4.3 Discrete First-Price Auction: An item is up for auction. Player 1 values the item at 3 while player 2 values the item at 5. Each player can bid either

4.3 Discrete First-Price Auction: An item is up for auction. Player 1 values the
item at 3 while player 2 values the item at 5. Each player can bid either 0, 1,
or 2. If player 1′ bids more than player j then 1′ wins the good and pays his bid,
while the loser does not pay. If both players bid the same amount then a coin
is tossed to determine who the winner is, and the winner gets the good and
pays his bid while the loser pays nothing. a. Write down the game in matrix form.
b. Does any player have a strictly dominated strategy?
c. Which strategies survive IESDS? 4.5
Iterated Elimination: In the following normal-form game, which strategy
profiles survive iterated elimination of strictly dominated strategies?
Player 2
L
C
R
U
6, 8
2, 6
8, 2
Player 1 M
8, 2
4, 4
9, 5
D
8, 10
4, 6
6, 7 4.6 Roommates: TWO roommates each need to choose to clean their apartment,
and each can choose an amount of time t,- :3 0 to clean. If their choices are t,- and tr" then player i ‘s payoff is given by (10 — Wt; — If. (This payoff function
implies that the more one roommate cleans, the less valuable is cleaning for
the other roommate.) a. is the best response correspondence of each player i ‘3 b. Which choices survive one round of IESDS’?
c. Which choices survive IESDS?

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