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LECTURE 10 AUCTIONS

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What is an auction? Economic markets: Many buyers & many sellers  traditional markets One buyer & one seller  bargaining Many buyers & one seller  auctions A public sale in which property or merchandise are sold to the highest bidder.

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Terminology and auction types Terminology: Bids B, Bidder’s valuation V, Next-highest rival bid R Small in/decrement in current highest bid: e Classifying auctions: Open or sealed Multiple or single bids Ascending or descending First-price or second-price Private or common-value

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Sources of uncertainty Private Value Auction Bidders differ in their values for the object e.g., memorabilia, consumption items Each bidder knows only his value for the object Common Value Auction The item has a single though unknown value Bidders differ in their estimates of the true value of the object e.g. drilling for oil

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Four standard types of auction (private value auctions) Open Auctions (sequential) English Auctions Dutch Auctions Sealed Auctions (simultaneous) First Price Sealed Bid Second Price Sealed Bid

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English Auction (Ascending Bid) Bidders call out prices Highest bidder wins the item Auction ends when the 2nd highest bid R is made, and the bidder with Vmax will bid extra e and wins Winner’s profit is Vmax-(R+e)>0 Strategy: keep bidding up to your valuation V.

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Dutch auction “Price Clock” ticks down the price. First bidder to “buzz in” and stop the clock is the winner. Pays price indicated on the clock.

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Dutch auction Strategy: Buzz in after price falls sufficiently below V, and make a positive profit. “Shading”: waiting longer may increase the profit, but also increases the chance of losing the auction.

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Dutch auction for British CO2 emissions Greenhouse Gas Emissions Trading Scheme Auction, United Kingdom, 2002. UK government aimed to spend £215 million to get firms reduce CO2 emissions. Clock auction used to determine what price to pay per unit, which firms to reward. The clearing price was £53.37 per metric ton.

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First Price Auctions All buyers submit bids simultaneously. The bidder who submits the highest bid wins, and the price he pays is the value of his bid.

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First Price Auctions Profit is Vmax - B Shading: B must be below V to generate profit. Amount of shading is trade-off between risk of losing and greater profit (similar to Dutch auction). Shading depends on risk attitude and beliefs about other bidders’ Vs.

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Second Price Auctions All bidders submit bids simultaneously. The bidder who submits the highest bid wins, and the price he pays the second highest bid.

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Second Price Auctions It is strategically equivalent to an English auction

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Second Price Auctions Possible bids: B>V or B=V or B<V: which is best? Bidding V is a dominant strategy Second price auctions makes bidders reveal their true valuations Why bid V? The amount a bidder pays does not depend on his bid, so no reason to bid less than V.

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Second Price Auctions Bidding higher than my valuation B wins, pays R, profit is V-R, same result if B=V B wins, pays R, negative profit B loses, profit is 0, same result if B=V

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Second Price Auctions Bidding lower than my valuation B wins, pays R, profit is V-R, same result if B=V B loses, while bidding B=V would have won a profit B loses, same result if B=V

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Second Price Auction In a second price auction, always bid your true valuation (Vickrey’s truth serum). Winning bidder’s surplus: Difference between the winner’s valuation and the second highest valuation.

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Which auction is better for the seller? In a second price auction Bidders bid their true value Seller receives the second highest bid In a first price auction Bidders bid below their true value Seller receives the highest bid

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Revenue Equivalence All 4 standard auction formats yield the same expected revenue Any auctions in which: The prize always goes to the person with the highest valuation A bidder with the lowest possible valuation expects zero surplus …yield the same expected revenue The seller is indifferent between the 4 standard auctions.

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Revenue Equivalence

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Are all auctions truly equivalent? For sellers, all 4 standard auctions are theoretically equivalent. However, this may not be the case if bidders are risk-averse or inexperienced. Risk Aversion Does not affect the outcomes of 2nd price auctions and English auctions. However, in 1st price auctions and Dutch auctions, risk-averse bidders are more aggressive than risk-neutral bidders. Bidders ‘shade’ less, so bid higher than if risk-neutral! Risk aversion  1st price or Dutch are better for the seller, because bidders shade less.

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Are all auctions truly equivalent? Inexperienced bidders In second-price auctions, it is optimal to bid V. Inexperienced bidders tend to overbid in 2nd price auctions (B>V), in order to increase their odds of winning. With inexperienced bidders  second-price auctions increase the revenue of the seller.

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Collusion in auctions In second-price auctions, bidders may agree not to bid against a designated winner. e.g. there are 10 bidders, John’s valuation is $20, others have valuation of $18. Bidders agree that the designated winner John bids any amount more than $18, others bid $0 - no incentive for anyone to do differently. The bidder wins the item for $0. In first-price auctions, instead, if John bids $18, he pays $18 to the seller.

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Collusion in auctions Collusion is also possible in English auctions. Bidders may be able to signal their true valuations the way that they bid in early stages. Bidders who realize that they do not have the highest valuations may collude with the Vmax bidder by accepting not to raise their bid.

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Number of Bidders Having more bidders leads to higher prices. Example: Second price auction Two bidders Each has a V of either 20 or 40. There are four possible combinations: Pr{20,20}=Pr{20,40}=Pr{40,20}=Pr{40,40}= ¼ Expected price = ¾ (20)+ ¼ (40) = 25

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Number of Bidders Three bidders Each has a V of either 20 or 40 There are eight possible combinations: Pr{20,20,20}=Pr{20,20,40}=Pr{20,40,20} = Pr{20,40,40}=Pr{40,20,20}=Pr{40,20,40} = Pr{40,40,20}=Pr{40,40,40}= 1/8 Expected price = ½ (20)+ ½ (40) = 30

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Number of Bidders Assume more generally that valuations are drawn uniformly from [20,40]:

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The European 3G telecom auctions The 2000-2001 European auctions of 3G mobile telecommunication licenses were some of the largest in history. The total revenue raised was above $100bn, with enormous variations between countries. UK 5 licences; 4 incumbents. At least one new entrant would win a license. Used English auction. New entrants knew they had a chance so they bid aggressively, forcing incumbents to do the same. Revenue: 39bn euros.

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The European 3G telecom auctions Netherlands 4 licences; 4 incumbents. Potential entrants could not realistically compete with the incumbents. Therefore they decided to collude with them. They let them win against compensation. Used English auction. Raised only 3bn euros. Another problem is the sequencing. Because the auction took place after the UK one, bidders had learned how to collude. The same problem occurred in countries that organized auctions later, e.g. Italy and Switzerland. Bidders had learned how to collude.

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Common Value Auctions Common Value Auction The item has a single though unknown value, and bidders differ in their estimates. Example: Oil drilling lease Value of oil is roughly the same for every participant. No bidder knows for sure how much oil there is. Each bidder has some information.

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Hypothetical Oil Field Auction

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The winner’s curse The estimates are correct, on average

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The winner’s curse Winner’s curse = In common value auctions, winners are likely to overpay, and make a loss.

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Dealing with the winner’s curse Given that I win an auction …All others bid less than me …Thus the true value must be lower than I thought. Winning the auction is “bad news”. One must incorporate this into one’s bid, i.e. lower your bid. Assume that your estimate is the most optimistic.

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Avoiding the winner’s curse Bidding with no regrets: Since winning means you have the most optimistic signal, always bid as if you had the highest signal, i.e. lower your bid. If your estimate is the most optimistic –what is the item worth? Use that as the basis of your bid.

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All-pay auctions Common value first-price auction in which bidders pays the amount of their bid, even if they lose. Example 1: Olympic games Competing cities spend vast amount of resources to win the vote. Example 2: Political contests (elections) Candidates spend time and money, whether they win or lose. In the 2012 US presidential election, total campaign spending was close to $2bn.

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All-pay auctions Example 3: Research and development, patent race. Competing pharmaceutical firms search for a new treatment/molecule; only one winner. Investment in R&D is risky, since even losers lose their “bid”. Bid is useless unless you win…hence bid aggressively or don’t bid at all. Typically, the sum of the bids is much higher than the value of the prize, which is good for the seller.

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All-pay auctions Optimal strategy If everyone else bids aggressively, your best response is to bid 0 If everyone else bids 0, your best response is to bid a small positive amount  Equilibrium bidding strategy must be a mixed strategy.

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All-pay auctions Equilibrium Consider an all-pay auction with prize worth 1, n bidders. Bid x between 0 and 1 Let P(x) be the probability one’s bid is not higher than x. Indifference principle: With mixed strategies bidders must be indifferent between the choice of x

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All-pay auctions Equilibrium The bidder win if all remaining bids are less than x. The expected payoff for bidding x is then: 1*[P(x)]n-1-x Indifference condition between bidding 0 and x (the expected profit is 0): [P(x)]n-1-x =0, i.e. P(x)=x 1/(n-1)

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All-pay auctions Equilibrium When n=2, players play each value of x with equal probability. P(x)=x  choose each x with equal probability Expected profit: 1*x-x=0 As n increases, bidders bid lower. For n=3, P(x)=√x E.g. x=1/4  P(x)=1/2, i.e. the probability to bid less than ¼ is ½. The higher is n, the less likely bidders are to win, and the lower they bid.

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All-pay auctions Overbidding Class experiments: Auction of a $20 bill Students start bidding $3, $4… When the price approaches $20, the bidders realize that they could end up having to pay a lot of money and not win. If you had bid $19, and another bidder bids $20. What would you do? Is it better to bid $21 or pay $19 for nothing? These games routinely end with the winning bid being 50 percent higher than the value of the prize.

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Summary Different types of auctions Bidding strategies Implications for sellers: Revenue equivalence Risk aversion /collusion Common value auctions: Winner’s curse. All-pay auctions: mixed strategies, and overbidding.

Теги Auctions. (Lecture 10)

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