Guessing two thirds of the group average

Each participant privately writes a number between $0$ and $100$. The winner is whoever is closest to two thirds of the mean of all the numbers. What number should you write?

With fully rational players, $0$; in practice something well below $33$. No guess above $66\tfrac23$ can win, so rational players avoid it; then $44\tfrac49$ is a ceiling, and iterating the elimination drives the unique equilibrium to $0$. Real groups stop after a few levels of reasoning, so winning guesses are often near $20$.