2 What is an auction ?A method for allocating scarce resources based on competitionBidding mechanism:the seller (auctioneer) defines the auction rules:how the winner is determinedhow much he must payeach buyer chooses a bidding strategyThe auction rules define a game among buyersshould use game-theoretic concepts to analyze auctions
3 Examples Ancient cases: More recent cases: auctions 500BC: Herodotus mentions about auctions in BabylonAncient Rome: commercial trading, selling war booty193 A.D.: auction for the entire empireMore recent cases: auctionsfor rare collective itemsin wholesale markets of fish, flowers, etc.for public contractsin stock marketVery recent cases: auctionsover Internet (E-bay, ONSALE, etc.)for bandwidth (Interxion, RateX, etc.) , spectrum
4 Auctions and resource allocation An auction is a market mechanism thatallocates resources (goods) to buyersgenerates value for the consumersgenerates revenue for the sellergenerates revenue for the producerIs used where traditional market mechanisms (e.g. fixed price) can not be usedcan serve as an internal mechanismvalueSellerbuyersrevenue
5 Performance MeasuresWhen 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 profittime, complexity, susceptibility to collusionWhy is it hard to design? Due to lack of information!sellerAuction: incentive mechanismbuyer: maximizes expected profitseller: maximizes performance measure
6 Bidder and seller characteristics Valuationprivate valuescommon valuescorrelationRisk assessmentrisk neutralrisk averseSymmetrysymmetricasymmetriciBuyer 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 English Auction ascending bid, open-outcry item is sold at least at the reserve pricebest strategy for bidderbid a small amount more than the previous high bid until bidder’s valuation is reached, then stopauctioneer has great influencemost emotional and competitive of auctionsmuch information regarding demand is revealed
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, sealed-bid first price winssealed (each bidder is ignorant of other bids)usually each participant is allowed one bidtwo partsbidding periodresolution (winner determination) phasebidder’s strategy: shade bidsto generate positive profitto avoid winner’s curse (for common value)little information on demand is revealed
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, sealedthe item is awarded to the highest bidder at a price equal to the second highest biddominant strategy: submit a bid equal to true valuation incentive compatibilityless fear of winner’s curse (for common value)
14 Different distributions for bidders’ valuations Why???? Asymmetric CasesDifferent distributions for bidders’ valuationsRevenue equivalence does not applyFirst price auctions not socially optimalPublic authorities should use second price auctions for efficiency purposesotherwise, possibility for inefficiencyu
15 IntuitionAggressive bidders receive sure and certain awards but pay a price closer to market consensus.The price that winning bidder pays is determined by competitors' bids alone and does not depend upon any action the bidder undertakesHence, closer to real market valuation and socially optimalLess bid shading or collusion occurs because people don't fear winner's curse.Hence, they may adjust bid upwards.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 Dutch Auction descending price (often by “Dutch clock”), open-outcry first price winsauctioneer usually has no influencelittle information on demand is revealedprice
18 Information Structures Independent private valuesBidders know their own valuation of the item, but not other bidders’ valuationsBidders’ valuations do not depend on those of other biddersAffiliated (or correlated) value estimatesBidders do not know their own valuation of the item or the valuations of othersBidders use their own information to form a value estimateValue 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 becauseBidders 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 CurseIn 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 definedValue to bidder i depends on other bidder’s valuesexamples: sealed box with coins, oil-leaseComplex strategies, no general resultsWinner’s curse: the winner discovers that he overestimated the value of the itemStrategic approach: shade the bid to account for the adverse selection bias
26 Expected Revenues in Auctions with Risk Neutral Bidders Independent Private ValuesEnglish = Second Price = First Price = DutchAffiliated Value EstimatesEnglish > Second Price > First Price = DutchBids are more closely linked to other players information, which mitigates players’ concerns about the winner’s curse.
27 CollusionBidders 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 punishmentIn FP: winner places bid = other bidders may abstain or break the ring by bidding slightly higherIn 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 againIn SP: winner’s bid = valuation of others’ bid