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Welcome Auctions Jonathan D. Wareham

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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: 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 Seller value revenue buyers

5  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 Performance Measures

6  Valuation private values common values correlation  Risk assessment risk neutral risk averse  Symmetry symmetric asymmetric Bidder and seller characteristics 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  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 English Auction

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 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 First price, sealed-bid

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 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 1.Aggressive bidders receive sure and certain awards but pay a price closer to market consensus. 2.The price that winning bidder pays is determined by competitors' bids alone and does not depend upon any action the bidder undertakes 3.Hence, closer to real market valuation and socially optimal 4.Less bid shading or collusion occurs because people don't fear winner's curse. 5.Hence, they may adjust bid upwards. 6.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  descending price (often by “Dutch clock”), open-outcry  first price wins  auctioneer usually has no influence  little information on demand is revealed Dutch Auction 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


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