Exercise 3.14: Challenging Question. In an attempt to reduce the deficit, the government of Italy has decided to sell a 14th century palace near Rome. The palace is in disrepair and is not generating any revenue for the government. From now on we'll call the government Player G. A Chinese millionaire has offered to purchase the palace for $p. Alternatively, Player G can organize an auction among n interested parties (n ≥ 2). The participants to the auction (we'll call them players) have been randomly assigned labels 1,2,...,n. Player is willing to pay up to $p, for the palace, where p, is a positive integer. For the auction assume the following: (1) it is a simultaneous, sealed-bid second-price auction, (2) bids must be non-negative integers, (3) each player only cares about his own wealth, (4) the tie-breaking rule for the auction is that the palace is given to that player who has the lowest index (e.g. if the highest bid was submitted by Players 3, 5 and 12 then the palace is given to Player 3). All of the above is commonly known among everybody involved, as is the fact that for every i, j = {1,...,n} with ij, p; p;. We shall consider various scenarios. In all scenarios you can assume that the p's are common knowledge. Scenario 1. Player G first decides whether to sell the palace to the Chinese millionaire or make a public and irrevocable decision to auction it. (a) Draw the extensive form of this game for the case where n = 2 and the only possible bids are $1 and $2. [List payoffs in the following order: first G then 1 then 2.1
Exercise 3.14: Challenging Question. In an attempt to reduce the deficit, the government of Italy has decided to sell a 14th century palace near Rome. The palace is in disrepair and is not generating any revenue for the government. From now on we'll call the government Player G. A Chinese millionaire has offered to purchase the palace for $p. Alternatively, Player G can organize an auction among n interested parties (n ≥ 2). The participants to the auction (we'll call them players) have been randomly assigned labels 1,2,...,n. Player is willing to pay up to $p, for the palace, where p, is a positive integer. For the auction assume the following: (1) it is a simultaneous, sealed-bid second-price auction, (2) bids must be non-negative integers, (3) each player only cares about his own wealth, (4) the tie-breaking rule for the auction is that the palace is given to that player who has the lowest index (e.g. if the highest bid was submitted by Players 3, 5 and 12 then the palace is given to Player 3). All of the above is commonly known among everybody involved, as is the fact that for every i, j = {1,...,n} with ij, p; p;. We shall consider various scenarios. In all scenarios you can assume that the p's are common knowledge. Scenario 1. Player G first decides whether to sell the palace to the Chinese millionaire or make a public and irrevocable decision to auction it. (a) Draw the extensive form of this game for the case where n = 2 and the only possible bids are $1 and $2. [List payoffs in the following order: first G then 1 then 2.1
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.10P
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Transcribed Image Text:Exercise 3.14: Challenging Question. In an attempt to reduce the deficit, the
government of Italy has decided to sell a 14th century palace near Rome. The palace is in
disrepair and is not generating any revenue for the government. From now on we'll call the
government Player G. A Chinese millionaire has offered to purchase the palace for $p.
Alternatively, Player G can organize an auction among n interested parties (n ≥ 2). The
participants to the auction (we'll call them players) have been randomly assigned labels
1,2,...,n. Player is willing to pay up to $p, for the palace, where p, is a positive integer. For
the auction assume the following: (1) it is a simultaneous, sealed-bid second-price auction, (2)
bids must be non-negative integers, (3) each player only cares about his own wealth, (4) the
tie-breaking rule for the auction is that the palace is given to that player who has the lowest
index (e.g. if the highest bid was submitted by Players 3, 5 and 12 then the palace is given to
Player 3). All of the above is commonly known among everybody involved, as is the fact
that for every i, j = {1,...,n} with ij, p; p;. We shall consider various scenarios. In
all scenarios you can assume that the p's are common knowledge.
Scenario 1. Player G first decides whether to sell the palace to the Chinese millionaire
or make a public and irrevocable decision to auction it.
(a) Draw the extensive form of this game for the case where n = 2 and the only
possible bids are $1 and $2. [List payoffs in the following order: first G then 1 then
2.1
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