How should I call a "part" of an extensive form game which is neither (i) a subgame, nor (ii) a stage in a repeated game?
For instance, consider the class of games constructed by "stacking" 2 Stackelberg games, but where the identity of the player who choses first in the second part may depend on the actions in the first part.
I believe these kinds of games are not strictly speaking repeated games (right?). If that's correct, I cannot really speak of the first "part" of the game as the first "stage" (or can I?).
Do you know of any standard terminology to talk about such "parts" of games which are not strictly speaking stages of repeated games?
Edit: if you can substantiate your answer with examples of papers where the terminology you propose is used, that would be even better.