One-Third of the Average Example

The game is: Choose an integer between 0 and 100. The student who guesses the integer which is 1/3 of the average of all the responses rounded up to the nearest integer, wins.

Consider for the first player

It is reasonable that the player wouldn’t choose any number that is larger than 33.3. (It is dominating all other numbers greater than it, see Dominant Strategy)

And for player 2, she would consider the $\frac{1}{3}$ of the 33, and repeatedly, the only rational answer would be $1$. See Iterated Dominance