Confusion about multiple information Sets I'm confronted with the following situation: 

First of all nature decides which of two games is played. Then each of two players make a simultaneous move, but only player I knows which game is played. 

How can I display this information in extensive form?

The root will be the nature, which decides whether Game I or Game II is played. Now we have two additional layers for each game. Now I would use an information set to display that the moves are taken simultaneously, but how can I display that only player I knows about which game is played?
You could represent the game in extensive form like this:



The dashed lines enclose player 2's information set. This encompasses all of player 2's nodes because player 2 observes neither nature's nor player 1's choice. Player 1's information sets are the two singleton nodes because player 1 knows which branch nature has chosen.