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119FinalAK

# 119FinalAK - Psychology and Economics Final Suggested...

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Psychology and Economics Final - Suggested Solutions Botond K˝oszegi May 20, 2007 PLEASE ANSWER ALL THREE QUESTIONS. 1. Two players simultaneously guess a number, with player 1’s pick restricted to be between 300 and 500 (including the endpoints), and player 2’s pick restricted to be between 100 and 900 (including the endpoints). Each player has a “target,” and the closer is her guess to her target, the higher is her payoff. Player 1’s target is 0.9 times player 2’s guess, and player 2’s target is 1.3 times player 1’s guess. All this is known to both players. (a) Suppose both players behave according to the cognitive-hierarchy model discussed in class. Derive the guesses of a level-0, level-1, level-2, and level-3 player 1. Do the same for player 2. Player 1 Player 2 Level 0 300+500 2 = 400 100+900 2 = 500 Level 1 500 × . 9 = 450 400 × 1 . 3 = 520 Level 2 520 × . 9 = 468 450 × 1 . 3 = 585 Level 3 585 × . 9 = 526 . 5 (500) 468 × 1 . 3 = 608 . 4 (b) What is the Nash equilibrium of this game? Player 1 guesses 500 and player 2 guesses 650. 1

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2. Consider the following simplified two-person public-goods game. Each of two roommates si- multaneously decides whether to contribute \$100 to buying a common stereo. (Roommates contribute either the full \$100 or nothing; they cannot contribute an intermediate amount. Also, they cannot change their minds after making the decision.) If both roommates con- tribute, so that they buy a \$200 stereo, they both get an enjoyment benefit out of it that is worth \$150. If one of them contributes, so that they buy a \$100 stereo, they both get a benefit worth \$75. If neither contributes, they do not buy a stereo and do not get the benefits.
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