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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?

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You could represent the game in extensive form like this:

enter image description here

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.

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    $\begingroup$ Thank you! This is exactly what I was looking for. If Player 2 knows which game is played as well I'd circle the first two branches and last to branches, right? If Player 2 doesn't know which game is played, but which action Player 1 took, I'd connect the first and third branch and the second and forth branch, right? $\endgroup$ – user7802048 Jun 23 at 12:34
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    $\begingroup$ @user7802048 yes, that's right $\endgroup$ – Ubiquitous Jun 23 at 12:35

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