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Problem_Set_12_Solutions

# Problem_Set_12_Solutions - Kaushik Basu Spring 2008 Econ...

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Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 12 1. Consider the game tree described below. Now suppose y can take two possible values, 2 or 1. Player 1 always gets to know which value y has taken, but player 2 does not (though she knows that it is either 2 or 1). 1 1 -1 y 2 0 l r L R 2 x 1 w

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(a) Imagining that there is an initial move made by nature, draw a game tree of this 'larger' game, with the incompleteness of information, described above, captured through the appropriate use of information sets. Answer: In this tree, N is nature and p is the probability that nature picks either branch. Notice the dashed line on player 2’s choice nodes that represents the fact that she does not know which node she is at. (b) What will the outcome of this game be? Answer: For P2 it is a dominant strategy to pick l no matter which node he is at (this is because 2>0 and 1>0). Thus player one will always choose L because 1 > -1. Therefore the outcome of this game is (LL, l ) 2. Consider a two-player game involving a politician and an adviser. The politician has to choose between two projects, n and t . Consider the case where state of nature w 1 occurs (or, equivalently, Nature chooses w 1 ): If the politician chooses n , the adviser and the politician get payoffs of 1 and 0 respectively; and if the politician chooses t the payoffs are 0 and 1 . If state of nature w 2 occurs, the payoffs are reversed. The politician does not know the state of nature but the adviser does. After seeing the state of nature the adviser tells the politician "Do t " or "Do n ". Describe the above game as a game tree. -1 2 2 0 1 1 1 r l L R 1-p -1 1 2 0 1 1 1 r l L R p 2 2 N
Answer: Note that the different colored lines and circles are information sets.

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Problem_Set_12_Solutions - Kaushik Basu Spring 2008 Econ...

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