presentation on auction theory by simon herrmann
DESCRIPTION
A short presentation on auctions, including Dutch, English and First price vs. second price auctions.TRANSCRIPT
Introduction to Auctions
A short history of auctions
• 500 B.C. Babylon: women were auctioned off as wives (Herodot)
• ~150: Roman soldiers sold war plunder at auction.
• 1744: Sotheby's was created and Christie's in 1766. (mainly art)
• 1887: Sale of fruits and vegetables in the Netherlands through auctions
• 1995: eBay was launched
• 2000/01: UMTS - G3 auction for radio spectrum in Europe (revenue of >50bn EUR)
Use of auctions today
• Treasury bills
• Drilling rights on oil fields
• Privatisation of firms and other assets
• Takeover battles
• Procurement
• and many more
An auction is a market institution with an explicit set of rules determining resource allocation and prices on the basis of bids from the market participants.(McAfee, McMillan, 1987) e.g. used for
• Price Setting - difficult to determine the highest willingness to pay, however lower search cost for customer
• Lottery: not efficient since not necessarily the participant with the highest value for the good wins
• Contract awarding (Beauty Contest): might easily yield a political outcome and might lower the chance of getting new entrants to the market.
Why selling through auctions
Four basic types of auctions
• Ascending bid (English) auction the price is successively raised until only one bidder remains, and that bidder wins at the final price.
• Descending bid (Dutch) auction the price is lowered continuously; the first bidder calling out wins the object at this price.
• First Price sealed bid auction each bidder independently submits a single bid, without seeing others’ bids, the object is sold to the bidder who makes the highest bid; at a price of his bid.
• Second Price sealed bid (Vickrey) auction each bidder independently submits a single bid, without seeing others’ bids, the object is sold to the bidder with the highest bid at the second highest bid.
Strategical equivalent auctions I
• Ascending bid (English) auction the price is successively raised until only one bidder remains, and that bidder wins at the final price.
• Descending bid (Dutch) auction the price is lowered continuously; the first bidder calling out wins the object at this price.
• First Price sealed bid auction each bidder independently submits a single bid, without seeing others’ bids, the object is sold to the bidder who makes the highest bid; at a price of his bid.
• Second Price sealed bid (Vickrey) auction each bidder independently submits a single bid, without seeing others’ bids, the object is sold to the bidder with the highest bid at the second highest bid.
Strategical equivalent auctions II
• Ascending bid (English) auction the price is successively raised until only one bidder remains, and that bidder wins at the final price.
• Descending bid (Dutch) auction the price is lowered continuously; the first bidder calling out wins the object at this price.
• First Price sealed bid auction each bidder independently submits a single bid, without seeing others’ bids, the object is sold to the bidder who makes the highest bid; at a price of his bid.
• Second Price sealed bid (Vickrey) auction each bidder independently submits a single bid, without seeing others’ bids, the object is sold to the bidder with the highest bid at the second highest bid.
Strategic under-bidding(three cases)
Strategic over-bidding(three cases)
my bid opponents bid my profitmy loss
Truth telling a dominant strategySecond Price Auctions
v
price
Truth Telling is the dominant strategy for Second Price auctions => bid shading is not a good (dominant) strategy.
What happens in a First Price auction? Truce telling can not be a optimal strategy since:
for a bid b=vi the expected revenue is 0; E[r]=0
Therefore the optimal bid b* must be smaller than bidders i true value vi => bid shading is a good (dominant) strategy.
Truth telling a dominant strategy
Recall the first price auction: all players state a bid, and the winner is the player with maximum bid, and has to pay his bid as price.
Assumptions:- there are n>=2 bidders- every bidder draws (independently) a valuation v from [0,1]- if bidder i submits the highest bid b* she realizes a economic gain of vi-b*
Claim: best strategy for bidder with value vi is to bid:
Proof: probability of winning for bid b is: and the expected value:
First derivative with respect to b (set equal to 0 to find the maximum) gives:
which reduces to:
Strategy for first price auction
vi
(n !1)
n
bn
n !1
"
# $
%
& '
n!1
(vi! b)
bn
n !1
"
# $
%
& '
n!1
!bn
n !1
"
# $
%
& '
n!1
+ (vi! b)(n !1)bn!2
n
n !1
"
# $
%
& '
n!1
= 0
!b + (vi! b)(n !1) = 0
b = vi
(n !1)
n
Strategy for first price auction
In a First price auction the dominant strategy is given by:
optimal bid is in case of n=2
According to the Revenue Equivalence Theorem (here without proof): Second and First Price auctions generate the same revenue for bidder and auctioneer. If so, why bother about auction design at all?
b = vi
(n !1)
n
bi
=1
2vi
• Available time to sell the goods (fish, flowers, tobacco) =>Dutch auction
• Risk of collusion (limited amount of buyers) => First Price auction
• Predatory behavior (a strong bidder participating might discourage new entrants) => Sealed bid auction
Auction design needs to consider
v
price
First Price Auction
profit
my bid opponents bid my profitmy loss
Collusion
lossSecond Price Auction
agreed priceagreed price
• Bidding on drilling rights on oil fields
• All bidders form their estimate value vi
according to their own geological evaluation
• Each bidder makes a single bid
• If you win you probably overestimated the true value of the oil field
The Winners Curse
Interdependent valuation
• All bidders are risk neutral
• private values are independent drawn from a uniform distribution
Underlying assumptions
The marriage market