2- Simple auctions II Flashcards
What is a first-price sealed-bid auction?
Bidders simultaneously submit a secret bid, whichever is highest wins paying their own bid
Why is there no incentive to bid one’s valuation (or above) in a first-price auction?
Since you pay your own bid, any price at your valuation or above yields no utility
What are the 3 main assumptions on bidders’ functions?
-Bidders’ strategies are symmetric: If two bidders have the same valuation, v, they bid the same s(v)
-Bidders’ strategies are strictly increasing in valuation
-For each bidder i, s(vi) ≤ vi
What is the fundamental trade off for bidders in a first-price sealed auction?
Higher bids increase probability of winning but reduce payoff if they do
What is the strategy of a bidder [s(v)]?
The strategy maps a valuation to a bid e.g. bid half my valuation s(v) = v/2
What is a simple way of expressing a bidding strategy?
b = αv
where 0≤α≤1 scales down bidder’s valuation
What is the optimal bid in first-price sealed with n i.i.d bidders with private valuations?
(n-1)v/n
i.e. second highest valuation, if we win our valuation v is the highest
Outline how a Dutch/descending price auction works
Price clock showing a decreasing price, auction stops as soon as someone says ‘mine’
Why are Dutch auctions strategically equivalent to first-price sealed-bid?
Because bidding one’s true valuation is not a dominant strategy
What is the main difference between Dutch and first-price sealed-bid auctions?
First-price is a strategic form game, Dutch is an extensive form game
What is the revenue equivalence theorem?
Expected seller revenue is the same for first-price & second-price sealed-bid auctions
What are the 4 conditions for the revenue equivalence theorem?
-Private and i.i.d valuations
-Strictly increasing CDF F(v) = v/r
-Winner is bidder with highest valuation
-Bidder with lowest valuation has expected payoff 0
What is a reserve price?
Only bids above the reserve price are considered
What is a main pro and con of having a reserve price?
-Pro: guarantees a minimum revenue for seller if sold
-Con: if no bid meets the reserve price then the seller will make nothing
What is the fundamental trade off when setting a reserve price?
Lower probability of selling but higher revenue if you do