![Page 1: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/1.jpg)
Information Design: Murat Sertel LectureIstanbul Bilgi University: Conference on Economic Design
Stephen Morris
July 2015
![Page 2: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/2.jpg)
Mechanism Design and Information Design
I Mechanism Design:I Fix an economic environment and information structureI Design the rules of the game to get a desirable outcome
I Information DesignI Fix an economic environment and rules of the gameI Design an information structure to get a desirable outcome
![Page 3: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/3.jpg)
Mechanism Design and Information Design
I Mechanism Design:I Fix an economic environment and information structureI Design the rules of the game to get a desirable outcome
I Information DesignI Fix an economic environment and rules of the gameI Design an information structure to get a desirable outcome
![Page 4: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/4.jpg)
Mechanism Design and Information Design
I Mechanism Design:I Can compare particular mechanisms
I e.g., �rst price auctions versus second price auctions
I Can work with space of all mechanisms
I e.g., Myerson�s optimal mechanism
I Information DesignI Can compare particular information structures
I Linkage Principle: Milgrom-Weber (1982)I Information Sharing in Oligopoly: Novshek and Sonnenschein(1982)
I Can work with space of all information structures
I "Bayesian Persuasion": Kamenica-Genzkow (2011), oneperson case
I Application of "Robust Predictions": Bergemann-Morris(2013, 2015) and co-authors (this talk)
I "Information Design": Taneva (2015)
![Page 5: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/5.jpg)
Mechanism Design and Information Design
I Mechanism Design:I Can compare particular mechanisms
I e.g., �rst price auctions versus second price auctions
I Can work with space of all mechanisms
I e.g., Myerson�s optimal mechanism
I Information DesignI Can compare particular information structures
I Linkage Principle: Milgrom-Weber (1982)I Information Sharing in Oligopoly: Novshek and Sonnenschein(1982)
I Can work with space of all information structures
I "Bayesian Persuasion": Kamenica-Genzkow (2011), oneperson case
I Application of "Robust Predictions": Bergemann-Morris(2013, 2015) and co-authors (this talk)
I "Information Design": Taneva (2015)
![Page 6: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/6.jpg)
Mechanism Design and Information Design
I Mechanism Design:I Can compare particular mechanisms
I e.g., �rst price auctions versus second price auctions
I Can work with space of all mechanisms
I e.g., Myerson�s optimal mechanism
I Information DesignI Can compare particular information structures
I Linkage Principle: Milgrom-Weber (1982)I Information Sharing in Oligopoly: Novshek and Sonnenschein(1982)
I Can work with space of all information structures
I "Bayesian Persuasion": Kamenica-Genzkow (2011), oneperson case
I Application of "Robust Predictions": Bergemann-Morris(2013, 2015) and co-authors (this talk)
I "Information Design": Taneva (2015)
![Page 7: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/7.jpg)
Mechanism Design and Information Design
I Mechanism Design:I Can compare particular mechanisms
I e.g., �rst price auctions versus second price auctions
I Can work with space of all mechanisms
I e.g., Myerson�s optimal mechanism
I Information DesignI Can compare particular information structures
I Linkage Principle: Milgrom-Weber (1982)
I Information Sharing in Oligopoly: Novshek and Sonnenschein(1982)
I Can work with space of all information structures
I "Bayesian Persuasion": Kamenica-Genzkow (2011), oneperson case
I Application of "Robust Predictions": Bergemann-Morris(2013, 2015) and co-authors (this talk)
I "Information Design": Taneva (2015)
![Page 8: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/8.jpg)
Mechanism Design and Information Design
I Mechanism Design:I Can compare particular mechanisms
I e.g., �rst price auctions versus second price auctions
I Can work with space of all mechanisms
I e.g., Myerson�s optimal mechanism
I Information DesignI Can compare particular information structures
I Linkage Principle: Milgrom-Weber (1982)I Information Sharing in Oligopoly: Novshek and Sonnenschein(1982)
I Can work with space of all information structures
I "Bayesian Persuasion": Kamenica-Genzkow (2011), oneperson case
I Application of "Robust Predictions": Bergemann-Morris(2013, 2015) and co-authors (this talk)
I "Information Design": Taneva (2015)
![Page 9: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/9.jpg)
Mechanism Design and Information Design
I Mechanism Design:I Can compare particular mechanisms
I e.g., �rst price auctions versus second price auctions
I Can work with space of all mechanisms
I e.g., Myerson�s optimal mechanism
I Information DesignI Can compare particular information structures
I Linkage Principle: Milgrom-Weber (1982)I Information Sharing in Oligopoly: Novshek and Sonnenschein(1982)
I Can work with space of all information structures
I "Bayesian Persuasion": Kamenica-Genzkow (2011), oneperson case
I Application of "Robust Predictions": Bergemann-Morris(2013, 2015) and co-authors (this talk)
I "Information Design": Taneva (2015)
![Page 10: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/10.jpg)
Mechanism Design and Information Design
I Mechanism Design:I Can compare particular mechanisms
I e.g., �rst price auctions versus second price auctions
I Can work with space of all mechanisms
I e.g., Myerson�s optimal mechanism
I Information DesignI Can compare particular information structures
I Linkage Principle: Milgrom-Weber (1982)I Information Sharing in Oligopoly: Novshek and Sonnenschein(1982)
I Can work with space of all information structures
I "Bayesian Persuasion": Kamenica-Genzkow (2011), oneperson case
I Application of "Robust Predictions": Bergemann-Morris(2013, 2015) and co-authors (this talk)
I "Information Design": Taneva (2015)
![Page 11: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/11.jpg)
Mechanism Design and Information Design
I Mechanism Design:I Can compare particular mechanisms
I e.g., �rst price auctions versus second price auctions
I Can work with space of all mechanisms
I e.g., Myerson�s optimal mechanism
I Information DesignI Can compare particular information structures
I Linkage Principle: Milgrom-Weber (1982)I Information Sharing in Oligopoly: Novshek and Sonnenschein(1982)
I Can work with space of all information structures
I "Bayesian Persuasion": Kamenica-Genzkow (2011), oneperson case
I Application of "Robust Predictions": Bergemann-Morris(2013, 2015) and co-authors (this talk)
I "Information Design": Taneva (2015)
![Page 12: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/12.jpg)
Mechanism Design and Information Design
I Mechanism Design:I Can compare particular mechanisms
I e.g., �rst price auctions versus second price auctions
I Can work with space of all mechanisms
I e.g., Myerson�s optimal mechanism
I Information DesignI Can compare particular information structures
I Linkage Principle: Milgrom-Weber (1982)I Information Sharing in Oligopoly: Novshek and Sonnenschein(1982)
I Can work with space of all information structures
I "Bayesian Persuasion": Kamenica-Genzkow (2011), oneperson case
I Application of "Robust Predictions": Bergemann-Morris(2013, 2015) and co-authors (this talk)
I "Information Design": Taneva (2015)
![Page 13: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/13.jpg)
This Talk
1. Leading Example to Understand Structure of Problem
2. A General Approach
3. Some Applications:I OligopolyI Price DiscriminationI AuctionsI Volatility
4. Literature Review
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Bank Run: one depositor and no initial information
I A bank depositor is deciding whether to run from the bank ifhe assigns probability greater than 1
2 to a bad state
Payo¤ θG θBStay 1 �1Run 0 0
I The depositor knows nothing about the stateI The probability of the bad state is 23
I Outcome distribution with no information:
Outcome θG θBStay 0 0Run 1
323
I Probability of run is 1
![Page 15: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/15.jpg)
Bank Run: one depositor and no initial information
I A bank depositor is deciding whether to run from the bank ifhe assigns probability greater than 1
2 to a bad state
Payo¤ θG θBStay 1 �1Run 0 0
I The depositor knows nothing about the stateI The probability of the bad state is 23I Outcome distribution with no information:
Outcome θG θBStay 0 0Run 1
323
I Probability of run is 1
![Page 16: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/16.jpg)
Optimal Information Design with one depositor and noinitial information
I The regulator cannot stop the depositor withdrawing....I ... but can choose what information is made available toprevent withdrawals
I Best information structure:I tell the depositor that the state is bad exactly often enough sothat he will stay if he doesn�t get the signal.....
Outcome θG θBStay (intermediate signal) 1
313
Run (bad signal) 0 13
I Think of the regulator as a mediator making an actionrecommendation to the depositor subject to an obedienceconstraint
I Probability of run is 13
![Page 17: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/17.jpg)
Optimal Information Design with one depositor and noinitial information
I The regulator cannot stop the depositor withdrawing....I ... but can choose what information is made available toprevent withdrawals
I Best information structure:I tell the depositor that the state is bad exactly often enough sothat he will stay if he doesn�t get the signal.....
Outcome θG θBStay (intermediate signal) 1
313
Run (bad signal) 0 13
I Think of the regulator as a mediator making an actionrecommendation to the depositor subject to an obedienceconstraint
I Probability of run is 13
![Page 18: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/18.jpg)
Optimal Information Design with one depositor and noinitial information
I The regulator cannot stop the depositor withdrawing....I ... but can choose what information is made available toprevent withdrawals
I Best information structure:I tell the depositor that the state is bad exactly often enough sothat he will stay if he doesn�t get the signal.....
Outcome θG θBStay (intermediate signal) 1
313
Run (bad signal) 0 13
I Think of the regulator as a mediator making an actionrecommendation to the depositor subject to an obedienceconstraint
I Probability of run is 13
![Page 19: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/19.jpg)
Optimal Information Design with one depositor and noinitial information
I The regulator cannot stop the depositor withdrawing....I ... but can choose what information is made available toprevent withdrawals
I Best information structure:I tell the depositor that the state is bad exactly often enough sothat he will stay if he doesn�t get the signal.....
Outcome θG θBStay (intermediate signal) 1
313
Run (bad signal) 0 13
I Think of the regulator as a mediator making an actionrecommendation to the depositor subject to an obedienceconstraint
I Probability of run is 13
![Page 20: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/20.jpg)
Lessons
1. Without loss of generality, can restrict attention toinformation structures where each player�s signal space isequal to his action space
I compare with the revelation principle of mechanism design:
I without loss of generality, we can restrict attention tomechanisms where each player�s message space is equal to histype space
![Page 21: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/21.jpg)
Lessons
1. Without loss of generality, can restrict attention toinformation structures where each player�s signal space isequal to his action space
I compare with the revelation principle of mechanism design:
I without loss of generality, we can restrict attention tomechanisms where each player�s message space is equal to histype space
![Page 22: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/22.jpg)
Bank Run: one depositor with initial information
I If the state is good, with probability 12 the depositor will
already have observed a signal tG saying that the state is good
I Outcome distribution with no additional information:
Payo¤ θG , tG θG , t0 θB , t0Stay 1
6 0 0Run 0 1
623
I Probability of run is 56
![Page 23: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/23.jpg)
Bank Run: one depositor with initial information
I If the state is good, with probability 12 the depositor will
already have observed a signal tG saying that the state is goodI Outcome distribution with no additional information:
Payo¤ θG , tG θG , t0 θB , t0Stay 1
6 0 0Run 0 1
623
I Probability of run is 56
![Page 24: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/24.jpg)
Bank Run: one depositor with initial information
I If the state is good, with probability 12 the depositor will
already have observed a signal tG saying that the state is goodI Outcome distribution with no additional information:
Payo¤ θG , tG θG , t0 θB , t0Stay 1
6 0 0Run 0 1
623
I Probability of run is 56
![Page 25: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/25.jpg)
Optimal Information Design with one depositor with initialinformation
I Best information structure:I tell the depositor that the state is bad exactly often enough sothat he will stay if he doesn�t get the signal.....
Payo¤ θG , tG θG , t0 θB , t0Stay 1
616
16
Run 0 0 12
I Probability of run is 12
![Page 26: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/26.jpg)
Optimal Information Design with one depositor with initialinformation
I Best information structure:I tell the depositor that the state is bad exactly often enough sothat he will stay if he doesn�t get the signal.....
Payo¤ θG , tG θG , t0 θB , t0Stay 1
616
16
Run 0 0 12
I Probability of run is 12
![Page 27: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/27.jpg)
Is initially more informed depositor good or bad?
I With no information design....I ...and no initial information, probability of run is 1I ...and initial information, probability of run is 56
I With information design....I ...and no initial information, probability of a run is 13I ...and initial information, probability of a run is 12
I Initial information always hurts the regulator
![Page 28: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/28.jpg)
Is initially more informed depositor good or bad?
I With no information design....I ...and no initial information, probability of run is 1I ...and initial information, probability of run is 56
I With information design....I ...and no initial information, probability of a run is 13I ...and initial information, probability of a run is 12
I Initial information always hurts the regulator
![Page 29: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/29.jpg)
Is initially more informed depositor good or bad?
I With no information design....I ...and no initial information, probability of run is 1I ...and initial information, probability of run is 56
I With information design....I ...and no initial information, probability of a run is 13I ...and initial information, probability of a run is 12
I Initial information always hurts the regulator
![Page 30: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/30.jpg)
Lessons
1. Without loss of generality, can restrict attention toinformation structures where each player�s signal space isequal to his action space
2. Prior information limits the scope for information design
![Page 31: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/31.jpg)
Bank Runs: two depositors and no initial information
I A bank depositor would like to run from the bank if he assignsprobability greater than 1
2 to a bad state OR the otherdepositor running
state θG Stay RunStay 1 �1Run 0 0
state θB Stay RunStay �1 �1Run 0 0
I Probability of the bad state is 23
![Page 32: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/32.jpg)
Bank Runs: two depositors and no initial information
I Outcome distribution with no information
outcome θG Stay RunStay 0 0Run 0 1
3
outcome θB Stay RunStay 0 0Run 0 2
3
I Best information structure:I tell the depositors that the state is bad exactly often enough sothat they will stay if they don�t get the signal.....
outcome θG Stay RunStay 1
3 0Run 0 0
outcome θB Stay RunStay 1
3 0Run 0 1
3
I ...with public signals optimal
![Page 33: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/33.jpg)
Bank Runs: two depositors and no initial information
I Outcome distribution with no information
outcome θG Stay RunStay 0 0Run 0 1
3
outcome θB Stay RunStay 0 0Run 0 2
3
I Best information structure:I tell the depositors that the state is bad exactly often enough sothat they will stay if they don�t get the signal.....
outcome θG Stay RunStay 1
3 0Run 0 0
outcome θB Stay RunStay 1
3 0Run 0 1
3
I ...with public signals optimal
![Page 34: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/34.jpg)
Bank Runs: two depositors and no initial information
I Outcome distribution with no information
outcome θG Stay RunStay 0 0Run 0 1
3
outcome θB Stay RunStay 0 0Run 0 2
3
I Best information structure:I tell the depositors that the state is bad exactly often enough sothat they will stay if they don�t get the signal.....
outcome θG Stay RunStay 1
3 0Run 0 0
outcome θB Stay RunStay 1
3 0Run 0 1
3
I ...with public signals optimal
![Page 35: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/35.jpg)
Bank Runs: two depositors, no initial information andstrategic substitutes
I Previous example had strategic complementsI Strategic substitute example: a bank depositor would like torun from the bank if he assigns probability greater than 1
2 to abad state AND the other depositor staying
state θG Stay RunStay 1 1Run 0 0
state θB Stay RunStay �1 1Run 0 0
I Probability of the bad state is 23
![Page 36: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/36.jpg)
Bank Runs: two depositors, no initial information andstrategic substitutes
I Previous example had strategic complementsI Strategic substitute example: a bank depositor would like torun from the bank if he assigns probability greater than 1
2 to abad state AND the other depositor staying
state θG Stay RunStay 1 1Run 0 0
state θB Stay RunStay �1 1Run 0 0
I Probability of the bad state is 23
![Page 37: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/37.jpg)
Bank Runs: two depositors and no initial information
I Outcome distribution with no information: mixed strategyequilibrium
I Best information structure:I tell the depositors that the state is bad exactly often enough sothat they will stay if they don�t get the signal.....
outcome θG Stay RunStay 1
3 0Run 0 0
outcome θB Stay RunStay 4
919
Run 19 0
I ....with private signals optimal
![Page 38: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/38.jpg)
Bank Runs: two depositors and no initial information
I Outcome distribution with no information: mixed strategyequilibrium
I Best information structure:I tell the depositors that the state is bad exactly often enough sothat they will stay if they don�t get the signal.....
outcome θG Stay RunStay 1
3 0Run 0 0
outcome θB Stay RunStay 4
919
Run 19 0
I ....with private signals optimal
![Page 39: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/39.jpg)
Bank Runs: two depositors and no initial information
I Outcome distribution with no information: mixed strategyequilibrium
I Best information structure:I tell the depositors that the state is bad exactly often enough sothat they will stay if they don�t get the signal.....
outcome θG Stay RunStay 1
3 0Run 0 0
outcome θB Stay RunStay 4
919
Run 19 0
I ....with private signals optimal
![Page 40: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/40.jpg)
Lessons
1. Without loss of generality, can restrict attention toinformation structures where each player�s signal space isequal to his action space
2. Prior information limits the scope for information design
3. Public signals optimal if strategic complementarities; privatesignals optimal if strategic substitutes
![Page 41: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/41.jpg)
Bank Run: two depositors with initial information
have also analyzed elsewhere....
![Page 42: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/42.jpg)
General Formulation (in words!)
I Fix a game with incomplete information about payo¤ statesI Ask what could happen in equilibrium for any additionalinformation that players could be given....
I Equivalent to looking for joint distribution over payo¤ states,initial information signals and actions satisfying an obediencecondition ("Bayes correlated equilibrium")
I This is general statement of lesson 1: can restrict attention toinformation structures where each player�s signal space is equalto his action space
I Bayes correlated equilibrium reduces to....I ....Aumann Maschler (1995) concavi�cation /Kamenica-Genzkow (2011) Bayesian persuasion in case of oneplayer
I ....Aumann (1984, 1987) correlated equilibrium in case ofcomplete information
I ....Forges (1993) Bayesian solution if no distributed uncertainty
![Page 43: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/43.jpg)
General Formulation (in words!)
I Fix a game with incomplete information about payo¤ statesI Ask what could happen in equilibrium for any additionalinformation that players could be given....
I Equivalent to looking for joint distribution over payo¤ states,initial information signals and actions satisfying an obediencecondition ("Bayes correlated equilibrium")
I This is general statement of lesson 1: can restrict attention toinformation structures where each player�s signal space is equalto his action space
I Bayes correlated equilibrium reduces to....I ....Aumann Maschler (1995) concavi�cation /Kamenica-Genzkow (2011) Bayesian persuasion in case of oneplayer
I ....Aumann (1984, 1987) correlated equilibrium in case ofcomplete information
I ....Forges (1993) Bayesian solution if no distributed uncertainty
![Page 44: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/44.jpg)
General Formulation (in words!)
I Fix a game with incomplete information about payo¤ statesI Ask what could happen in equilibrium for any additionalinformation that players could be given....
I Equivalent to looking for joint distribution over payo¤ states,initial information signals and actions satisfying an obediencecondition ("Bayes correlated equilibrium")
I This is general statement of lesson 1: can restrict attention toinformation structures where each player�s signal space is equalto his action space
I Bayes correlated equilibrium reduces to....I ....Aumann Maschler (1995) concavi�cation /Kamenica-Genzkow (2011) Bayesian persuasion in case of oneplayer
I ....Aumann (1984, 1987) correlated equilibrium in case ofcomplete information
I ....Forges (1993) Bayesian solution if no distributed uncertainty
![Page 45: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/45.jpg)
General Formulation (in words!)
I Fix a game with incomplete information about payo¤ statesI Ask what could happen in equilibrium for any additionalinformation that players could be given....
I Equivalent to looking for joint distribution over payo¤ states,initial information signals and actions satisfying an obediencecondition ("Bayes correlated equilibrium")
I This is general statement of lesson 1: can restrict attention toinformation structures where each player�s signal space is equalto his action space
I Bayes correlated equilibrium reduces to....I ....Aumann Maschler (1995) concavi�cation /Kamenica-Genzkow (2011) Bayesian persuasion in case of oneplayer
I ....Aumann (1984, 1987) correlated equilibrium in case ofcomplete information
I ....Forges (1993) Bayesian solution if no distributed uncertainty
![Page 46: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/46.jpg)
General Formulation (in words!)
I Fix a game with incomplete information about payo¤ statesI Ask what could happen in equilibrium for any additionalinformation that players could be given....
I Equivalent to looking for joint distribution over payo¤ states,initial information signals and actions satisfying an obediencecondition ("Bayes correlated equilibrium")
I This is general statement of lesson 1: can restrict attention toinformation structures where each player�s signal space is equalto his action space
I Bayes correlated equilibrium reduces to....I ....Aumann Maschler (1995) concavi�cation /Kamenica-Genzkow (2011) Bayesian persuasion in case of oneplayer
I ....Aumann (1984, 1987) correlated equilibrium in case ofcomplete information
I ....Forges (1993) Bayesian solution if no distributed uncertainty
![Page 47: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/47.jpg)
General Formulation (in words!)
I Fix a game with incomplete information about payo¤ statesI Ask what could happen in equilibrium for any additionalinformation that players could be given....
I Equivalent to looking for joint distribution over payo¤ states,initial information signals and actions satisfying an obediencecondition ("Bayes correlated equilibrium")
I This is general statement of lesson 1: can restrict attention toinformation structures where each player�s signal space is equalto his action space
I Bayes correlated equilibrium reduces to....I ....Aumann Maschler (1995) concavi�cation /Kamenica-Genzkow (2011) Bayesian persuasion in case of oneplayer
I ....Aumann (1984, 1987) correlated equilibrium in case ofcomplete information
I ....Forges (1993) Bayesian solution if no distributed uncertainty
![Page 48: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/48.jpg)
Comparing Information Structures
I Increasing prior information must reduce the set of outcomesthat can arise (lesson 2)
I But what is the right de�nition of increasing information(generalizing Blackwell�s ordering) in many player case....?
I One information structure is "individually su¢ cient" foranother if you can embed both information structures in acombined information structure where a player�s signal in theformer information structure is su¢ cient for his signal in thelatter...
I This ordering characterizes which information structureimposes more incentive constraints
![Page 49: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/49.jpg)
Comparing Information Structures
I Increasing prior information must reduce the set of outcomesthat can arise (lesson 2)
I But what is the right de�nition of increasing information(generalizing Blackwell�s ordering) in many player case....?
I One information structure is "individually su¢ cient" foranother if you can embed both information structures in acombined information structure where a player�s signal in theformer information structure is su¢ cient for his signal in thelatter...
I This ordering characterizes which information structureimposes more incentive constraints
![Page 50: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/50.jpg)
Comparing Information Structures
I Increasing prior information must reduce the set of outcomesthat can arise (lesson 2)
I But what is the right de�nition of increasing information(generalizing Blackwell�s ordering) in many player case....?
I One information structure is "individually su¢ cient" foranother if you can embed both information structures in acombined information structure where a player�s signal in theformer information structure is su¢ cient for his signal in thelatter...
I This ordering characterizes which information structureimposes more incentive constraints
![Page 51: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/51.jpg)
Comparing Information Structures
I Increasing prior information must reduce the set of outcomesthat can arise (lesson 2)
I But what is the right de�nition of increasing information(generalizing Blackwell�s ordering) in many player case....?
I One information structure is "individually su¢ cient" foranother if you can embed both information structures in acombined information structure where a player�s signal in theformer information structure is su¢ cient for his signal in thelatter...
I This ordering characterizes which information structureimposes more incentive constraints
![Page 52: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/52.jpg)
Application 1: Oligopoly
I Lesson 3:I with strategic complementaries, public information is bestI with strategic substitutes, private (conditionally independent)information is best
I In oligopoly...I strategic substitutesI if uncertainty about demand, �rms would like to have
I good information about the state of demandI BUT would like signals to be as uncorrelated as possible withothers�signals
I in general, intermediate conditionally independent privatesignals about demand are optimal for cartel problem
![Page 53: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/53.jpg)
Application 2: Price Discrimination
I Fix a demand curveI Interpret the demand curve as representing single unit demandof a continuum of consumers
I How much revenue could a monopolist producer/seller get?
I If the seller cannot discriminate between consumers, he mustcharge uniform monopoly price
I Write u� for the resulting consumer surplus and π� for theproducer surplus ("uniform monopoly pro�ts")
![Page 54: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/54.jpg)
Application 2: Price Discrimination
I Fix a demand curveI Interpret the demand curve as representing single unit demandof a continuum of consumers
I How much revenue could a monopolist producer/seller get?I If the seller cannot discriminate between consumers, he mustcharge uniform monopoly price
I Write u� for the resulting consumer surplus and π� for theproducer surplus ("uniform monopoly pro�ts")
![Page 55: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/55.jpg)
Application 2: Price Discrimination
I Fix a demand curveI Interpret the demand curve as representing single unit demandof a continuum of consumers
I How much revenue could a monopolist producer/seller get?I If the seller cannot discriminate between consumers, he mustcharge uniform monopoly price
I Write u� for the resulting consumer surplus and π� for theproducer surplus ("uniform monopoly pro�ts")
![Page 56: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/56.jpg)
The Uniform Price Monopoly
0Consumer surplus
Pro
duce
r sur
plus
No information
I producer charges (uniform) monopoly priceI consumers get positive consumer surplus, socially ine¢ cientallocation
![Page 57: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/57.jpg)
Perfect Price Discrimination
I But what if the producer could observe each consumer�svaluation perfectly?
I Pigou (1920) called this "�rst degree price discrimination"I In this case, consumer gets zero surplus and producer fullyextracts e¢ cient surplus w � > π� + u�
![Page 58: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/58.jpg)
Perfect Price Discrimination
I But what if the producer could observe each consumer�svaluation perfectly?
I Pigou (1920) called this "�rst degree price discrimination"
I In this case, consumer gets zero surplus and producer fullyextracts e¢ cient surplus w � > π� + u�
![Page 59: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/59.jpg)
Perfect Price Discrimination
I But what if the producer could observe each consumer�svaluation perfectly?
I Pigou (1920) called this "�rst degree price discrimination"I In this case, consumer gets zero surplus and producer fullyextracts e¢ cient surplus w � > π� + u�
![Page 60: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/60.jpg)
First Degree Price Discrimination
0Consumer surplus
Pro
duce
r sur
plus
Complete information
![Page 61: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/61.jpg)
Imperfect Price Discrimination
I But what if the producer can only observe an imperfect signalof each consumer�s valuation, and charge di¤erent pricesbased on the signal
I Equivalently, suppose the market is split into di¤erentsegments (students, non-students, old age pensioners, etc....)
I Pigou (1920) called this "third degree price discrimination"I What can happen?I A large literature (starting with Pigou (1920)) asks whathappens to consumer surplus, producer surplus and thus totalsurplus if we segment the market in particular ways
![Page 62: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/62.jpg)
Imperfect Price Discrimination
I But what if the producer can only observe an imperfect signalof each consumer�s valuation, and charge di¤erent pricesbased on the signal
I Equivalently, suppose the market is split into di¤erentsegments (students, non-students, old age pensioners, etc....)
I Pigou (1920) called this "third degree price discrimination"I What can happen?I A large literature (starting with Pigou (1920)) asks whathappens to consumer surplus, producer surplus and thus totalsurplus if we segment the market in particular ways
![Page 63: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/63.jpg)
Imperfect Price Discrimination
I But what if the producer can only observe an imperfect signalof each consumer�s valuation, and charge di¤erent pricesbased on the signal
I Equivalently, suppose the market is split into di¤erentsegments (students, non-students, old age pensioners, etc....)
I Pigou (1920) called this "third degree price discrimination"
I What can happen?I A large literature (starting with Pigou (1920)) asks whathappens to consumer surplus, producer surplus and thus totalsurplus if we segment the market in particular ways
![Page 64: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/64.jpg)
Imperfect Price Discrimination
I But what if the producer can only observe an imperfect signalof each consumer�s valuation, and charge di¤erent pricesbased on the signal
I Equivalently, suppose the market is split into di¤erentsegments (students, non-students, old age pensioners, etc....)
I Pigou (1920) called this "third degree price discrimination"I What can happen?
I A large literature (starting with Pigou (1920)) asks whathappens to consumer surplus, producer surplus and thus totalsurplus if we segment the market in particular ways
![Page 65: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/65.jpg)
Imperfect Price Discrimination
I But what if the producer can only observe an imperfect signalof each consumer�s valuation, and charge di¤erent pricesbased on the signal
I Equivalently, suppose the market is split into di¤erentsegments (students, non-students, old age pensioners, etc....)
I Pigou (1920) called this "third degree price discrimination"I What can happen?I A large literature (starting with Pigou (1920)) asks whathappens to consumer surplus, producer surplus and thus totalsurplus if we segment the market in particular ways
![Page 66: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/66.jpg)
The Limits of Price Discrimination
I Questions:I What is the maximum possible consumer surplus, and whatsegmentation attains it?
I What consumer surplus and producer surplus pairs could arise,and which segementations attain those pairs?
I These are information design questions:I segmenting the market is the same thing as providinginformation to the monopolist about buyers�valuations
I by maximizing di¤erent (positive and negative) weighted sumsof consumer and producer surplus, we will map out feasibleconsumer surplus and producer surplus pairs
![Page 67: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/67.jpg)
The Limits of Price Discrimination
I Questions:I What is the maximum possible consumer surplus, and whatsegmentation attains it?
I What consumer surplus and producer surplus pairs could arise,and which segementations attain those pairs?
I These are information design questions:I segmenting the market is the same thing as providinginformation to the monopolist about buyers�valuations
I by maximizing di¤erent (positive and negative) weighted sumsof consumer and producer surplus, we will map out feasibleconsumer surplus and producer surplus pairs
![Page 68: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/68.jpg)
Three Welfare Bounds
1. Voluntary Participation: Consumer Surplus is at least zero
![Page 69: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/69.jpg)
Welfare Bounds: Voluntary Participation
0Consumer surplus
Prod
ucer
sur
plus
Consumer surplus is at least zero
![Page 70: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/70.jpg)
Three Welfare Bounds
1. Voluntary Participation: Consumer Surplus is at least zero
2. Non-negative Value of Information: Producer Surplusbounded below by uniform monopoly pro�ts π�
![Page 71: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/71.jpg)
Welfare Bounds: Nonnegative Value of Information
0Consumer surplus
Prod
ucer
sur
plus
Producer gets at least uniform price profit
![Page 72: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/72.jpg)
Three Welfare Bounds
1. Voluntary Participation: Consumer Surplus is at least zero
2. Non-negative Value of Information: Producer Surplusbounded below by uniform monopoly pro�ts π�
3. Social Surplus: The sum of Consumer Surplus and ProducerSurplus cannot exceed the total gains from trade
![Page 73: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/73.jpg)
Welfare Bounds: Social Surplus
0Consumer surplus
Prod
ucer
sur
plus
Total surplus is bounded by efficient outcome
![Page 74: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/74.jpg)
Beyond Welfare Bounds
1. Includes points corresponding uniform price monopoly,(u�,π�), and perfect price discrimination, (0,w �)
2. Convex
![Page 75: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/75.jpg)
Welfare Bounds and Convexity1. Includes points corresponding uniform price monopoly,(u�,π�), and perfect price discrimination, (0,w �)
2. Convex
0Consumer surplus
Prod
ucer
sur
plus
What is the feasible surplus set?
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Welfare Bounds are Sharp
0Consumer surplus
Prod
ucer
sur
plus
Main result
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Maximizing Consumer Surplus
I Any (consumer surplus, producer surplus) pair consistent withthree bounds arises with some segmentation / informationstructure
I In particular, there exists a consumer surplus maximizingsegmentation (corresponding to the bottom right handcorner) where
1. the producer earns uniform monopoly pro�ts
2. the allocation is e¢ cient
3. the consumers attain the di¤erence between e¢ cient surplusand uniform monopoly pro�t.
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An Information Structure Attaining Consumer SurplusMaximizing Segmentation
I Consider a �nite set of values
I Create a segment consistent of all consumers with the lowestvalue and the proportion of consumers with all other highervalues such that the monopolist is indi¤erent betweencharging the lowest value and uniform monopoly price
I Then a segment consistent of all remaining consumers withthe second lowest value and the proportion of consumers withall other higher values such that the monopolist is indi¤erentbetween charging the second lowest value and uniformmonopoly price
I And so on...I Charge lowest price in each segmentI Monopolist earns uniform monopoly pro�tI Allocation is e¢ cientI Consumer earns total feasible surplus minus uniform monopolypro�t
![Page 79: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/79.jpg)
An Information Structure Attaining Consumer SurplusMaximizing Segmentation
I Consider a �nite set of valuesI Create a segment consistent of all consumers with the lowestvalue and the proportion of consumers with all other highervalues such that the monopolist is indi¤erent betweencharging the lowest value and uniform monopoly price
I Then a segment consistent of all remaining consumers withthe second lowest value and the proportion of consumers withall other higher values such that the monopolist is indi¤erentbetween charging the second lowest value and uniformmonopoly price
I And so on...I Charge lowest price in each segmentI Monopolist earns uniform monopoly pro�tI Allocation is e¢ cientI Consumer earns total feasible surplus minus uniform monopolypro�t
![Page 80: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/80.jpg)
An Information Structure Attaining Consumer SurplusMaximizing Segmentation
I Consider a �nite set of valuesI Create a segment consistent of all consumers with the lowestvalue and the proportion of consumers with all other highervalues such that the monopolist is indi¤erent betweencharging the lowest value and uniform monopoly price
I Then a segment consistent of all remaining consumers withthe second lowest value and the proportion of consumers withall other higher values such that the monopolist is indi¤erentbetween charging the second lowest value and uniformmonopoly price
I And so on...I Charge lowest price in each segmentI Monopolist earns uniform monopoly pro�tI Allocation is e¢ cientI Consumer earns total feasible surplus minus uniform monopolypro�t
![Page 81: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/81.jpg)
An Information Structure Attaining Consumer SurplusMaximizing Segmentation
I Consider a �nite set of valuesI Create a segment consistent of all consumers with the lowestvalue and the proportion of consumers with all other highervalues such that the monopolist is indi¤erent betweencharging the lowest value and uniform monopoly price
I Then a segment consistent of all remaining consumers withthe second lowest value and the proportion of consumers withall other higher values such that the monopolist is indi¤erentbetween charging the second lowest value and uniformmonopoly price
I And so on...
I Charge lowest price in each segmentI Monopolist earns uniform monopoly pro�tI Allocation is e¢ cientI Consumer earns total feasible surplus minus uniform monopolypro�t
![Page 82: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/82.jpg)
An Information Structure Attaining Consumer SurplusMaximizing Segmentation
I Consider a �nite set of valuesI Create a segment consistent of all consumers with the lowestvalue and the proportion of consumers with all other highervalues such that the monopolist is indi¤erent betweencharging the lowest value and uniform monopoly price
I Then a segment consistent of all remaining consumers withthe second lowest value and the proportion of consumers withall other higher values such that the monopolist is indi¤erentbetween charging the second lowest value and uniformmonopoly price
I And so on...I Charge lowest price in each segment
I Monopolist earns uniform monopoly pro�tI Allocation is e¢ cientI Consumer earns total feasible surplus minus uniform monopolypro�t
![Page 83: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/83.jpg)
An Information Structure Attaining Consumer SurplusMaximizing Segmentation
I Consider a �nite set of valuesI Create a segment consistent of all consumers with the lowestvalue and the proportion of consumers with all other highervalues such that the monopolist is indi¤erent betweencharging the lowest value and uniform monopoly price
I Then a segment consistent of all remaining consumers withthe second lowest value and the proportion of consumers withall other higher values such that the monopolist is indi¤erentbetween charging the second lowest value and uniformmonopoly price
I And so on...I Charge lowest price in each segmentI Monopolist earns uniform monopoly pro�t
I Allocation is e¢ cientI Consumer earns total feasible surplus minus uniform monopolypro�t
![Page 84: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/84.jpg)
An Information Structure Attaining Consumer SurplusMaximizing Segmentation
I Consider a �nite set of valuesI Create a segment consistent of all consumers with the lowestvalue and the proportion of consumers with all other highervalues such that the monopolist is indi¤erent betweencharging the lowest value and uniform monopoly price
I Then a segment consistent of all remaining consumers withthe second lowest value and the proportion of consumers withall other higher values such that the monopolist is indi¤erentbetween charging the second lowest value and uniformmonopoly price
I And so on...I Charge lowest price in each segmentI Monopolist earns uniform monopoly pro�tI Allocation is e¢ cient
I Consumer earns total feasible surplus minus uniform monopolypro�t
![Page 85: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/85.jpg)
An Information Structure Attaining Consumer SurplusMaximizing Segmentation
I Consider a �nite set of valuesI Create a segment consistent of all consumers with the lowestvalue and the proportion of consumers with all other highervalues such that the monopolist is indi¤erent betweencharging the lowest value and uniform monopoly price
I Then a segment consistent of all remaining consumers withthe second lowest value and the proportion of consumers withall other higher values such that the monopolist is indi¤erentbetween charging the second lowest value and uniformmonopoly price
I And so on...I Charge lowest price in each segmentI Monopolist earns uniform monopoly pro�tI Allocation is e¢ cientI Consumer earns total feasible surplus minus uniform monopolypro�t
![Page 86: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/86.jpg)
Application 3: First Price Auction
I Four Cases:
1. Symmetric / Complete Information (Bertrand Competition)2. Independent Private Values3. a few more special cases, e.g., A¢ liated Values4. (this paper) All Information Structures
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A Leading Example
I 2 bidders with private values uniformly distributed on theinterval [0, 1]; bidders know their private values
1. Symmetric Information (Bertrand Competition):I each bidder bids lower valueI revenue is expectation of lower value = 1
3I total e¢ cient surplus is expectation of higher value = 2
3I bidder surplus is 13 (
16 each)
2. No Additional Information = Independent Private Values
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A Leading Example
I 2 bidders with private values uniformly distributed on theinterval [0, 1]; bidders know their private values
1. Symmetric Information (Bertrand Competition):I each bidder bids lower valueI revenue is expectation of lower value = 1
3I total e¢ cient surplus is expectation of higher value = 2
3I bidder surplus is 13 (
16 each)
2. No Additional Information = Independent Private Values
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A Leading Example
I 2 bidders with valuations uniformly distributed on the interval[0, 1]
1. Symmetric Information (Bertrand Competition)
2. Independent Private ValuesI each bidder bids half his valueI revenue equivalence holds....as under complete information orsecond price auction...
I revenue is expectation of low value = 13
I total e¢ cient surplus is expectation of high value = 23
I bidder surplus is 13
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Graphical Representation
0 0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Bidder surplus (U)
Rev
enue
(R)
BNE, NE
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Failure of Revenue (and Surplus) Equivalence: Intuition
I Increase revenue, lower bidder surplus by telling bidders who isthe highest valuation bidder and giving the high valuationbidder partial information about highest loser�s value
I Decrease revenue, increase bidder surplus by maintainingbidder uncertainty about whether they will win and having allconstraints on bidding higher binding (and no constraints onbidding lower)
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Failure of Revenue (and Surplus) Equivalence: Intuition
I Increase revenue, lower bidder surplus by telling bidders who isthe highest valuation bidder and giving the high valuationbidder partial information about highest loser�s value
I Decrease revenue, increase bidder surplus by maintainingbidder uncertainty about whether they will win and having allconstraints on bidding higher binding (and no constraints onbidding lower)
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Failure of Revenue (and Surplus) Equivalence
0 0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Bidder surplus (U)
Rev
enue
(R)
BNE, NE
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Feasibility and Participation Bounds
0 0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Bidder surplus (U)
Rev
enue
(R)
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Two Cases: Known and Unknown Values
I Can assume you know your own value or not
I Lesson 2: more initial information reduces the set of thingsthat can happen
I Obedience constraints even in unknown values caseI More obedience constraints in known values case
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Two Cases: Known and Unknown Values
I Can assume you know your own value or notI Lesson 2: more initial information reduces the set of thingsthat can happen
I Obedience constraints even in unknown values caseI More obedience constraints in known values case
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Two Cases: Known and Unknown Values
I Can assume you know your own value or notI Lesson 2: more initial information reduces the set of thingsthat can happen
I Obedience constraints even in unknown values case
I More obedience constraints in known values case
![Page 98: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/98.jpg)
Two Cases: Known and Unknown Values
I Can assume you know your own value or notI Lesson 2: more initial information reduces the set of thingsthat can happen
I Obedience constraints even in unknown values caseI More obedience constraints in known values case
![Page 99: Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · · 2015-08-04Information Design: Murat Sertel Lecture Istanbul Bilgi University: Conference on Economic](https://reader035.vdocuments.us/reader035/viewer/2022062908/5aebdfaf7f8b9ab24d8f55b6/html5/thumbnails/99.jpg)
Incentive Constraints
0 0.2 0.4 0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Bidder surplus (U)
Rev
enue
(R)
Unknown valuesKnown values
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Application 4: Aggregate Volatility
I Fix an economic environment with aggregate and idiosyncraticshocks
I What information structure generates the most aggregatevolatility?
I In general (symmetric normal) setting, confoundinginformation structure (Lucas (1982))
I Without aggregate uncertainty, intermediate information withcommon shock
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Application 4: Aggregate Volatility
I Fix an economic environment with aggregate and idiosyncraticshocks
I What information structure generates the most aggregatevolatility?
I In general (symmetric normal) setting, confoundinginformation structure (Lucas (1982))
I Without aggregate uncertainty, intermediate information withcommon shock
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Application 4: Aggregate Volatility
I Fix an economic environment with aggregate and idiosyncraticshocks
I What information structure generates the most aggregatevolatility?
I In general (symmetric normal) setting, confoundinginformation structure (Lucas (1982))
I Without aggregate uncertainty, intermediate information withcommon shock
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Leading Example References
I Single player case with no information is leading example inKamenica-Gentzkow (2011)
I Two player two action example with prior informationanalysed in Bergemann-Morris (2015)
I Goldstein and Leitner (2014) develop (rich) stress testapplication
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References
I General Approach:I Bergemann and Morris (2013), Robust Predictions inIncomplete Information Games, Econometrica.
I Bergemann and Morris (2015), Bayes CorrelatedEquilibrium and the Comparison of InformationStructures, forthcoming in Theoretical Economics.
I Applications:I Oligopoly, Ecta paperI Price Discrimination: Bergemann, Brooks and Morris (2015),The Limits of Price Discrimination, American EconomicReview.
I Auctions: Bergemann, Brooks and Morris (2015), Informationin the First Price Auction.
I Volatility: Bergemann, Heumann and Morris (2015),Information and Volatility, forthcoming in JET
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Information Design Recap
I Mechanism Design:I Incentive constraint: truth-tellingI Other constraint: participation
I Information DesignI Incentive constraint: obedienceI Other constraint: prior information