game theory “a cynic knows the price of everything and the value of nothing” - oscar wilde, lady...

Game Theory

“A cynic knows the price of everything

and the value of nothing”- Oscar Wilde, Lady Windemere’s Fan

Mike ShorLecture 11

Mike ShorGame Theory & Business Strategy

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What is an Auction?

auc•tion1. A public sale in which property or

merchandise are sold to the highest bidder.

2. A market institution with explicit rulesdetermining resource allocation and prices on the basis of bids from participants.

3. Games: The bidding in bridge

[Latin: auctiō, auctiōn – from auctus, past participle of augēre, to increase]


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Examples of Auctions Definition:

A market institution with rules governing resource allocation on the basis of bids from participants

Over 30% of US GDP moves through auctions: Wine Art Flowers Fish Electric power Treasury bills

IPOs Emissions permits Radio Spectrum Import quotas Mineral rights Procurement


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Sample Auction

“Mistakes are the portals of discovery”

- James Joyce


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Going Once, Going Twice, …

Bidding starts at $1

Who will make the first bid?


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Overview of Auctions

Auctions are a tricky business Different auction mechanisms

sealed vs. open auctions first vs. second price optimal bidding & care in design

Different sources of uncertainty private vs. common value auctions the winner’s curse


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Private Value Auction

Dinner


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Common Value Auction

Unproven oil fields


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Sources of Uncertainty Private Value Auction

Each bidder knows his or her value for the object Bidders differ in their values for the object e.g., memorabilia, consumption items

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., FCC spectrum, drilling,

disciplinary corporate takeovers


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Basic Auction Types

Open Auctions (sequential)English AuctionsDutch AuctionsJapanese Auctions

Sealed Auctions (simultaneous)First Price Sealed BidSecond Price Sealed Bid


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English Auctions (Ascending Bid)

Bidders call out prices (outcry) Auctioneer calls out prices (silent) Bidders hold down button (Japanese)

Highest bidder gets the object Pays a bit over the next highest bid


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Dutch (Tulip) Auction Descending Bid

“Price Clock” ticks down the price

First bidder to “buzz in” and stop the clock is the winner

Pays price on clock


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Sample Dutch AuctionMinimum Bid: $10


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Sealed-Bid First Price Auctions All buyers submit bids Buyer submitting the highest bid wins

and pays the price he or she bid

$700

$400

$500

$300

WINNER! Pays $700


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Sealed-Bid Second Price Auctions All buyers submit bids Buyer submitting the highest bid wins

and pays the second highest bid

$700

$400

$500

$300

WINNER! Pays $500


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Why Second Price?

It is strategically equivalent to an English Auction

$300$400

$500


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Why Second Price?

Bidding strategy is easy Bidding one’s true valuation

is a dominant strategy

Intuition: The amount a bidder pays is not

dependent on her bid


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Optimal Bidding Strategyin Second Price Auctions

You Lose

You Win

hig

her

Your bid

Others’ bids

Your value


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Bidding Higher Than My Valuation

Case 1 Case 2 Case 3

No difference No difference Lose money


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Bidding Lower Than My Valuation

Case 1 Case 2 Case 3

No difference No difference Lose money


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Second Price Auction

In a second price auction, always bid your true valuation

Winning bidder’s surplusDifference between the winner’s valuation and

the second highest valuationSurplus decreases with more bidders


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First Price Auction

First price auction presents tradeoffs If bidding your valuation – no surplus

Lower your bid below your valuationSmaller chance of winning, lower price

Bid shadingDepends on the number of biddersDepends on your informationOptimal bidding strategy is complicated!Rule of thumb: bid (N-1)/N of your value


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Which is Better?

In a second price auction bidders bid their true value auctioneer receives the second highest bid

In a first price auction bidders bid below their true value auctioneer receives the highest bid


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Which is Better?

Draw 4 keep highest

Draw 4 keep 2nd highest


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Revenue Equivalence

All common auction formats yield the same expected revenue (in theory)

In fact, any auction satisfying: 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


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Revenue Equivalence in the Real World Risk Aversion

Does not influence 2nd price auctionsRisk averse bidders are more aggressive

in first price auctionsRisk aversion 1st price or Dutch are better

Non-familiarity with auctionsMore overbidding in second-price auctionsMore overbidding in sealed-bid auctionsInexperience 2nd price sealed bid is better


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More Bidders

More bidders lead to higher prices

Example Second price auction Each bidder has a valuation of either

$20 or $40, each with equal probability What is the expected revenue?


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Number of Bidders Two bidders

Each has a value of 20 or 40 There are four value 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 value of 20 or 40 There are eight value 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]:

20

25

30

35

40

1 10 100 1000Number of Bidders

Ex

pe

cte

d P

ric

e


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Designing Auction Rules

Every rule may have unintended consequences

What is the minimum bid for a new bidder?

What kind of financing can bidders present?

How much must bids be beaten by?


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“Tweaking the Rules” IeBay …

Three laptops for sale Top three bidders pay the

third highest bid Opening bid: $1 Current high bids: $50, $80, $400

How high should the next bid be?


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“Tweaking the Rules” IIFCC Spectrum Auctions…

Want to encourage minority and female-owned firms to bid but licenses are very expensive. Reserve several frequency blocks for

smaller bidders. Allow 10% down, low interest, remaining

principal owed in 7 years. What happens?


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“Tweaking the Rules” II(continued)

Bid high! If licenses end up being worth less, default!

Of the four largest winners, one went bankrupt and defaulted one had $1B reduced to $66M in

bankruptcy court one was a front for Qualcomm one was sold to Siemens


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“Tweaking the Rules” III FCC Spectrum Auctions… Discouraging Collusion

Do not identify highest bidders

Capturing SurplusDo not set a bidding increment

“I bid $8,000,483”

“I bid $3,000,395”


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Summary

Bidding: Bid true valuation in 2nd price auctions Shade bids in 1st price auctions

Designing: Take advantage of inexperience Take advantage of risk aversion Do sweat the little stuff

game theory “a cynic knows the price of everything and the value of nothing” - oscar wilde, lady...

Documents

price auctions

highest bid slide

price sealed bid slide

overview of auctions

clock slide

highest bid wins

james joyce slide

true value