Guess 2/3 of the average: every player picks 0–100, winner is closest to 2/3 of the group average. What do you pick?

How to answer

By iterated dominance: if everyone picked randomly (avg 50), best response is 2/3·50 ≈ 33; if everyone reasons that way, target is ~22, then ~15, etc. The unique Nash equilibrium is 0. Against perfectly rational players pick 0; against real, imperfect players the empirical winner is often ~20–25, so apply a couple of levels of depth rather than the full equilibrium.

Key idea: Stopping at the first level (33) and calling it optimal, or insisting on 0 against humans who don't iterate.