Auction Theory Auction theory is important for • practical reason • empirical reason • testing-ground for economic theory, especially of game theory with incomplete information • theoretical reason
Theoretical Reason • Help us understand other methods of price formation (posted prices and negotiation) • Close connections between auctions and competitive markets • Close analogy between theory of optimal auctions and theory of monopoly pricing
Types of Auctions • English auction • ascending-price, open-outcry • Dutch auction • descending-price, open-outcry • 1st price sealed bid auction • known as discriminatory auction when multiple items are being auctioned • 2nd price sealed bid (Vickrey auction) • known as uniform-price auction ...
Confusing... In the financial community, • 1st price sealed bid auction is termed an English auction (except by English, who call it an American auction); • 2nd price sealed bid auction is called a Dutch auction.
1st Price Sealed Bid Auction(In the Financial Community) Price Auction size Awarded price quantity
2nd Price Sealed Bid Auction(In the Financial Community) Price Auction size Awarded price quantity
What are they? • Yankee auction • multiple-items auction • winners are determined by some ranking • successful bidders pay what they bid • simultaneous ascending auction • began in the US in July 1994 • US spectrum auction #4 in Dec. 1994
General Remarks about Auction • Complex auction strategies • risk attitude, one or multiple items, private or common value, secret information, etc. • The only piece of information available to all is the rules of an auction. • Economists use the framework of game theory to study auction behavior.
Key Feature of Auctions The Presence of asymmetric information • private-value model • pure common-value model • general model • each bidder’s value is a general function of all the privately-received signals
Theoretical Predictions • English and 2nd price sealed bid auctions are strategically equivalent, or isomorphic. • Dutch and 1st price sealed bid auctions are also strategically equivalent, at least in theory.
Buyer’s Bidding Strategy (I) • English auction • bid a small amount more until reaching the valuation, then stop • 2nd price sealed bid auction • the dominant strategy is to submit a bid equal to his valuation, namely truth-telling
Buyer’s Bidding Strategy (II) • Dutch auction • no “optimal” bidding strategies • decide in advance the maximum amount to bid • 1st price sealed bid auction • no “optimal” bidding strategies • tradeoff is between winning more often and benefiting more
Dutch/FPSB Auctions Suppose only two bidders. Both bidders’ valuation of the good are taken independently from a uniform distribution over values between 0 and 1. Bidder 1’s expected return is E(R1) = (V1-b1) Prob(b1b2)
Recall “After work…” Suppose you are one of the two bidders involved in the first price sealed-bid auction of a rare stamp. The stamp is worth $700 to you. Having sized up your opponent, you think it could be worth anything between $0 and $1000.
NE in Dutch/FPSB Auctions • bi = Vi/2 for the case of two bidders • bi = (n-1)Vi/n for the case of N bidders
Bidder’s Winning Strategy • Avoid pitfalls • winner’s curse • Always bid cautiously • Don’t let the presence of several competing bidders push you into making too aggressive a bid.
You cannot make moneyif you are too cautious? Milgrom (1989, JEP) ...returns in bidding come from cost and information advantages, ... bidders without some advantage have little hope of earning much profit, but could with a little bit of carelessness suffer large losses.
Common Values Independent Private Values Seller’s Expected Revenue (Risk Neutral Bidders) < = English > 2nd price Dutch = 1st price English = 2nd price
Common Values Independent Private Values Seller’s Expected Revenue (Risk Averse Bidders) ? < English > 2nd price Dutch = 1st price English = 2nd price
Seller’s Auction Strategy Revealing information removes uncertainty • link the final price to outside indicators of value (an authoritative evaluation)
Buyers One Many Negotiations using EDI Web-based sales auctions Web-based Procurement auctions Web-based many-to-many auctions Auctions in E-Commerce One Sellers Many
Auctions in E-Commerce • Web-based sales auctions • Onsale • Web-based procurement auctions • GE TPN • Web-based many-to-many auctions • Arizona Stock Exchange
Auction in E-Marketplace • Seller controlled marketplace • vendor web sites with auction • Buyer controlled marketplace • web site procurement posting • purchasing agents • purchasing aggregators • Neutral marketplace
Role of Neutral Intermediary • Advantage of scale of transaction processing • may act as service bureaus • collect valuable selling/buying information • How to provide more value to sellers and buyers