Auction Theory

• First-price sealed-bid auction: bidders simultaneously write down their bids, highest bidder wins the object and pays the bid they wrote
• Dutch auction: price starts high and gradually falls until one bidder agrees to buy the object at the price
• winner's curse: if bidders act as if the value of the good is the estimate of the value before any information is revealed by other bidders' behaviour, then the winner is likely to have paid too much - if you win, you probably had the highest estimate, so knowing that everyone else has lower estimates you probably want to revise your estimate downwards
• in a pure common values sealed-bid auction, those with no information should bid 0
• Entry deterrence: disadvantaged bidder wins rarely and earns very little when he does win
• entry problems often arise with common values but do not require common values
• common values - the eventual value of the object will be the same for all bidders, but different bidders may have different estimates of this value e.g an oil-field when all bidders have the same production costs
• private values - each bidder has some value for the object which does not depend on the information or values of other bidders e.g wine of known characteristics that the winner drinks on her own
• ascending auction: bidding continues until no-one wants to top current highest bid (which everyone can see) - highest bidder then wins and pays own bid
• Revenue equivalence theorem: assume each of n risk-neutral potential buyers has a privately-known value independently drawn from a common distribution F(z) that is strictly increasing and atomless for the support of z. Then any auction mechanism in which 1. the object always goes to the buyer with the highest value/signal and 2. any bidder with value/signal z expects zero surplus, yields the same expected revenue and results in a buyer with value/signal z making the same expected payment
• all auctions with a suitable public reserve price yield the maximum possible expected revenue for the seller
• all standard auctions with no reserve price yield the same expected revenue for the seller
• Abilities firms require to collude: agree division of market, detect defection from agreement, credibly punish defection, deter new entry
• simultaneous ascending auction likely to be efficient if it can attract entrants and prevent demand reduction
• auctions: efficient, transparent, speedy, fair, seller gets most of value
• administrative allocation: often inefficient, hard to specify criteria, time-consuming, outcome often contested, seller gets little or nothing
• Product-mix auction: each participant simultaneously states its preferences (as a set of bids) across multiple units of many objects, then implement competitive equilibrium allocation consistent with stated preferences
• simplicity important so: bidder can express preferences easily, solving the auction is possible, so everyone understands and trusts the outcome
• complementarities can make collusion valuable