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And given that, given that Player 2 is going to choose right, Player 1 is essentially choosing between 1, if she chooses up, which would be followed by right and down; and 2, which is what happened if she chooses down followed by right.
Finally, Player 1 at the beginning of the game, knows that Player 2 is going to choose left whereupon she's going to choose up, so if she chooses Up she's going to end up getting 4, and if she chooses Down she's going to get 2, so she's going to choose Up.
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In fact she chose up.
If Player 1 chooses (Up, up) then Player 2 is going to choose left.
Then if Player 2 chooses up and Player 3 chooses left, we end up here so that's (0,1,1).
If Player 1 chooses (Up, down) then Player 2's best response is to choose right.
Conversely, if 1 chooses up then 2 wants to choose left.
So the Nash equilibria in this trivial sub-game is 1 just chooses up.
Cornell chooses up to four students as nominees to the national Truman Scholarship competition.
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The problem is that now in this new game Player 2 doesn't know whether she's here, in which case she would want to choose down, or here, in which case she'd want to choose up.
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