Information Design: Murat Sertel Lecture - Home | …smorris/pdfs/Sertel.pdf · ·...

Information Design: Murat Sertel LectureIstanbul Bilgi University: Conference on Economic Design

Stephen Morris

July 2015

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

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

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)

I Linkage Principle: Milgrom-Weber (1982)

I Information Sharing in Oligopoly: Novshek and Sonnenschein(1982)

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

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

I Probability of run is 1

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

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

Run (bad signal) 0 13

I Think of the regulator as a mediator making an actionrecommendation to the depositor subject to an obedienceconstraint

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

Lessons

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

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

already have observed a signal tG saying that the state is goodI Outcome distribution with no additional information:

6 0 0Run 0 1

already have observed a signal tG saying that the state is goodI Outcome distribution with no additional information:

6 0 0Run 0 1

Optimal Information Design with one depositor with initialinformation

Run 0 0 12

Optimal Information Design with one depositor with initialinformation

Run 0 0 12

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

Lessons

2. Prior information limits the scope for information design

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

I Outcome distribution with no information

outcome θG Stay RunStay 0 0Run 0 1

outcome θB Stay RunStay 0 0Run 0 2

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

I ...with public signals optimal

3 0Run 0 0

3 0Run 0 1

3 0Run 0 0

3 0Run 0 1

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

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 Outcome distribution with no information: mixed strategyequilibrium

3 0Run 0 0

Run 19 0

I ....with private signals optimal

3 0Run 0 0

Run 19 0

3 0Run 0 0

Run 19 0

Lessons

2. Prior information limits the scope for information design

3. Public signals optimal if strategic complementarities; privatesignals optimal if strategic substitutes

Bank Run: two depositors with initial information

have also analyzed elsewhere....

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

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

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

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")

I How much revenue could a monopolist producer/seller get?I If the seller cannot discriminate between consumers, he mustcharge uniform monopoly price

The Uniform Price Monopoly

0Consumer surplus

No information

I producer charges (uniform) monopoly priceI consumers get positive consumer surplus, socially ine¢ cientallocation

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�

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�

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�

First Degree Price Discrimination

0Consumer surplus

Complete information

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

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

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

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

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

Three Welfare Bounds

1. Voluntary Participation: Consumer Surplus is at least zero

Welfare Bounds: Voluntary Participation

0Consumer surplus

Consumer surplus is at least zero

2. Non-negative Value of Information: Producer Surplusbounded below by uniform monopoly pro�ts π�

Welfare Bounds: Nonnegative Value of Information

0Consumer surplus

Producer gets at least uniform price profit

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

Welfare Bounds: Social Surplus

0Consumer surplus

Total surplus is bounded by efficient outcome

Beyond Welfare Bounds

1. Includes points corresponding uniform price monopoly,(u�,π�), and perfect price discrimination, (0,w �)

2. Convex

Welfare Bounds and Convexity1. Includes points corresponding uniform price monopoly,(u�,π�), and perfect price discrimination, (0,w �)

2. Convex

0Consumer surplus

What is the feasible surplus set?

Welfare Bounds are Sharp

0Consumer surplus

Main result

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.

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

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 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

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

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

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

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

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

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

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

Graphical Representation

0 0.2 0.4 0.6

Bidder surplus (U)

BNE, NE

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)

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)

Failure of Revenue (and Surplus) Equivalence

0 0.2 0.4 0.6

Bidder surplus (U)

BNE, NE

Feasibility and Participation Bounds

0 0.2 0.4 0.6

Bidder surplus (U)

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

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

Incentive Constraints

0 0.2 0.4 0.6

Bidder surplus (U)

Unknown valuesKnown values

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

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

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

Information Design Recap

I Mechanism Design:I Incentive constraint: truth-tellingI Other constraint: participation

I Information DesignI Incentive constraint: obedienceI Other constraint: prior information

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