"LEVELED!"

Sorry about this if it doesn't really belong in BC, but if feels like a very beginner question to me.

As I've been reading more and more lately, It appears that the "Levels" of thinking are more of a defined thought process rather than a simple expression. So my question is, what are the "levels" if they are infact defined so clearly. My understanding is this:
Level 1 thinking: A player who considers villains range.
Level 2 thinking: A player who considers both villains represented range, as well as the range they themselves are representing.
Level 3+ ???

level 3 a player who consideres villans range, and considers the range they are themselves representing AND considers the villians consideration of the range we are representing.

"What do I think he thinks I have"

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