Let’s play a game. Pick a number between 0 and 100 and submit it from your phone. We take the average of everyone’s numbers and multiply it by 2/3 — that’s the target. Whoever came closest to the target wins a prize!
Example: if the class average turns out to be 60, the target is 2/3 × 60 = 40 — the guess closest to 40 wins.
Round history — converging on the Nash equilibrium
Why zero? The equilibrium math
Whatever everyone guesses, the target is only 2/3 of it — so the best response always undercuts. The only guess that is a best response to itself is 0. Keynes: prices work the same way — what matters is what average opinion expects average opinion to be.