ECON207 -Week 8 Auctions

English - A traditional auction.

• Bids increase in sequential fashion until no one wishes to increase the bid.
• Highest bidder pays their highest bid.
• Bidders continually gain information about eachother.
• The person who values the item the most ends up with the item.

Dutch - Descending Price 

• Auctioner begins at a very high price.
• Gradually lowers the price until someone bids
• The bidder buys the item at their bid.
• No information is available until the auction is over. 

First - Price Sealed Auctions 

• Bidders write bids on hidden paper without knowledge of bids made by other players.
• Highest bidder wins and pays their bid.
• Information available is identical to that in a dutch auction. 

Strategically equivalent to dutch auctions - no information revealed in the auction.

Second - Price Sealed Auctions

• Bidders submit bid without knowledge of other bids.
• Person submitting the highest bid wins but has to pay the second highest bid. 

Strategically identical to english auctions - if bidders bid truthfully the outcomes will be the same.

• Perfect Information - each bidder knows what the item is worth and all players know each individuals valuations. 
• Independent Private Values - each bidder knows own valuation but does not know other bidders' valuation
• Affiliated (correlated) value estimates - bidders do not know their own valuation or others valuations. Each bidder uses their own information to estimate their valuations. The higher a bidder value estimates,  other bidders will have higher estimates
• Common-value auction - true underlying value of item is the same for all bidders. Individual tastes play no role. Bidders use different information to form their value estimates e.g oil/gas 

Optimal bidding stategy : remain active until price exceeds your own valuation of the object. 

b1 = v2 + 0.01

Bid just one penny above the highest valuation. 

Optimal bidding strategy : bid your own valuation of the item because if you pay less you only increase your chand of loosing and if you bid more you risk paying more than the value to you.

Example

• v1 is highest bid - b2 is second highest
• Winners surplus is v1-b2 > 0.
• Bidding just slightly above b2 will not change anything - still pay b2.
• Bidding less than b2 - you lose.

Example

• b2 is highest bid - v1<b2 - v1 loses.
• Only bid below b2 - zero surplus - loses
• Only bid above b2 - negative surplus - losing the better

Optimal bidding strategy: 'shade your bid' and bid below your valuation.

If you hide your valuation, you could win but have 0 surplus. 

b = v - (v-L)/n

b=optimal bid   v=valuation     L=lowest possible valuation    n=no of bidders

Example

• Each bidder perceives that valuations are evenly distributed between £1 and £10 
• Sam's valuation is £2.
• A dutch auction with 3 bidders
• b=v-(v-L)/n   b=2-(2-1)/3  b=£1.67

Paying way more than what you could have done.

When the winners estimate of the value is way above the 2nd highest bid. 

In Common Value Auctions

• Item for sale has the same value to all potential buyers.
• Potential Buyers own estimates of the value differ.
• Bidder i's estimate is : vi = v + Ei     v=common value     Ei=i's estimation error
• If every bidder is truthful the winner has the biggest estimation error - Eimax
• Pay more than v if Eimax > 0
• So bids in common value auctions should be less than v

English = 2nd- Price = 1st- Price =  Dutch

English - Price paid is the second highest plus a penny - b1=v2+0.01

2nd- Price - Price paid is the second highest price

1st- Price - Each bidder estimates how much his valuation is more than the the second highest bid and then shrinks is by that much. 

Dutch - Strategically equivilant to 1st Price. 

Revenue Equiviance Theorem

Players shrink below they're value estimate to avoid the winners curse

English > 2nd- Price > 1st- Price = Dutch

English - Max information = shrink their bids the least = highest expected revenue for auctioner

2nd- Price - Players learn nothing - paying the second price does mitigate winners curse to some extent = players shrink by more than english but not as much as in 1st- price

1st- Price - Players learn nothing and pay own bid = highest chance of winners curse =shrink bids the most

Dutch - strategically equvilant to 1st- Price