201Midterm1Answers-2007spring

201Midterm1Answers-2007spring - SABANCI UNIVERSITY ECON 201...

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SABANCI UNIVERSITY ECON 201 – A GAMES AND STRATEGY FIRST MIDTERM EXAMINATION ANSWERS March 20, 2007 1. ( 20 points ). It is a fact that “if in a dynamic game no player ever gets the same payoff in two terminal nodes, then there is a unique bacward induction solution.” Draw the extensive form of a game in which player 1 moves first and chooses between A and B, followed by player 2 choosing between ‘left’ and ‘right’ and the game ends. Choose the payoffs for the two players so that (a) Player 2’s payoffs are all different whereas Player 1 gets the same payoff in two terminal nodes and (b) the game has two backward induction solutions. Write down the two solutions (with complete strategies). ANSWER… #1 A B #2 #2 left right left right (3 , 5) (2 , 4) (1 , 7) (3 , 8) The payoffs are my choices. Player 2’s payoffs are all different, while Player 1’s gets the same payoff 3 in the outcome (A,left) and (B,right). The backward induction solutions are, “Player 2 plays right if B, left if A” in both solutions. Player 1 is indifferent between A and B, which yields two solutions. 2. ( 25 points ) In the rural areas around Ithaca, US, farmers put some fresh produce on a table by the road. There is a cash box on the table and customers are expected to put money in the box for the vegetables they take. The box is attached to the table (so no one can make off with the money) and has just a small slit (so money can only be put in, not taken out.) Consider the following game, as in the story above. A farmer decides on whether to (a) leave his
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201Midterm1Answers-2007spring - SABANCI UNIVERSITY ECON 201...

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