Auctions 1

SIGNALING QUALITY IN LABOR MARKET

Education as a Signal

• Two Groups- Group 1 (Average Product= 1)• Group 2 (Average Product = 2)• Each output sells at Rs 1 lakh• If you knew each firm’s quality what would be

the salary of Group 1 . Group 2?• What if you did not know the quality of the

two?


• Y: years of education• Higher education , higher costs• Each group has different costs of education• Group 1, C1 (Y) = Rs 4,00,000 Y

• Group 2, C2 (Y) = Rs 2,00,000 Y


• Assume the following decision rule is followed by the firm

“ Anyone with education higher than y* or more is a Group 2 person and will be given an income of Rs 2lkh. Anyone with education less than y* will be given an income of Rs 1lkh.”

Education as a SignalValue of education

B(y)

y*0

10,00,000


• No education level between 0 and y* will be chosen

• No education level more than y* will be chosen

Choice of Education

• Group 1 Benefit: Rs 10,00,000Cost: 4,00,000y*

Choose that y* such that Group 1 does not educate him self

• y*> 2.5

Choice of Education

• Group 2 Benefit: Rs 10,00,000Cost: 2,00,000y*

Choose that y* such that Group 1 does not educate him self

• y*<5• Any y* such that 2.5 <y*< 5 would do


C1 (y) = 40,000y

B(y)

y*0

1,00,000

Optimal Choice Group 1


C2 (y) = 20,000y

B(y)

40

10,00,000

Optimal Choice Group 2


• Low productivity people do not get education• High productivity people get education• On observing education level of 4 years the

employers rightly believe the person to be of High productivity

• Even if education does nothing to increase productivity, some people may want to differentiate themselves by education.

Warranties and Service Plans

• What is the use of Warranties?

• Can Warranties act as signal?

• Signal to what?

Warranties

• Problems with the car led consumers to loose faith in Audi in late 1970s.

• In response Audi introduced “ Audi Card” or “ bumper to bumper” warranty scheme

• Audi sales increased• Besides improving the benefit of having an

Audi, what else could have been the effect of this warranty?

Audi’s Warranty

• Warranty a signal that Audi is reliable.• If Audi was not reliable or of high quality, the

probability of repair would be high, leading to high costs for Audi (because of the warranty)

• Any other car maker with probability of defect higher than that of Audi would not have offered this warranty.

• Warranties of gadgets, battery life. Duration

Other Examples

• Appearance a signal of wealth• Advertising as a signal:- Carorder.com: 50,000 , $3 metro cards for NYC

subway and paid tolls for 100 cars at all area bridges

- “ Your commute brought to you by Carorder.com”

Auction Theory

“Everything is worth what its purchaser will pay for it.”

- Publilius Syrus (Maxim 847, 42 B.C.)

Auction

• Mechanism to allocate resources

• Competing against other bidders

• How much they value the product?

What is an Auction?

• 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 :Sotheby’s,

Chiristie’s Flowers Fish Houses: Australia Treasury bills

IPOs Emissions permits Radio Spectrum Import quotas Advertisement slots:

Google, Yahoo! Procurement Books: eBay, Amazon

Procurement Auctions

• Government takes bids for building a road

• Lowest bid wins the auction

• One Buyer, many sellers

• Issues of quality, reputation , efficiency

Strategy in Auctions

• How much to bid?• When to bid?• Whether to bid at all ?• How to avoid winning but not regretting?

Can of Coins on Auction

• Write the number of coins you think are in the can

• Write the bid that you would like to make.

• Make a personal note of these and hand over the chit

Auction of Coins

Rule for Group I:• Highest Bid wins the pot• Pays the second highest bid

Rule for Group II:• Highest Bid wins the pot• Pays the your bid

Valuation

• Highest price at which you are indifferent between winning and losing the object.

• Can includeI. Excitement from winning the objectII. Premium that you put on the object not

landing in your rivals hands.III. Expected resale value

Private V/S Common Valuation

• Common Value Auction– True value of the good for sale is same for all– Bidders differ in their estimates of the true value– e.g., FCC spectrum, drilling,

• Private Value Auction– Each bidder knows his or her value for the object– Independent Valuation– Bidders differ in their values for the object– e.g., Houses, consumption items

Private Value Auction

• Dinner

25

Common Value Auction

• Unproven oil fields

26

Common and PrivateValue Auctions

• Each good is a composite of both Common and Private Value goods.

• Oil Fields: Different costs of drilling the oil field• Houses: Resale value

Auction of Coins

• Winner: How did you bid for this can?

• How do you feel you have done?

• How did others bid for the can?

Bidding in Common Value

• Bid your estimate?

• Bid less than your estimate?

• What if everyone bid their estimate?

Auction as a Game

• Payoff in an Auction

• Estimate

• If v is the true value of the object and ε is the error

• ε is standard normally distributed• yi has an unbiased normal distribution

vyi

Winner of Auction

• If everyone bids their estimate

• Winner is the one who has the highest estimate

• And the one with the highest error

Winner’s Curse

• If the average bid in an auction is the actual value of the object (Law of Large Numbers)

• If everyone bids according to their estimate

• Winner of the highest estimate would be the one with highest error.

Examples

• After WW II, US govt auctioned out rights to drill in Gulf of Mexico.

• Those who won where constantly loosing money

• IPL (??)

Auction 1

Rules:• Highest Bid wins the pot• Pays the own bid

Sealed-Bid First Price Auctions

• All buyers submit bids • Buyer submitting the highest bid wins

and pays the price he or she bid

35

$700

$400

$500

$300

WINNER! Pays $700

Auction 2: 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

36

Examples of Dutch Auctions

• Amsterdam’s flower market

• US T-bills

• Google IPO

Auction 3: 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

Auction 3: Vickery Auction

• Attributed to William Vickery, Nobel Laureate, 1961

• Also called, Second price sealed bid auction • Bids placed in a sealed bid• Highest bidder wins• Pays second highest bid

Examples of Vickery Auctions

• Stamps

• eBay

• Google and Yahoo! : GSP

Auction 4: Japanese Auction

• Let us change the game now.• All teams will drop/fold their hands to indicate

no participation in the auction• Price will rise.• Auction will end at the price when only one

team remains in auction• Once you drop out you can not re enters

Comparing Vickery and Japanese Auction

• What is a strategy in this case? • The bid at which you will lower your hand.• Who wins? The one who has the highest

intended bid.• When does it stop? When the 2nd highest

bidder stops.

Comparing Vickery and Japanese Auction

• Are the winners same in Vickery and Japanese Auction?

• Is the price that the winner pays same in both?

English Auction

• Variation of Japanese Auction

• Price is raised

• Interested parties can raise the price

• Auction ends when no one raises the price• Houses and Antique, Cattle

Difference between English and Japanese Auction

• Knowledge of who is in the auction• Knowledge of when a player drops out

Unknown in English Auction

Known in Japanese Auction

Comments

• Optimal Bidding strategy • Which type of auction should be chosen? First

or Second Price Auction• Should the products be sold sequentially or

simultaneously

Documents

Auctions 1