Lab 1: Playing Games
Textbook reading: none. This lab needs no preparation.
Key Ideas
A game is a situation in which several people choose at once, without seeing the others’ choices, and each person’s outcome depends on everyone’s choices together. You cannot pick your best move without a theory of what the others will do, and they face the same problem about you.
Today’s lab asks you to build that theory yourself, before anyone has taught you one. For four small games you will predict, on the whiteboard, what a room of your classmates will do. In the last ten minutes the room will play the games, and you will find out.
Two predictions are worth separating. What would people do if they cared only about the points? And what will this room actually do? Where those two come apart, the gap is the most interesting thing on your board.
Problem of the Day
Four games:
- Two thirds. Everyone picks a whole number 0 to 100. Closest to two thirds of the average wins.
- Cooperate or fink. Pairs, one shot. Both cooperate: 5 each. Both fink: 0 each. One finks: finker 8, cooperator −3.
- Take it or leave it. Proposer splits 10 points. Responder accepts (split happens) or rejects (both get 0).
- Five or three. Everyone picks 5 or 3. Pick 3: get 3, guaranteed. Pick 5: get 5 if everyone in the room picked 5, lose 4 if anyone picked 3.
For each game, on your board: (a) what a player who cares only about points does; (b) your prediction of what this room will do, as a number; (c) if (a) and (b) differ, why. Which game are you most and least confident about in your prediction?
Solutions
Two thirds. If nobody guesses above 100, the target is at most 67, so no guess above 67 makes sense; if everyone sees that, the target is at most 44; and so on down to 0. The only combination from which nobody wants to move is everyone guessing 0. In practice the first-round average in a room like ours lands between 20 and 40, so the winning guess is around 15 to 25, and a second round drops sharply. People win by reasoning a step or two ahead of the crowd, not all the way down.
Cooperate or fink. Fink beats cooperate whichever the partner does (8 versus 5, 0 versus −3), so both finking is the points-only prediction. In Kreps’ sample of Stanford MBA students, 74% said they would cooperate. Points are not the whole payoff: facing a classmate, people also care about not being the one who finks.
Take it or leave it. A points-only responder accepts any positive offer, so the proposer offers 1. In practice offers cluster around 4 or 5, and offers of 2 or less are rejected roughly half the time. Responders will pay to punish an insulting offer, and proposers know it.
Five or three. Everyone writing 5 and everyone writing 3 are both combinations from which nobody wants to move. A whole room nearly always lands on 3, because each person only has to doubt one other person to make 5 too dangerous. Played in a pair of friends, the same game almost always lands on 5. The game does not change; what changes is whether everyone can count on everyone.
The ranking. Predictions are reliable where the points-only answer follows from one step of reasoning about your own payoffs, or where there is one obvious combination everyone can see. They fail when the answer needs many steps of “they know that I know” (Two thirds), when the points leave out what people actually care about (Cooperate or fink, Take it or leave it), or when there are several stable combinations and no way to know which one everyone else expects (Five or three).