Part III: Big Applications Repetition Asymmetric Information Signaling Long-Run Relationships Auctions & Market Design Credibility & Reputation Classes 12-14 Classes 15-18 Classes 19-21 MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 1
Signaling Games How to Make Communication Credible Chapter 1 (Today): Costly Signaling MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 2
Signaling Examples Entry deterrence: Incumbent tries to signal its resolve to fight to deter entrants How can strong informed players distinguish themselves? Credence Goods: Used car warranties Can weak players signal-jam? Social interactions Fashion Two of your class projects already using this (pitching a lemon, Estonia) MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 3
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
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
What s Beer? Toughness Excess Capacity Low Costs Deep Pockets Beer High Output Low Prices Beat up Rivals & Previous Entrants MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 6
Beer & Quiche: first model enter 1,-1 beer Incumbent quiche enter 2,-1 3,0 out Pr = x tough [½] Pr = y out 4,0 Entrant Nature Entrant enter -1,2 Pr = 1-x wimp [½] Pr = 1-y enter 2,2 1,0 out beer Incumbent quiche out 4,0 MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 7
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
enter 1,-1 Beer & Quiche Incumbent beer quiche enter 2,-1 3,0 out Pr = 1 Pr = 0 tough [½] out 4,0 Entrant Nature Entrant -1,2 enter Pr = 0 wimp [½] Pr = 1 enter 2,2 1,0 out beer Incumbent quiche out 4,0 MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 9
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
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
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
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
Poker 200, -200 call raise Got Card check fold good [1/3] No Card Nature -200, 200 call bad [2/3] fold raise Got Card check -100, 100 MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 14
How Did You Play? MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 15
200, -200 call fold No Separating Equilibrium Pr = 1 Got Card raise check good [1/3] No Card Nature -200, 200 call fold Pr = 0 raise bad [2/3] check Got Card -100, 100 MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 16
No Pooling Equilibrium 200, -200 call raise Got Card check fold Pr = 1/3 good [1/3] No Card Nature -200, 200 call fold Pr = 2/3 raise bad [2/3] check Got Card -100, 100 MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 17
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
Poker: Equilibrium 200, -200 call weakly dominant raise Got Card check fold Pr = x good [1/3] Must randomize No Card Nature -200, 200 fold call bad [2/3] Pr = 1-x -100, 100 raise check Got Card Must randomize MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 19
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
Poker: Equilibrium 200, -200 call raise Got Card check fold Pr = 3/4 good [1/3] No Card Nature -200, 200 call Pr = 1/4 bad [2/3] fold raise Got Card check Pr = 1/6 Pr = 5/6-100, 100 MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 21
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
Let s Compare MIT Sloan 15.025 S15 Prof. Alessandro Bonatti 23
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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