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Unformatted text preview: Econ 410 Spring, 2010
Basak Altan Problem Set 6
Please wr/fe leg/b/y and Show a// your work. THE DUE DATE OF THIS PROBLEM SET IS APRIL 27. 1- Consider the following game. _
Player 1 chooses the row (U or D). Her payoffis the ﬁrst number in the cell.
Player 2 chooses the column (L or R). Her payoffis the second number in the cell.
Player 3 chooses the box (1, 2, or 3). Her payoffis the third number in the cell. Choices are made simultaneously. L l R l L R L R
0 4,2,2 ‘ 0,0,0 ‘ u W 0 4,1,4 1,1,1
D 2,2,0 2,3,2 D 4,1,0 1,0,3 D 1,1,1 1,3,2
Box 1 Box 2 Box 3 Find all Nash equilibria ofthis game. 2— In this game there are two players and two boxes. One of the boxes is marked “player 1” and
the other is marked “player 2.” At the beginning of the game, each box contains three dollars.
Player 1 is given the choice between stopping the game and continuing. If he chooses to stop
then each player receives the money in his own box and the game ends. If player 1 chooses to
continue, then two dollars are removed from his box and three dollars are added to player 2’s
box. Then player 2 must choose between stopping the game and continuing. If he stops, then the
game ends and each player keeps the money in his own box. If player 2 elects to continue, then
two dollars are removed from his box and three dollars are added to player [’5 box. Play continues like this, alternating between players, until either one of them decides to stop or k rounds of play have elapsed. At each round both players play unless player 1 chooses to stop. If
neither player chooses to stop by the end of the kth round, then both players obtain 9 dollars. Assume each player wants to maximize the amount of money he earns. a. Draw this game’s tree for k=2. b. Find the subgame perfect equilibrium ofthis game. Good Luck @ ...
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