Consider a game where everyone in a classroom picks a number between 0 and 100. The person closest to half the average wins.

Obviously, picking a number over 50 would be silly. Based on this, picking a number over 25 would be silly. Similarly, picking a number over 12.5 would be silly. Continuing
this line of thought, picking any number other than 0 would be silly. These thoughts
show the level of thinking of those involved, from level-1 to level-.

Level-k thinking analyzes such games. In actual experiments, players never pick 0, which would be suggested by a Nash equilibrium.
Instead, they utilize many different levels of thinking.