lecture 8 auctions

7/30/2019 Lecture 8 Auctions

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AuctionsLecture 8 Tom Holden

Intermediate Microeconomics Semester 2

http://micro2.tholden.org/

ECO2051 Intermediate Microeconomics 1
http://micro2.tholden.org/http://micro2.tholden.org/


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Introduction to Auctions

Auctions are another solution to an AI problem.

The seller wants to charge the maximum willingness to pay, but doesnot know what this level is.

A form of price discrimination.

A well designed auction encourages the buyer (bidder) to reveal theirwillingness to pay.

Auctions are most commonly used where there are a few items ofhigh value to sell.



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Auctions reading

Chapter 17 in Varian. MKR have a sub-section in the AI chapter, but its not very detailed.

Klemperer, P. (2001) Why every economist should learn some auction theory. http://www.nuff.ox.ac.uk/users/klemperer/WhyEveryEconomist.pdf

Milgrom, P. (1989) Auctions and Bidding: A Primer Journal of EconomicPerspectives

http://rru.worldbank.org/Documents/PapersLinks/auctions_and_bidding_a_primer.pdf

Dustmann and Borgers (2005) Strange Bids: Bidding Behaviour in the UnitedKingdoms Third Generation Spectrum Auction Economic Journal

http://www.ucl.ac.uk/~uctpb21/Cpapers/strangebids.pdf

Thaler, R. (1988) Anomalies: The Winners Curse Journal of Economic

Perspectives. http://users.tricity.wsu.edu/~achaudh/thaler02.pdf

Roth and Ockenfels (2002) Last-Minute Bidding and the Rules for EndingSecond-Price Auctions: Evidence from eBay and Amazon Auctions on theInternet American Economic Review.

http://kuznets.fas.harvard.edu/~aroth/papers/eBay.veryshortaer.pdf

http://www.nuff.ox.ac.uk/users/klemperer/WhyEveryEconomist.pdfhttp://www.nuff.ox.ac.uk/users/klemperer/WhyEveryEconomist.pdfhttp://rru.worldbank.org/Documents/PapersLinks/auctions_and_bidding_a_primer.pdfhttp://rru.worldbank.org/Documents/PapersLinks/auctions_and_bidding_a_primer.pdfhttp://www.ucl.ac.uk/~uctpb21/Cpapers/strangebids.pdfhttp://www.ucl.ac.uk/~uctpb21/Cpapers/strangebids.pdfhttp://users.tricity.wsu.edu/~achaudh/thaler02.pdfhttp://users.tricity.wsu.edu/~achaudh/thaler02.pdfhttp://kuznets.fas.harvard.edu/~aroth/papers/eBay.veryshortaer.pdfhttp://kuznets.fas.harvard.edu/~aroth/papers/eBay.veryshortaer.pdfhttp://kuznets.fas.harvard.edu/~aroth/papers/eBay.veryshortaer.pdfhttp://users.tricity.wsu.edu/~achaudh/thaler02.pdfhttp://www.ucl.ac.uk/~uctpb21/Cpapers/strangebids.pdfhttp://rru.worldbank.org/Documents/PapersLinks/auctions_and_bidding_a_primer.pdfhttp://www.nuff.ox.ac.uk/users/klemperer/WhyEveryEconomist.pdf


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Auction design

Two factors to consider when evaluating auctions:

Profit maximisation

Is the seller achieving the maximum price?

Pareto efficiency

Is the good going to the bidder who values it the most?



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Theoretical frameworks for valuations

Private values Each bidder knows what the good is worth to him/herself. Valuations are different across bidders. Individuals valuations are not common knowledge. E.g. buying truffles.

In a private value set-up, individual As valuation is unchanged by learningindividual Bs valuation.

Common values There is a unique true value for the item (perhaps its resale value), but this

value is unknown. Each bidder receives some noisy private signal about this true value. Signals are not common knowledge.

E.g. buying an oil field. In a common value setting, if individual A learns that individual B values the goodhighly, then individual A will increase their valuation of the good.

Affiliated values Half-way between the two previous cases. Valuations across individuals are non-independent, but not perfectly correlated.



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Example

Imagine a painting is auctioned.

Auction is the usual Sothebys type where individuals shout out theirbids and the highest wins.

There are four individuals with private valuations of 10, 40, 60 and100.

How much does the painting sell for?



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Auction types (1/3)

English (or ascending) auction: The auctioneer begins with a reserve price.

Bidders call out a price until only one bidder remains.

The good is then sold to the highest bidder at the last bid they made.

Second-price sealed-bid auction (Vickrey auction): Each individual writes down their bid without knowledge of what others are

bidding.

The auctioneer collects up the bids and the good goes to the highest bidder,who pays the second highest price bid.

These two auctions are equivalent in many circumstances. Collusion, information revelation, entry deterrence etc. can break the

equivalence.



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Auction types (2/3)

Dutch auction:

The auctioneer starts with a high price and then brings the price downprogressively until a bidder calls out and claims the good at that price.

First-price sealed-bid auction:

Each individual writes down their bid without knowledge of what others arebidding.

The auctioneer collects up the bids and the good goes to the highest bidderfor the price they bid.

These two auctions are also usually equivalent.



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Auction types (3/3)

(Sealed) All pay auctions: Everyone pays their bid, regardless of whether their bid was the highest.

The person who bid the most wins the item.

An unsealed, ascending version of this auction is also possible. The auctioneer collects 1 from everyone interested in the item.

If more than one person was interested, the auctioneer collects another 1from everyone still interested.

This process is repeated until there is only one person left, who gets theitem.

This type of auction is rare with money, but many wars of attrition havethis form.

Again, these two auctions are usually equivalent.



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Bidding strategy with independent values:English and second price auctions

Optimal to bid your valuation, . Deviating from will not affect the price you end up paying (which is

determined by the second highest valuation), but it will affect the probabilityof winning.

To see this, suppose the highest bid by other bidders is

. You win whenever you make a bid above . Your surplus from this is positive providing that > . If you dont win, you obtain 0 surplus. Its optimal then to choose your bid so that you win the item whenever > . If you bid , then you will indeed win whenever > . Bidding a higher amount will mean you sometimes win and make a negative surplus,

and bidding a lower amount will mean you sometimes lose when you could have won.

With either type of auction, bidders bid their valuation, and the pricepaid is the second-highest valuation.



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Bidding strategy with independent values:Dutch and first price auctions

Optimal to shade your bid, and bid below your valuation. If you bid your valuation, although you will win often, when you do win you

will gain zero surplus, since surplus is just your valuation minus your bid,under a first price auction.

Thus you want to trade off the probability of winning, with the amount you

obtain when you win.

Optimal strategy is to bid your expectation of what you would havepaid had a second price auction been run instead, and had you wonthat auction.

Justification for this will be seen shortly.

This is an increasing function of valuations, as you would expect.

How much below the valuation it is will depend on how many bidders thereare.

With more bidders, bids will be nearer true valuations.

This is why attracting bidders is an important element of auction design.



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Bidding strategy with independent values:All pay auctions

How do you think people should bid in an all pay auction?

Lets run an experiment to see what you think.

You should have all received an email with a secret amount of moneyin it, last night. The amount in that email is the amount youll win ifyou win the auction.

The auction will be an all pay one though, so everyone who

participates will pay their bid.

If you want to participate, write down your name and your bid on ascrap of paper, fold it over, and pass it to the end of your row.



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The revenue equivalence theorem (1/2)

The revenue equivalence theorem is a general result stating thatgiven certain technical assumptions, any reasonable mechanism forallocating goods will generate the same expected revenue for theseller.

It is this that means that in the first price auction, bidders willoptimally bid what they would have paid had a second price auctionbeen run instead (and had they won that auction).

This ensures that the sellers revenue is the same in both first priceand second price auctions, so the revenue equivalence theorem issatisfied.



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The revenue equivalence theorem (2/2)

any allocation mechanism/auction in which

(i) the bidder with the highest type/signal/valuation always wins,

(ii) the bidder with the lowest possible type/valuation/signal expects zero

surplus, (iii) all bidders are risk neutral and

(iv) all bidders are drawn from a strictly increasing and atomless distribution

will lead to the same expected revenue for the seller (and player of

type can expect the same surplus across auction types).

The winning bid should be epsilon above the second highestvaluation. (Source: Wikipedia)
https://en.wikipedia.org/wiki/Auction_theoryhttps://en.wikipedia.org/wiki/Auction_theory


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Diversion: Product patent races

Suppose risk-neutral firms compete to invent a new product.

The inventor of the product will be granted a patent, enabling themto extract some monopoly profits.

Firms differ in their costs to produce the product if they invent it, andthus differ in the amount of monopoly profits they would receive.

Each firms profits if they are a monopolist are drawn uniformly at randomfrom the interval [0,].

Firms know their own profit draws, but not those of their rivals.

The firm that performs the most units of research will win the patentrace.


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Applying the RET to our patent race model(1/4)

Bidders = firms.

Valuations = profits if they invent the product.

Check each point in turn:

(i) holds as the amount of research firms will want to do will be increasing intheir profits if they win.

(ii) holds because the lowest type of firm makes zero profits if they win.

(iii) and (iv) holds by assumption.

So the RET holds.


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Useful fact

The expected th lowest draw out of from a uniform distribution onthe interval , is

+ .

The expected

th

highest draw out of from a uniform distributionon the interval , is

+

+ .

E.g. the expected highest is

+ .



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Given the RET holds, we can derive firms expected surplus, andhence their bids.

Consider this alternative mechanism (the ascending auction AKA thesecond-price auction):

Sells the good at the second highest valuation.

Immediately from the RET we have that the total amount of researchperformed by all firms is given by the expected second highest profit draw,

i.e.

+ .


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Suppose then that a firm would make profits of if they were amonopolist.

Their expected surplus under a second price auction is the probability thattheir valuation is the highest, times minus the expected valuation of thesecond highest bidder, conditional on the original firms valuation being the

highest.

What is the probability that is the highest draw? It is the probability thatthe 1 other draws were below , i.e.

.

Conditional on the highest of the draws being , it may be shown that theother 1 draws are uniform on 0, . Thus the highest of these other 1 (i.e. the second highest overall) is expected to be at

.

Hence the firms expected surplus is

.


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So how much research should they do?

Expected surplus under the patent race is the probability that you have thehighest profit draw times your profit draw, all minus your researchexpenditure (which you pay even if you do not win the race).

I.e.

, where is the research expenditure of a firm that drew .

By the RET, this expected surplus must equal the expected surplus from the

ascending auction, hence

.

I.e.

.

For even moderately large ,

will be tiny for all but the very highest

, so performing near zero amounts of research is optimal.


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Risk aversion

Risk aversion removes the revenue equivalence of first and second-price auctions.

With risk aversion, people will bid higher in first price auctionscompared to the risk neutral benchmark, since they prefer winning asmall surplus with a high probability to winning a larger surplus withlow probability.

First price auctions are thus likely to lead to higher revenue in thepresence of risk aversion.



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Optimal reserve prices

Setting an appropriate reserve price can lead to an increase in profit, but is oftenPareto inefficient.

Varian example: 2 bidders, seller thinks each has a value of 10 or 100.

Possible combinations are (10,10), (10,100), (100,10) (100,100).

Seller runs an ascending auction with a 1 increment, and ties are resolved by flipping a coin.

With no reserve price:

The good will go to the bidder with the highest value.

The price will be (10, 11, 11, 100) (depending on which state of the world were in).

Expected revenue is 33.

With a reserve price of 100:

In three cases the seller will get 100, and once he will not sell. Expected revenue is 75.

Or consider the case with only one bidder. Optimal to make a take it or leave it offer that has a positive probability of being rejected.



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Myerson: Optimal auction design

In the special case in which valuations are independent acrossbidders, and they are drawn from a common distribution satisfying atechnical requirement (regularity), the optimal auction is a secondprice, sealed-bid auction in which the seller first announces an

(optimally chosen) reserve price.

More generally, we can define a notion of marginal revenue (seethe Klemperer paper) under which the auctioneer should sell to thebuyer with the highest marginal revenue.



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Common values

Lets auction the contents of some of your wallets!

English auction.

participants.

Participant has in their wallet. Participant bids . They are allowed to bid more than , but all debts must

be settled in full one way or another.

Total in all of the wallets is = . The winner receives this amount,

and pays the final bid with which they won.

I.e. if participant wins, they get = , from the auctioneer.

(If this is negative they must pay the auctioneer.) If the winner just bid the contents of their own wallet, then they are guaranteed a

positive value, so it certainly makes sense to set > . Everyone else keeps their money.

What have we learned?



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The winners curse

This occurs in a common value framework.

As bids are a consequence of estimated valuations, those who win will always bethose who had the highest valuations.

If people stay in the auction until the price is equal to their expected valuation,they will over-bid, and suffer the winners curse.

Rational bidders shade their bids to avoid the curse. I care about the value of the item conditional on me winning.

Shading will be greater if there are more bidders; its worse to be the highest ofmany bidders.

The English auction is no longer equivalent to the second-price sealed-bidauction, as the extra information modifies the impact of the winners curse.



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Example of a common value auction:3G spectrum

In Spring 2000 5 radio licenses to operate third-generation mobilephone systems were auctioned in the UK.

This raised 26.3 billion or 2.5% of UK GDP.

2G licenses had been disposed of by beauty contest and had raised40,000.

The auction was overseen by a team of academics acting as

consultants: But perhaps the most important lesson of all was not tosell ourselves too cheap. Ideas that seem obvious to a trainedeconomist are often quite new to layfolk. Our marginal product inpreventing mistakes can therefore sometimes be surprisingly large.



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The mechanics of the 3G auction

Simultaneous ascending price auction.

All licenses are auctioned at the same time.

All bidders must bid in each round (a few waivers permitted).

Auction only ends when bidding on all licenses has stopped.

5 licenses auctioned, 3 small, 2 large. One large was reserved for anentrant in recognition of competition issues.

Auction took almost 8 weeks, 150 rounds of bidding.



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Bidders



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Winners



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The outcome luck or judgement

The UK auctions were seen as among most successful in Europe.

Many that followed were a disaster. e.g. Dutch, Turkish.

Some evidence of first-mover advantage.

Klemperer argues that attention to industrial organization issues was crucial.

Binmore and Klemperer: Of course, confidence in hi-tech industries in

general has waned since that time. But the auction designs deserves neitherpraise nor blame if the values placed on the 3G licenses have now fallenbecause of a change in the capital markets view of 3Gs prospects.

There could be an element of winners curse here too.



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The sequel: The 4G spectrum auction

Raised 2.3 billion, which was 1.2 billion less than the treasuryexpected.

Recall that the 3G one raised 26.3 billion.

Low revenue is being investigated by the National Audit Office.

Mixed results for competition:

More effective competition for EE from an enlarged Vodafone.

BT was a new entrant.

But the existing smaller players (O2 and 3) both shrunk in relative size afterthe auction.



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Did the bidders behave rationally? (1/2)

Investigated by Borgers and Dustmann.

Hypothesise straightforward bids

Bidders enter the auction with fixed valuations for each license.

They always bid the minimum increment.

They will bid for the license which offers the highest current surplus (the onefor which the gap between the valuation and the current highest bid isgreater).

Bidders drop out once the maximum surplus is negative.



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Did the bidders behave rationally? (2/2)

If we observe a firm bidding for a given license, say A rather than acheaper license B, we can deduce that in this round, the pricedifference must be less than the difference in valuations for this firm.

If the smaller licenses were identical you would expect firms toalways bid for the cheaper license.

Example: Orange only bid for license E, this is only rational if Orangeperceived E to be much more valuable than the other small licenses.

Some evidence of irrational bidding, which goes against Klemperersidea that good design alone led to high prices.



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Bidding by Orange makes sense


Source: Borgers and Dustmann


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Bidding by BTcellnet seems irrational


Theres an interesting paper, Maldoon, EJ 2005, who explains BT strategy in terms of

common values. Switching was an attempt to confuse competitors. Or drive up the

price paid by Vodaphone.


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Online auctions

You bid on an Ebay auction by inserting a maximum bid.

The auction proceeds by using a proxy bidder who raises your bid asnecessary by the minimum increment provided it doesnt exceed

your maximum.

This is very close to a second-price auction, the bidder with thehighest valuation will win but at the second highest bid (plusminimum increment).



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Late bidding

The analysis of the second price auction implies that people willmake straightforward bids and reveal their true valuation early on.

In practice this does not happen. Late bidding or sniping is

extremely common.

Two explanations:

If there is an element of common value, no one wishes to reveal theirvaluation, as it could drive the final price up.

Early bids make it likely that you will be bid right up to true valuation, latebidding adds an element of randomness which might be better for bidderson average.



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Other results on eBay auctions

Lucking-Reiley, Bryan, Prasad, Reeves, (2007) Pennies from eBay: theDeterminants of Price in Online Auctions. Journal of IndustrialEconomics.

From data on selling US 1 cent coins.

Only negative feedback affects selling prices. Longer auctions lead to higher prices.

Weekend closes good.

Worth having a reserve price and minimum bid (but theres a chance youwont sell).

More bidders are good (probably why longer and weekend auctions increase

selling price).



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Advantages of auctions

Auctions are generally efficient. We want to allocate the good to thebidder who values it most.

As we have seen, auctions do this.

In beauty contests, its easy to say you value the good the most, buthere you must put your money where your mouth is. (AI again)

From the sellers point of view, they are the most effective way ofgaining surplus.

Transparent particularly important for Govt.

But auctions are expensive to run, so not suitable for all goods.

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