[pengstrom]

My stab:

2: implicit world. Reacts to but not modeled. 3: explicit world and your separation from it. 4: Model that includes other intelligences of level 3 that you have to take into consideration. World resources can be shared or competes for. 5: Language. Model of others as yourself, their model include yours too. Mutual recursion. Information can be transmitted mind-to mind.

[blamestross]

Looks a lot like the game theory concept of the "level" of a player. (how many levels of metacognition in others can it practically take into account)