Professor Rod Garratt
ECON 171
Midterm
April 27, 2011
This exam is worth a total of 40 Points. You have 1 hour and 15 minutes to complete
this exam. Good Luck!
1.
Consider the game of Marienbad which, like the game of Nim, is zerosum (there
is a winner and a loser). As in Nim, there are two piles of match sticks and two
players, player 1 and player 2. Let m be the number of sticks in the first pile and
let n be the number of sticks in the second pile. Player 1 moves first and thereafter
the players take turns. At each turn, a player can pick up any number of available
matches from one of the two piles. The player who removes the last match in
Marienbad loses the game (this is just the opposite of the rule for winning Nim).
Prove/explain the following claims:
a)
If m=n=1, then player 1 has a winning strategy. (2 points)
b)
If m=n>1 (e.g. m=5, n=5), then player 2 has a winning strategy. (2
points)
c)
If m
≠
n, then player 1 has a winning strategy.
(1 point)
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Use the minimax method to find the Nash equilibrium for the following zerosum
game. (3 points)
Column
Left
Right
Row
Up
2
5
Down
3
4
3.
Use successive elimination of dominated strategies to solve the following game.
(2 points)
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 Fall '08
 Charness,G
 Game Theory, player, Nash, Marienbad

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