EC1P1: Topic 8: Economics as Engineering || with 100%
Error-free Solutions.
In a basic auction, each bidder values the object, denoted by? correct answers va and vb > 0
Private value auction correct answers I know my value, but no one else does. Private
information.
The English Auction is also known as correct answers ascending auction, or open auction or oral
auction
How does English Auction correct answers an auctioneer states a price. The bidder states
whether they accept it or want to exit. Auctioneer raises price and asks again. Continues until all
but one bidder exits. She pays the price at which the rivals have all dropped out of auction.
While it seems dynamic the problem of the bidder is really ? correct answers static: to choose at
which price to call out, conditional on others not having called out yet.
In an ascending auction, what is the strategy? correct answers {STAY, LEAVE} when the
auctioneer calls the prize z.
If auctioneer calls z < Va
- if Amy stays, she may win, get Va - z
- if Amy leaves, she gets nothing 0
- Since Va - z > 0 , optimal strategy: STAY
If auctioneer calls z > Va
- if Amy stays, she may win, get Va - z
- if Amy leaves, she gets 0
- Since Va-z < 0 , optimal strategy = LEAVE
If z = Va, just indifferent
What is the dominant strategy in ascending auction? correct answers if no matter what the other
player does, following the strategy yields the highest payoff to the player.
In our case, STAY until z = Va for Amy, z = Vb for Ben
In ascending auction, when will Amy win over Ben? correct answers if Va > Vb, Amy wins -
gets the good.
An equilibrium in dominant strategies is? correct answers A Nash Equilbrium
In many games, there is no equilibrium in dominant strategies but there is.... correct answers a
Nash Equilibrium
, If the good goes to the highest-value bidder the outcome is? correct answers efficient
In ascending auction, the total surplus Va is split between who? correct answers winner and
seller
What is a second price sealed bid auction? correct answers Bidders independently submit bid,
don't know what each other's bid is. The bidder submitting the highest bid wins the item but pays
the amount bid by the second highest bidder.
What is the optimal strategy for second value sealed bid auction? correct answers bid true value,
Va
Proof that optimal strategy for second value auction is to bid true value: correct answers Say A
bids instead w < Va
- if w > Vb Amy wins, pays Vb. Same as if had bid Va. Not better off.
- If Vb > Va Amy loses. Same as if has bid Va. Not better
- If Va > Vb > w Amy loses. If had bid Va would have won and got Va-Vb > 0 . Worse off.
Say instead Amy bids w > Va
- If Va > Vb, Amy wins, pays Vb. same as if had just bet Va. not better
- If Vb > w, Amy loses. Same as if had bid Va. Not better.
- If w > Vb > Va, Amy wins, pays Va - Vb < 0 . Worse off.
SHOULD JUST BID ACTUAL VALUE
There is equivalence of auctions between? correct answers second-price sealed bid auctions and
ascending auctions - have equal strategies and outcomes.
Only true for private values and 2 players
Descending Auction correct answers An open-outcry auction in which the auctioneer announces
possible prices in descending order. The first person to accept the announced price makes her bid
and wins the auction. Also called Dutch auction.
First price sealed bid auction correct answers An auction in which envelopes containing bids are
opened simultaneously and the item is sold to the highest bidder.
A descending auction is strategically equivalent to correct answers first-price sealed bid auction
harder to find equilbrium strategy here, as have to form some beliefs on others value
In an auction we want 2 things correct answers 1) efficient outcome
2) maximise revenue of seller
What is the result of revenue equivalence theorem? correct answers the first and second price
sealed-bid auctions give the same expected revenue for seller
Error-free Solutions.
In a basic auction, each bidder values the object, denoted by? correct answers va and vb > 0
Private value auction correct answers I know my value, but no one else does. Private
information.
The English Auction is also known as correct answers ascending auction, or open auction or oral
auction
How does English Auction correct answers an auctioneer states a price. The bidder states
whether they accept it or want to exit. Auctioneer raises price and asks again. Continues until all
but one bidder exits. She pays the price at which the rivals have all dropped out of auction.
While it seems dynamic the problem of the bidder is really ? correct answers static: to choose at
which price to call out, conditional on others not having called out yet.
In an ascending auction, what is the strategy? correct answers {STAY, LEAVE} when the
auctioneer calls the prize z.
If auctioneer calls z < Va
- if Amy stays, she may win, get Va - z
- if Amy leaves, she gets nothing 0
- Since Va - z > 0 , optimal strategy: STAY
If auctioneer calls z > Va
- if Amy stays, she may win, get Va - z
- if Amy leaves, she gets 0
- Since Va-z < 0 , optimal strategy = LEAVE
If z = Va, just indifferent
What is the dominant strategy in ascending auction? correct answers if no matter what the other
player does, following the strategy yields the highest payoff to the player.
In our case, STAY until z = Va for Amy, z = Vb for Ben
In ascending auction, when will Amy win over Ben? correct answers if Va > Vb, Amy wins -
gets the good.
An equilibrium in dominant strategies is? correct answers A Nash Equilbrium
In many games, there is no equilibrium in dominant strategies but there is.... correct answers a
Nash Equilibrium
, If the good goes to the highest-value bidder the outcome is? correct answers efficient
In ascending auction, the total surplus Va is split between who? correct answers winner and
seller
What is a second price sealed bid auction? correct answers Bidders independently submit bid,
don't know what each other's bid is. The bidder submitting the highest bid wins the item but pays
the amount bid by the second highest bidder.
What is the optimal strategy for second value sealed bid auction? correct answers bid true value,
Va
Proof that optimal strategy for second value auction is to bid true value: correct answers Say A
bids instead w < Va
- if w > Vb Amy wins, pays Vb. Same as if had bid Va. Not better off.
- If Vb > Va Amy loses. Same as if has bid Va. Not better
- If Va > Vb > w Amy loses. If had bid Va would have won and got Va-Vb > 0 . Worse off.
Say instead Amy bids w > Va
- If Va > Vb, Amy wins, pays Vb. same as if had just bet Va. not better
- If Vb > w, Amy loses. Same as if had bid Va. Not better.
- If w > Vb > Va, Amy wins, pays Va - Vb < 0 . Worse off.
SHOULD JUST BID ACTUAL VALUE
There is equivalence of auctions between? correct answers second-price sealed bid auctions and
ascending auctions - have equal strategies and outcomes.
Only true for private values and 2 players
Descending Auction correct answers An open-outcry auction in which the auctioneer announces
possible prices in descending order. The first person to accept the announced price makes her bid
and wins the auction. Also called Dutch auction.
First price sealed bid auction correct answers An auction in which envelopes containing bids are
opened simultaneously and the item is sold to the highest bidder.
A descending auction is strategically equivalent to correct answers first-price sealed bid auction
harder to find equilbrium strategy here, as have to form some beliefs on others value
In an auction we want 2 things correct answers 1) efficient outcome
2) maximise revenue of seller
What is the result of revenue equivalence theorem? correct answers the first and second price
sealed-bid auctions give the same expected revenue for seller
