4. The Theories and the Real World

Strategic Behavior in Business and Econ

Outline

1. Introduction2. Individual Decision Making3. Basic Topics in Game Theory4. The Theories and the Real World

4.1 Applications4.1.1 Auctions 4.1.2 Negotiation

4.2 Alternative approaches4.2.1 Psychology 4.2.2 Evolution4.3.3 Artificial intelligence

4.3 What the theory does not reflect? (Back to The experiment)

Outline

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 rules

determining resource allocation and prices on the basis of bids from participants.

3. Games: The bidding in bridge

[Latin: auctio, auction – from auctus, past participle of augēre, to increase]

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 ArtFlowersFishElectric power

Treasury bills

IPOsEmissions permitsRadio SpectrumImport quotasMineral rightsProcurement

Real Figures• Currently, there are “open” opportunities in the US for 40 billion

$ in 5 years (public facilities)

La Vanguardia. April 10th , 2007

• Cellular phone licenses in Europe

– Germany 84 billion €

– United Kingdom 62 billion €

– France 33 billion €

– Spain ...

Real Figures

No Auction in Spain !!

The government issued licenses based on public examination/contest

The Spanish government raised

880 million €

( 35 times less than France !! )

Real Figures

Types of Auctions

• Different auction mechanisms– sealed vs. open auctions– first vs. second price– Issues: optimal bidding & care in design

• Different sources of uncertainty– private vs. common value auctions– Issue: the winner’s curse

Sources of Uncertainty

• Private Value Auction– Each bidder knows his or her value for the object (not the value

for others !)– Bidders differ in their values for the object– e.g., memorabilia, consumption items, fine arts

• 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 off-shore, IPOs

Basic Auction Types

• Open Auctions (sequential)• English Auctions• Dutch Auctions• Japanese Auctions

• Sealed Auctions (simultaneous)• First Price Sealed Bid• Second Price Sealed Bid

English Auctions (Ascending Bid)

• Bidders call out prices (English)• Bidders hold down button (Japanese)

• Highest bidder gets the object• Pays his or her bid

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

First Price Auction

• First price auction presents trade-offs• If bidding your valuation – no surplus

– Lower your bid below your valuation• Smaller chance of winning, lower price

– Bid shading• Depends on the number of bidders• Depends on your information• Optimal bidding strategy is complicated!

Bidding Strategy

Each bidder has a “private” valuation of the item

Bidding above your valuation is a bad choice (Dominated Strategy)

Hence, the choice is to either bid your valuation or below your valuation

Bidding Strategy

You Win

Your bid

Others’ bids

Your value

You Lose

Bidding Strategy (valuation vs below valuation)

Case 1 Case 2 Case 3

No difference No difference is better !!

Bidding Strategy

Bidding above your valuation is a bad choice (Dominated Strategy)

Hence, the choice is to either bid your valuation or below your valuation

Thus, the optimal strategy (weakly dominant) is to bid “slightly” below your valuation (bid shading)

First Price Auction

• In a first price auction, always bid below your true valuation

• bidding your own valuation is a Dominated Strategy• Winning bidder’s surplus:

• Difference between the winner’s valuation and the winner's bid

Bidding Strategy

Bidding above your valuation might not a bad choice in this case since thisthis is not the price you will have to pay ! (and might increase your chancesof winning)

Hence, we have to take into account the three possibilities:

Bidding your valuation Bidding above your valuation Bidding below your valuation

Optimal Bidding Strategy in Second Price Auctions

You LoseYou Win

Your bid

Others’ bids

Your value

Bidding Higher Than My Valuation

Case 1 Case 2 Case 3

No difference No difference Lose money !!

Bidding Lower Than My ValuationCase 1 Case 2 Case 3

No difference No difference Lose money !!

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

Second Price Auction

• In a second price auction, always bid your true valuation

• Winning bidder’s surplus• Difference between the winner’s valuation and the

second highest valuation• Surplus decreases with more bidders

Which is Better for the seller ?

• 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

Revenue Equivalence

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

In fact, any auction 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

Which is Better for the bidder?

• English and Second Price are equivalent

• Dutch and First Price are equivalent

• It's difficult to say in general

Revenue Equivalence in the Real World• Risk Aversion

• Does not influence 2nd price auctions• Risk averse bidders are more aggressive in first price

auctions• Risk aversion 1st price or Dutch are better

• Non-familiarity with auctions

• More overbidding in second-price auctions• More overbidding in sealed-bid auctions• Inexperience 2nd price sealed bid is better

Number of 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?

Number of Bidders

• Two bidders– Each has a value of 20 or 40– There are four value combinations:

Bidder 1

Bidder 2 Prob.

20 20 ¼

20 40 ¼

40 20 ¼

40 40 ¼

Number of Bidders

Bidder 1 Bidder 2 Prob. Outcome (revenue)

20 20 ¼ 20

20 40 ¼ 20

40 20 ¼ 20

40 40 ¼ 40

Number of Bidders

Expected revenue = ¾ (20)+ ¼ (40) = 25

Bidder 1 Bidder 2 Prob. Outcome (revenue)

20 20 ¼ 20

20 40 ¼ 20

40 20 ¼ 20

40 40 ¼ 40

Number of Bidders• Three bidders

– Each has a value of 20 or 40– There are eight value combinations:

Bidder 1 Bidder 2 Bidder 3 Prob

20 20 20 1/8

20 20 40 1/8

20 40 20 1/8

40 20 20 1/8

40 40 20 1/8

40 20 40 1/8

20 40 40 1/8

40 40 40 1/8

Bidder 1 Bidder 2 Bidder 3 Prob Outcome (revenue)

20 20 20 1/8 20

20 20 40 1/8 20

20 40 20 1/8 20

40 20 20 1/8 20

40 40 20 1/8 40

40 20 40 1/8 40

20 40 40 1/8 40

40 40 40 1/8 40

Expected Revenue = ½ (20)+ ½ (40) = 30

Bidder 1 Bidder 2 Bidder 3 Prob Outcome (revenue)

20 20 20 1/8 20

20 20 40 1/8 20

20 40 20 1/8 20

40 20 20 1/8 20

40 40 20 1/8 40

40 20 40 1/8 40

20 40 40 1/8 40

40 40 40 1/8 40

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

Sources of Uncertainty

Private Value Auction

Difficult to lose money

Do not bid more than your value (or less than your cost)

Common Value Auction

The item has a single though unknown value

Bidders differ in their estimates

The winner might be wrong!

Common Value Auctions

Example: Offshore oil leases

The true value of oil is roughly the same for every participant

No bidder knows value for sure

Each bidder has some information

Auction formats are not equivalent

Oral auctions provide information

Sealed-bid auctions do not

Avoiding the Winner’s Curse

Given that I win an auction …

All others bid less than me …

Thus the object’s value must be lower than I thought

Winning the auction is “bad news”

One must incorporate this into one’s bid

Assume that your estimate is the most optimistic

Outline

Strategic Bahavior in Business and Econ

Sequential Negotiation

Consider a situation in which two players must negotiate (bargain) about the distribution of a single itemThe negotiation proceeds by alternating offers and counteroffers until an agreement is achieved or a deadline is reachedUsually, the value of the item decreases as the negotiation unfolds (by some factor r<1)

The value of the itemIf x is accepted right away (first round) it has a value of x (full value)If x is accepted in round two, then it has a value of only r·x (discounted value)If x is accepted in round three, then it has a value of only r·r·x=r2·x (discounted value) . . . If x is accepted in round “t”, then it has a value of only

r(t-1)·x (discounted value)

The value of the item (Example if r=0.9)

If $10 is accepted right away (first round) it has a value of $10 (full value)If $10 is accepted in round two, then it has a value of only 0.9·10=$9 (discounted value)If $10 is accepted in round three, then it has a value of only 0.92·10=$8.1 (discounted value) . . . If $10 is accepted in round “t”, then it has a value of only 0.9(t-1)·10 (discounted value)

After each round the prize loses a 10% of its value

The value of the item (Interpretation)

If the item is a commodity, it might lose “quality” over time (Ex: ice cream)If the item is money, it looses value because of the inflation, or because of the interest rate that you are not earningPsychologically, r might represent your degree of patience. The higher is r, the more patient you are

The Game Player 1 makes a proposal s, (1-s) of distribution of the

item (s between 0 and 1)

Player 2 receives the offer by player 1 and decides whether to accept or to reject it

If accepts, the proposal by player 1 is implemented: s, 1-s If rejects, then is player 2's turn to make an offer s’,(1-s') Player 1 receives the offer by player 2 and decides whether

to accept or to reject it If accepts, the proposal by player 2 is implemented: s', 1-s',

but they get the discounted value: r·s' , r(1-s') If rejects, then the game is over (for simplicity) and

each player receives a disagreement payoff of 0 (for simplicity)

The Game

Accept

Reject

s, (1-s)

Accept

Reject

s', (1-s')

r·s', r·(1-s')

P 1 P 2

P 2 P 1

The Game (Solution)

Accept

Reject

s, (1-s)

Accept

Reject

s', (1-s')

r·s', r·(1-s')

P 1 P 2

P 2 P 1

P 1 will accept anyProposal

The Game (Solution)

Accept

Reject

s, (1-s)

Accept

Reject

s', (1-s')

r·s', r·(1-s')

P 1 P 2

P 2 P 1

P 1 will accept anyproposal

P 2 will propose s'=0 (hence, (1-s')=1)

The Game (Solution)

Accept

Reject

s, (1-s)

Accept

Reject

P 1 P 2

P 2 P 1

P 1 will accept anyproposal

P 2 will propose s'=0 (hence, (1-s')=1)

The Game (Solution)

Accept

Reject

s, (1-s)

0, rP 1 P 2

This will be the solutionif the game reachesthis point, that is, ifPlayer 2 Rejects theinitial offer by Player 1

The Game (Solution)

Accept

Reject

s, (1-s)

0, rP 1 P 2

P 2 will accept anyproposal such that (1 - s) ≥ rThat is, 1 - r ≥ s

The Game (Solution)

Accept

Reject

s, (1-s)

0, rP 1 P 2

P 1 will propose s = 1 – r, and P 2 will Accept right away

The Game (Solution)

Accept

Reject

s, (1-s)

0, rP 1 P 2

P 1 will get 1 – r and P 2 will get 1 – (1 – r) = r

The Game (Solution)

Accept

Reject

1-r, r

1 - r, r

0, rP 1 P 2

This will be the final solution of the game

P 1 will get 1 – r and P 2 will get 1 – (1 – r) = r

The Game (Solution)

Solution: 1 – r for Player 1

r for Player 2

The Game (Solution)

r for Player 2

What would you prefer ?

To be Player 1 (the Initiator) To be Player 2 (the respondent)

The Game (Solution)

r for Player 2

What would you prefer ?

To be Player 1 (the Initiator) To be Player 2 (the respondent)

Depends on r !!!!

The Game (Solution)

r for Player 2

If r is low (for instance r = 0.3 ) it is better to be the initiator (Player 1 gets 0.7 while Player 2 gets 0.3)

If r is high (for instance r = 0.7 ) it is better to be the respondent (Player 1 gets 0.3 while Player 2 gets 0.7)

This is another example in which “tweaking” the rules of thegame may be profitableIt also shows that the “first mover advantage” is not alwaysthe case

Comments: Theoretical Bargaining

Because the value of the item is decreasing (by r), Player 1 wants to strike an agreement as soon aspossible

Hence, Player 1 offers Player 2 a proposal Player 2 can not reject

And Player 2 will not reject the proposal since the item will loose more value otherwise !

Thus, the prediction is that the negotiation will end in the first round (if the initial proposal is carefully

computed) If the negotiation involved more than 2 rounds, the

result would be the same: agreement right away. Theonly difference would be the proposal by Player 1

If r is low it's better to be Player 1, and vice versa

Comments: Bargaining in the Real Life

Why this does not happen in real life ?

Reputation building Lack of information Different “r” for different players

But some lessons are useful in real life

Civil lawsuits: If both parties can predict the future jury award, can settle for same outcome and save litigation fees and time

What is your best strategy depends on information and Patience (r)

Delays are always less profitable

4. The Theories and the Real World

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