Information set (game theory)
Example

At the right are two versions of the battle of the sexes game, shown in extensive form. Below, the normal form for both of these games is shown as well.

The first game is simply sequential―when player 2 makes a choice, both parties are already aware of whether player 1 has chosen O(pera) or F(ootball).

The second game is also sequential, but the dotted line shows player 2's information set. This is the common way to show that when player 2 moves, he or she is not aware of what player 1 did.

This difference also leads to different predictions for the two games. In the first game, player 1 has the upper hand. They know that they can choose O(pera) safely because once player 2 knows that player 1 has chosen opera, player 2 would rather go along for o(pera) and get 2 than choose f(ootball) and get 0. Formally, that's applying subgame perfection to solve the game.

In the second game, player 2 can't observe what player 1 did, so it might as well be a simultaneous game. So subgame perfection doesn't get us anything that Nash equilibrium can't get us, and we have the standard 3 possible equilibria:
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