part iii: “big” applications · or a wimp (not tough). • incumbent earns 4 if the entrant...
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Part III: “Big” Applications
Auctions & Market Design
Classes 15-18
Credibility & Reputation
Classes 19-21 Classes 12-14
Long-Run Relationships
Asymmetric Information Repetition Signaling
MIT Sloan 15.025 S15 1 Prof. Alessandro Bonatti
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Signaling Games How to Make Communication Credible
Chapter 1 (Today): Costly Signaling
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 2
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Signaling Examples
• Entry deterrence: – Incumbent tries to signal its resolve to fight to
deter entrants
• Credence Goods: – Used car warranties
• Social interactions
– Fashion
Two of your class projects already using this… (pitching a lemon, Estonia)
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 3
How can strong informed players distinguish themselves? Can weak players signal-jam?
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The beer & quiche model
• A monopolist can be either a tough incumbent
or a wimp (not tough).
• Incumbent earns 4 if the entrant stays out.
• Incumbent earns 2 if the entrant enters.
• Entrant earns 2 if it enters against wimp.
• Entrant earns -1 if it enters against tough.
• Entrant gets 0 if it stays out.
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 4
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Beer & Quiche • Prior to the entrant’s decision to enter or stay out, the
incumbent gets to choose its “breakfast.”
• The incumbent can have beer or quiche for breakfast.
• Breakfasts are consumed in public.
• Eating quiche “costs” 0.
• Drinking beer costs differently according to type: – a beer breakfast costs a tough incumbent 1… – but costs a wimp incumbent 3.
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 5
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What’s Beer?
Toughness Beer
Excess Capacity High Output
Low Costs Low Prices
Deep Pockets Beat up Rivals & Previous Entrants
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 6
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Beer & Quiche: first model
Nature
tough
wimp
[½]
[½]
Incumbent
Incumbent
Entrant Entrant
beer
beer
quiche
quiche
enter
enter
out
out
enter
enter
out
out Pr = x
Pr = 1-x
Pr = y
Pr = 1-y
1,-1
3,0
-1,2
1,0
2,-1
4,0
2,2
4,0
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 7
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Signaling Equilibrium • Can the Incumbent credibly use Beer to signal Toughness?
Consistency Checklist
1. Is the Entrant’s strategy optimal given her beliefs?
2. Is Incumbent’s strategy a best response to the Entrant’s strategy?
3. Are Entrant’s beliefs correct given Incumbent’s strategy?
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 8
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Beer & Quiche
Nature
tough
wimp
[½]
[½]
Incumbent
Incumbent
Entrant Entrant
beer
beer
quiche
quiche
enter
enter
out
out
enter
enter
out
out
1,-1
3,0
-1,2
1,0
2,-1
4,0
2,2
4,0
Pr = 1 Pr = 0
Pr = 1 Pr = 0
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 9
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Separating Equilibrium
• Tough drinks beer.
• Wimp eats quiche.
• Entrant infers the true type.
• Degenerate beliefs (0 or 100%).
• Entrant should ignore prior information…
… and use strategic information.
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 10
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Credible Signals
• Why doesn’t Wimp drink beer & deter entry?
• It’s too costly
• This is the key feature of “credible signaling”!
• What if the signal (beer) were a bit less costly?
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 11
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Pooling Equilibrium
• Suppose the wimp prefers “beer & out” to “quiche & enter” • The “beer signal” can’t work! • If both types drank beer, the entrant would face 50:50
odds, and enter! • Both types of incumbent are then better off w/quiche
Cheap beer destroys signaling value
• Pooling equilibrium: both eat quiche, entrant enters
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 12
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Takeaways 1. Costly signals can be used more credibly:
– Warranties are expensive for sellers of bad cars – What is fashion? – Extra capacity must hurt inefficient firms more
2. Delicate balance:
– Cheap signals no persuasion – Expensive signals no profit
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 13
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Poker
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 14
Nature
good
bad
[1/3]
[2/3]
Got Card
Got Card
No Card
raise
raise
check
check
call
call
fold
fold
200 , -200
-200 , 200
100 , -100
-100 , 100
100 , -100
100 , -100
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How Did You Play?
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 15
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No Separating Equilibrium
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 16
Nature
good
bad
[1/3]
[2/3]
Got Card
Got Card
No Card
raise
raise
check
check
call
call
fold
fold
200 , -200
-200 , 200
100 , -100
-100 , 100
100 , -100
100 , -100
Pr = 1
Pr = 0
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No Pooling Equilibrium
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 17
Nature
good
bad
[1/3]
[2/3]
Got Card
Got Card
No Card
raise
raise
check
check
call
call
fold
fold
200 , -200
-200 , 200
100 , -100
-100 , 100
100 , -100
100 , -100
Pr = 1/3
Pr = 2/3
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Bluffing Game (poker)
How would you play against a game theory classmate?
1. Can you expect No-Card to always Fold?
2. What about always Call?
3. Can you expect Got-Good-Card to always raise?
… That’s a start!
4. Can you expect Got-Bad-Card to always raise?
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 18
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Poker: Equilibrium
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 19
Nature
good
bad
[1/3]
[2/3]
Got Card
Got Card
No Card
raise
raise
check
check
call
call
fold
fold
200 , -200
-200 , 200
100 , -100
-100 , 100
100 , -100
100 , -100
weakly dominant
Must randomize
Must randomize
Pr = x
Pr = 1-x
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Poker: Equilibrium
• Key property of Nash Equilibrium: “If a player randomizes in equilibrium, she must be indifferent between all the strategies she uses”
• Expected payoffs must be equal
• Otherwise, the player would choose the better strategy all (not some of) the time…
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 20
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Poker: Equilibrium
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 21
Nature
good
bad
[1/3]
[2/3]
Got Card
Got Card
No Card
raise
raise
check
check
call
call
fold
fold
200 , -200
-200 , 200
100 , -100
-100 , 100
100 , -100
100 , -100
Pr = 3/4
Pr = 1/4
Pr = 1/6 Pr = 5/6
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Calculations 1. If No-Card randomizes it must be that
E[u(call)] = E[u(fold)] = -100 200*Pr[bad | raise] – 200*Pr[good | raise] = -100 Pr[good | raise] = ¾ (no-card’s equilibrium belief)
2. We know Pr[raise | good] = 1; in order for Pr[good | raise] = (1/3)/(1/3+ Pr[raise | bad] 2/3) = ¾ it must be Pr[raise | bad] = 1/6.
3. If Bad-Card randomizes, it must be that E[u(raise)] = E[u(check)] = -100 -200*Pr[call]+100*Pr[fold] = -100 Pr[call]=2/3
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 22
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Let’s Compare
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 23
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Takeaways
1. Information is valuable, even in zero-sum games
2. Costly signals can be used more credibly
Next time • Cheap talk signals are less likely to be effective
• What does this have to do with R&D in large Pharma?
(aka, CEOs wish scientists were peacocks)
MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 24
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15.025 Game Theory for Strategic AdvantageSpring 2015
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