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4. The Theories and the Real World. Outline. 1. Introduction 2. Individual Decision Making 3. Basic Topics in Game Theory 4. The Theories and the Real World 4.1 Applications 4.1.1 Auctions 4.1.2 Negotiation 4.2 Alternative approaches 4.2.1 Psychology 4.2.2 Evolution - PowerPoint PPT Presentation
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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)
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)
Strategic Behavior in Business and Econ
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]
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
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 ...
Strategic Behavior in Business and Econ
Real Figures
No Auction in Spain !!
The government issued licenses based on public examination/contest
Strategic Behavior in Business and Econ
The Spanish government raised
880 million €
( 35 times less than France !! )
Real Figures
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
Basic Auction Types
• Open Auctions (sequential)• English Auctions• Dutch Auctions• Japanese Auctions
• Sealed Auctions (simultaneous)• First Price Sealed Bid• Second Price Sealed Bid
Strategic Behavior in Business and Econ
English Auctions (Ascending Bid)
• Bidders call out prices (English)• Bidders hold down button (Japanese)
• Highest bidder gets the object• Pays his or her bid
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
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!
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
Bidding Strategy
You Win
high
er
Your bid
Others’ bids
Your value
You Lose
Strategic Behavior in Business and Econ
Bidding Strategy (valuation vs below valuation)
Case 1 Case 2 Case 3
No difference No difference is better !!
Strategic Behavior in Business and Econ
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
Thus, the optimal strategy (weakly dominant) is to bid “slightly” below your valuation (bid shading)
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
Bidding Strategy
Each bidder has a “private” valuation of the item
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
Strategic Behavior in Business and Econ
Optimal Bidding Strategy in Second Price Auctions
You LoseYou Win
high
er
Your bid
Others’ bids
Your value
Strategic Behavior in Business and Econ
Bidding Higher Than My Valuation
Case 1 Case 2 Case 3
No difference No difference Lose money !!
Strategic Behavior in Business and Econ
Bidding Lower Than My ValuationCase 1 Case 2 Case 3
No difference No difference Lose money !!
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
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?
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
Number of Bidders
• Two bidders– Each has a value of 20 or 40– There are four value combinations:
Bidder 1 Bidder 2 Prob. Outcome (revenue)
20 20 ¼ 20
20 40 ¼ 20
40 20 ¼ 20
40 40 ¼ 40
Strategic Behavior in Business and Econ
Number of Bidders
• Two bidders– Each has a value of 20 or 40– There are four value combinations:
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
Strategic Behavior in Business and Econ
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
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 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
Number of Bidders• Three bidders
– Each has a value of 20 or 40– There are eight value combinations:
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
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
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!
Strategic Behavior in Business and Econ
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
Strategic Behavior in Business and Econ
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
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)
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)
Strategic Bahavior in Business and Econ
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)
Strategic Bahavior in Business and Econ
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
Strategic Bahavior in Business and Econ
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
Strategic Bahavior in Business and Econ
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)
Strategic Bahavior in Business and Econ
The Game
0
1
Accept
Reject
s, (1-s)
s, (1-s)
0
1
Accept
Reject
s', (1-s')
r·s', r·(1-s')
0, 0
P 1 P 2
P 2 P 1
Strategic Bahavior in Business and Econ
The Game (Solution)
0
1
Accept
Reject
s, (1-s)
s, (1-s)
0
1
Accept
Reject
s', (1-s')
r·s', r·(1-s')
0, 0
P 1 P 2
P 2 P 1
P 1 will accept anyProposal
Strategic Bahavior in Business and Econ
The Game (Solution)
0
1
Accept
Reject
s, (1-s)
s, (1-s)
0
1
Accept
Reject
s', (1-s')
r·s', r·(1-s')
0, 0
P 1 P 2
P 2 P 1
P 1 will accept anyproposal
P 2 will propose s'=0 (hence, (1-s')=1)
Strategic Bahavior in Business and Econ
The Game (Solution)
0
1
Accept
Reject
s, (1-s)
s, (1-s)
0
1
Accept
Reject
0, 1
0, r
0, 0
P 1 P 2
P 2 P 1
P 1 will accept anyproposal
P 2 will propose s'=0 (hence, (1-s')=1)
Strategic Bahavior in Business and Econ
The Game (Solution)
0
1
Accept
Reject
s, (1-s)
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
Strategic Bahavior in Business and Econ
The Game (Solution)
0
1
Accept
Reject
s, (1-s)
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
P 2 will accept anyproposal such that (1 - s) ≥ rThat is, 1 - r ≥ s
Strategic Bahavior in Business and Econ
The Game (Solution)
0
1
Accept
Reject
s, (1-s)
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
P 2 will accept anyproposal such that (1 - s) ≥ rThat is, 1 - r ≥ s
P 1 will propose s = 1 – r, and P 2 will Accept right away
Strategic Bahavior in Business and Econ
The Game (Solution)
0
1
Accept
Reject
s, (1-s)
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
P 2 will accept anyproposal such that (1 - s) ≥ rThat is, 1 - r ≥ s
P 1 will propose s = 1 – r, and P 2 will Accept right away
P 1 will get 1 – r and P 2 will get 1 – (1 – r) = r
Strategic Bahavior in Business and Econ
The Game (Solution)
0
1
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 propose s = 1 – r, and P 2 will Accept right away
P 1 will get 1 – r and P 2 will get 1 – (1 – r) = r
Strategic Bahavior in Business and Econ
The Game (Solution)
Solution: 1 – r for Player 1
r for Player 2
Strategic Bahavior in Business and Econ
The Game (Solution)
Solution: 1 – r for Player 1
r for Player 2
What would you prefer ?
To be Player 1 (the Initiator) To be Player 2 (the respondent)
Strategic Bahavior in Business and Econ
The Game (Solution)
Solution: 1 – r for Player 1
r for Player 2
What would you prefer ?
To be Player 1 (the Initiator) To be Player 2 (the respondent)
Depends on r !!!!
Strategic Bahavior in Business and Econ
The Game (Solution)
Solution: 1 – r for Player 1
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
Strategic Bahavior in Business and Econ
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
Strategic Bahavior in Business and Econ
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