes in the second round? Only what the room has seen. The same pairs pick again from the same six places, for the same 5 points, after the first round's bins have been on the screen. The second round's boards deal on their own, and the debrief compares how many found each other in each round. ### How are pairs made, and what if the class has an odd number? The room is dealt into numbered pairs at the start, and they stay together for both rounds. Students play through their phones, so nobody knows who their stranger is. With an odd number, one student is left without a partner: their phone says nobody was left to pair with them, and they have no result to count. ### Does anyone see who chose what? No. The big screen shows counts only: how many waited at each place and how many people ended up in each square, never a name, a seat or a pair. Each phone shows its own result and the place its stranger chose, never whose it was, and once the round has closed, the same count of where the room waited. While the room is choosing, the screen shows only how many have answered. ### How long does it take? Two rounds of choosing, each on its own clock, then the debrief at your pace; the saved default shows under the headline as "About N min", and every timer is a setting you control before you run it. ## Run the lesson Present the boards in PowerPoint and Decka. Students scan a QR code or open the session link to join from their phone browsers.