Solve the following exercises from the textbook: • 4.3 Discrete First-Price Auct

Solve the following exercises from the textbook:
• 4.3 Discrete First-Price Auction
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 i bids more than player j then i 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
Iterated Elimination: In the following normal-form game, which strategy
profiles survive iterated elimination of strictly dominated strategies?
Player 2
L CR
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
Roommates: Two roommates each need to choose to clean their apartment,
and each can choose an amount of time ti ≥ 0 to clean. If their choices are ti
and tj , then player i’s payoff is given by (10 − tj )ti − t2
i . (This payoff function
implies that the more one roommate cleans, the less valuable is cleaning for
the other roommate.)
a. What is the best response correspondence of each player i?
b. Which choices survive one round of IESDS?
c. Which choices survive IESDS?
(http://assets.press.princeton.edu/releases/tadelis/game-theory-tadelis-part2.pdf)

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