1. Welcome
Auctions
Jonathan D. Wareham

2. What is an auction ?
A method for allocating scarce resources based on competition
Bidding mechanism:
the seller (auctioneer) defines the auction rules:
how the winner is determined
how much he must pay
each buyer chooses a bidding strategy
The auction rules define a game among buyers
should use game-theoretic concepts to analyze auctions

3. Examples Ancient cases: More recent cases: auctions
500BC: Herodotus mentions about auctions in Babylon
Ancient Rome: commercial trading, selling war booty
193 A.D.: auction for the entire empire
More recent cases: auctions
for rare collective items
in wholesale markets of fish, flowers, etc.
for public contracts
in stock market
Very recent cases: auctions
over Internet (E-bay, ONSALE, etc.)
for bandwidth (Interxion, RateX, etc.) , spectrum

4. Auctions and resource allocation
An auction is a market mechanism that
allocates resources (goods) to buyers
generates value for the consumers
generates revenue for the seller
generates revenue for the producer
Is used where traditional market mechanisms (e.g. fixed price) can not be used
can serve as an internal mechanism
value
Seller
buyers
revenue

5. Performance Measures
When choosing an auction design, a variety of assessment criteria and measures may be used:
social efficiency (maximize the total value to buyers: Vickrey)
revenue (seller profit)
bidder profit
time, complexity, susceptibility to collusion
Why is it hard to design? Due to lack of information!
seller
Auction: incentive mechanism
buyer: maximizes expected profit
seller: maximizes performance measure

6. Bidder and seller characteristics
Valuation
private values
common values
correlation
Risk assessment
risk neutral
risk averse
Symmetry
symmetric
asymmetric i
Buyer i

7. Auctions Uses Major types of Auction English First-price, sealed-bid
Second-price, sealed-bid (Vickrey)
Dutch

8. English Auction An ascending sequential bid auction.
Bidders observe the bids of others and decide whether or not to increase the bid.
The item is sold to the highest bidder.

9. English Auction ascending bid, open-outcry
item is sold at least at the reserve price
best strategy for bidder
bid a small amount more than the previous high bid until bidder’s valuation is reached, then stop
auctioneer has great influence
most emotional and competitive of auctions
much information regarding demand is revealed

10. First-Price, Sealed-bid
An auction whereby bidders simultaneously submit bids on pieces of paper.
The item goes to the highest bidder.
Bidders do not know the bids of other players.

11. First price, sealed-bid
first price wins
sealed (each bidder is ignorant of other bids)
usually each participant is allowed one bid
two parts
bidding period
resolution (winner determination) phase
bidder’s strategy: shade bids
to generate positive profit
to avoid winner’s curse (for common value)
little information on demand is revealed

12. Second Price, Sealed-bid
The same bidding process as a first price auction.
However, the high bidder pays the amount bid by the 2nd highest bidder.

13. Developed for Social Efficiency: Vickrey auction
second price wins, sealed
the item is awarded to the highest bidder at a price equal to the second highest bid
dominant strategy: submit a bid equal to true valuation  incentive compatibility
less fear of winner’s curse (for common value)

14. Different distributions for bidders’ valuations
Why???? Asymmetric Cases
Different distributions for bidders’ valuations
Revenue equivalence does not apply
First price auctions not socially optimal
Public authorities should use second price auctions for efficiency purposes
otherwise, possibility for inefficiency u

15. Intuition
Aggressive bidders receive sure and certain awards but pay a price closer to market consensus.
The price that winning bidder pays is determined by competitors' bids alone and does not depend upon any action the bidder undertakes
Hence, closer to real market valuation and socially optimal
Less bid shading or collusion occurs because people don't fear winner's curse.
Hence, they may adjust bid upwards.
Bidders are less inclined to compare notes before an auction.

16. Dutch Auction A descending price auction.
The auctioneer begins with a high asking price.
The bid decreases until one bidder is willing to pay the quoted price.
Strategically equivalent to a first-price auction

17. Dutch Auction descending price (often by “Dutch clock”), open-outcry
first price wins
auctioneer usually has no influence
little information on demand is revealed
price

18. Information Structures
Independent private values
Bidders know their own valuation of the item, but not other bidders’ valuations
Bidders’ valuations do not depend on those of other bidders
Affiliated (or correlated) value estimates
Bidders do not know their own valuation of the item or the valuations of others
Bidders use their own information to form a value estimate
Value estimates are affiliated: the higher a bidder’s estimate, the more likely it is that other bidders also have high value estimates.
Common values is the special case in which the true (but unknown) value of the item is the same for all bidders

19. Optimal Bidding Strategy in an English Auction
With independent private valuations, the optimal strategy is to remain active until the price exceeds your own valuation of the object.

20. Optimal Bidding Strategy in a First-Price, Sealed-Bid Auction
If there are n bidders who all perceive valuations to be evenly (or uniformly) distributed between a lowest possible valuation of L and a highest possible valuation of H, then the optimal bid for a risk-neutral player whose own valuation is v is

21. Example Two bidders with independent private valuations (n = 2)
Lowest perceived valuation is unity (L = 1)
Optimal bid for a player whose valuation is two (v = 2) is given by

22. Optimal Bidding Strategy in a Second-Price Sealed-Bid Auction
The optimal strategy is to bid your own valuation of the item.
This is a dominant strategy.
You don’t pay your own bid, so bidding less than your value only increases the chance that you don’t win.
If you bid more than your valuation, you risk buying the item for more than it is worth to you.

23. Optimal Bidding Strategies with Affiliated Value Estimates
Difficult to describe because
Bidders do not know their own valuations of the item, let alone the valuations others.
The auction process itself may reveal information about how much the other bidders value the object.
Optimal bidding requires that players use any information gained during the auction to update their own value estimates.

24. The Winner’s Curse
In a common-values auction, the winner is the bidder who is the most optimistic about the true value of the item.
To avoid the winner's curse, a bidder should revise downward his or her private estimate of the value to account for this fact.
The winner’s curse is most pronounced in sealed-bid auctions.

25. Common value auctions Value of bidder is not fixed before the auction
True value of item is not known ex-ante, although defined
Value to bidder i depends on other bidder’s values
examples: sealed box with coins, oil-lease
Complex strategies, no general results
Winner’s curse: the winner discovers that he overestimated the value of the item
Strategic approach: shade the bid to account for the adverse selection bias

26. Expected Revenues in Auctions with Risk Neutral Bidders
Independent Private Values
English = Second Price = First Price = Dutch
Affiliated Value Estimates
English > Second Price > First Price = Dutch
Bids are more closely linked to other players information, which mitigates players’ concerns about the winner’s curse.

27. Collusion
Bidders make collusive agreements to get the item at a lower price:
they select their designated winner (the one with the highest valuation)
others promise to follow a specific strategy (abstain from bidding)
Which auctions are more collusive than others ?
Enforcement issue: incentives for non-winners to keep their promise

28. Collusion (cont.)
First price sealed bid and Dutch auctions: not self-enforcing! no possibility for punishment
In FP: winner places bid = other bidders may abstain or break the ring by bidding slightly higher
In Dutch: one of the others may shout “mine” and win!
English and Second price auctions: self-enforcing!
In English: if one of the others bids higher than promised, then the winner may overbid again
In SP: winner’s bid = valuation of others’ bid