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Flashcards in Information Deck (27)
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1
Q

[Reversed]

Good sellers trying to distinguish themselves from bad ones. Single seller context, only allowed to make truthful disclosures –> How much truth will they tell?

Case 1: ex-post verifiable, warranties eg. diamond weight

  • Less than full disclosure makes rational expectations belief worse possible trader

Case 2: ex-post non-verifiable, car quality…can see if it breaks down but not if the brake pads are dodgy!

  • Warranties less than full must signal consumer would be mistaken to purchase
  • Sharper conjectures than the signalling model, requiring consumers to have some information on warranty and quality relationship –> Consumers here cannot invert contract and find quality
  • Similar to optimal contracting, information rent story, “skim the cream” deviations etc.
  • No moral hazards on the consumer side is key assumption –> We dont tamper with the car as consumers

Struggle to extend to many type examples.

A

Grossman (1981)

2
Q

[Reversed]

Finanical market information strategic incentives between sender and receiver, usually sender has some vested interest.

  • Negative disclosures increase return variance –> Driving negative serial correlation of asset returns
  • Earnings season reports susceptible to influence, Whisper numbers circulate before that create expectations

Model: explains how uncertainty is resolved over time via public information disclosures from self interested disclosures

  • Interested party (Manager) and sophisticated traders in a game
  • M: well informed, wants to max. stock price, mandated reports which must contain verifiable evidence eg. accounts
  • T: discount reports given info asymmetry, places trades det. price
  • Binomial tree of up and down across many firm projects
  • Three dates: initial, interim, final –> some project outcomes realised at interim and some at final giving asymmetry in info at interim stage
  • Free to disclose some or all of what is known at any time with evidence - no false evidence allowed
  • Sequential eq*

Results: uncertainty increases during a crises, absence of news seen as bad news

  1. No full disclosure
  2. “Sanitization strategy” removing bad news –> similar intuition to pricing a compund lottery, option pricing
  3. Market responds putting all weight on bad outcomes when manager is well informed about all projects –> “Unravelling result”.
  4. Escape unravelling by imperfectly informed managers about projects
A

Shin (2003) [Etca]

3
Q

Mathevet, Perego and Taneva (2020)

A

Information provision in games distorts beliefs about the state but also higher order beliefs.

  • Characterise feasible belief distributions which are constrained ie. Bayes plausible, consistent with each other if many agents
  • Two step approach to finding optimal information structures, second step is the concavification –> First step optimises over only basic elements
    • 1: Optimise over private info
    • 2: Now incorporate public signal
  • Expand equivalend of K&G (2011) single agent setup to a “game” setup with consistency of belifs between players

Designer beliefs can be thought of as like the entire set of higher order beliefs, more informed than any given agent.

  • BP of each agent does not imply consistency
  • Consistency can be thought of as BP as designer level
  • Designer beleif should be same as any agents, if agent knew all other’s info
4
Q

Milgrom and Weber (1982)

A

Theory of auctions and competitive bidding:

  • Ascending auction generates higher average prices than second price sealed bid
  • Seller can raise expected price in many auction formats by providing expert appraisals on object quality
  • IPV model + appraisal impact resale value for example, hence impacting actual value to each bidder
  • No reporting can be better than always reporting
  • Revealing information adds an additiona link from player values to the price –> Raising expected prices
5
Q

Summary of Dan Topics:

A
  • Persuading one receiver –> No Type II errors
  • Persuading multiple receivers –> Type II errors useful
  • Private information can do better
  • Appel to Jensen’s inequality in Persuasion answers!
6
Q

[Reversed]

Theory of auctions and competitive bidding:

  • Ascending auction generates higher average prices than second price sealed bid
  • Seller can raise expected price in many auction formats by providing expert appraisals on object quality
  • IPV model + appraisal impact resale value for example, hence impacting actual value to each bidder
  • No reporting can be better than always reporting
  • Revealing information adds an additiona link from player values to the price –> Raising expected prices
A

Milgrom and Weber (1982)

7
Q

Summary of Dan Topics:

A
  • Persuading one receiver –> No Type II errors
  • Persuading multiple receivers –> Type II errors useful
  • Private information can do better
  • Appel to Jensen’s inequality in Persuasion answers!
8
Q

Kamenica and Gentzkow (2011) [AER]

A

Bayesian Persuation: can an informed sender succesfully persuade a receiver to change her action? eg. prosecutor provide evidence to a judge, lobbyist makes case to politician, car sales person to a customer –> split cutsomers into those that should not buy and those that are just convinced, gain credibility my being frank boosting WTP of indifferent consumers.

Model:

  • Sender chooses an informative signal about state which is known to S
  • R makes decisions based on posteriors from signals
  • Still some misalignment of payoffs
  • Sender preferred SGPNE

Assumptions:

  1. Strong commitment to signal structure –> conduct an investigation, Set of eq* coincides with a relaxation allowing some concealing if still verifiable.
  2. Symmetric information setting
  3. Prior –> Judge will always acquit, customer never buys etc.
  4. S cannot distort or conceal information –> abstract from IC issues
  5. Posterior distribution must be “bayes plausible” –> sum to the prior

Results:

  • Can focus entirely on posterior beleifs following Bayes’ rule for optimal signal structure –> subject to expected posterior = prior
  • Sender benefits from persuasion if
    • R action NOT linear in beliefs –> action must be constant in some neighborhood around the prior
    • Prior is unfavourable –> “dont preach to the converted”
  • S payoff concave in R beliefs ==> No disclosure optimal
  • S payoff convex in R belifes ==> Full disclosure optimal
    • Results depend upon whether there exists a set of beliefs with E[v(u)] > v(E[u]) linked to curvature!
  • Asymmetry in R uncertainty when choosing preferred and disliked action –> certain on disliked, perfectly unsure on preferred!
  • More aligned preferences can reduce eq* communication - opposite to cheap talk, but both directions happen
  • Concavification = “concave closure” of the indirect sender payoff function dependent upon R posterior beliefs –> this captures optimal information structure expected payoff
  • Want to maximise the height of the chord above the prior –> Bayes plausbility implies have to choose signal structure giving posterior mix above and below

Appeal to Jensen’s inequality in answers!

Convex: f(E[X]) < E[f(x)] –> f(u0) < E[f(u)] –> Like risk, randomise over posterior lottery

Concave: f(E[X]) > E[f(x)] –> f(u0) > E[f(u)] –> Dont like risk, don’t randomise

9
Q

Dye (1985)

A

Withholding nonproprietary information is puzzling, basic adverse selection argument.

  • In practice prices do not cascade down to 0 due to lack of disclosure, the disclosure principle does not hold…Why?
    1. Manager info may not be verifiable
    2. Tensions between managers and traders discourage info release
    3. Direct or indirect cost to disclose
    4. Investors uncertain about presence of information
    5. Compensation could be independent of disclosures
  • Two deviations considered in the paper: (i) investors unaware whether manger has info, and (ii) release affects firm future earnings only through effect on compensation

Distinctions arise in the amount of information disclosed across markets, depends upon investors knowledge on information and relative proprietary/non-proprietary information splits. Princiapl agent problem also arises between shareholders and managers.

10
Q

[Reversed]

Bayesian Persuation: can an informed sender succesfully persuade a receiver to change her action? eg. prosecutor provide evidence to a judge, lobbyist makes case to politician, car sales person to a customer –> split cutsomers into those that should not buy and those that are just convinced, gain credibility my being frank boosting WTP of indifferent consumers.

Model:

  • Sender chooses an informative signal about state which is known to S
  • R makes decisions based on posteriors from signals
  • Still some misalignment of payoffs
  • Sender preferred SGPNE

Assumptions:

  1. Strong commitment to signal structure –> conduct an investigation, Set of eq* coincides with a relaxation allowing some concealing if still verifiable.
  2. Symmetric information setting
  3. Prior –> Judge will always acquit, customer never buys etc.
  4. S cannot distort or conceal information –> abstract from IC issues
  5. Posterior distribution must be “bayes plausible” –> sum to the prior

Results:

  • Can focus entirely on posterior beleifs following Bayes’ rule for optimal signal structure –> subject to expected posterior = prior
  • Sender benefits from persuasion if
    • R action NOT linear in beliefs –> action must be constant in some neighborhood around the prior
    • Prior is unfavourable –> “dont preach to the converted”
  • S payoff concave in R beliefs ==> No disclosure optimal
  • S payoff convex in R belifes ==> Full disclosure optimal
    • Results depend upon whether there exists a set of beliefs with E[v(u)] > v(E[u]) linked to curvature!
  • Asymmetry in R uncertainty when choosing preferred and disliked action –> certain on disliked, perfectly unsure on preferred!
  • More aligned preferences can reduce eq* communication - opposite to cheap talk, but both directions happen
  • Concavification = “concave closure” of the indirect sender payoff function dependent upon R posterior beliefs –> this captures optimal information structure expected payoff
  • Want to maximise the height of the chord above the prior –> Bayes plausbility implies have to choose signal structure giving posterior mix above and below
A

Kamenica and Gentzkow (2011) [AER]

11
Q

[Reversed]

Information provision in games distorts beliefs about the state but also higher order beliefs.

  • Characterise feasible belief distributions which are constrained ie. Bayes plausible, consistent with each other if many agents
  • Two step approach to finding optimal information structures, second step is the concavification –> First step optimises over only basic elements
    • 1: Optimise over private info
    • 2: Now incorporate public signal
  • Expand equivalend of K&G (2011) single agent setup to a “game” setup with consistency of belifs between players

Designer beliefs can be thought of as like the entire set of higher order beliefs, more informed than any given agent.

  • BP of each agent does not imply consistency
  • Consistency can be thought of as BP as designer level
  • Designer beleif should be same as any agents, if agent knew all other’s info
A

Mathevet, Perego and Taneva (2020)

12
Q

[Reversed]

Withholding nonproprietary information is puzzling, basic adverse selection argument.

  • In practice prices do not cascade down to 0 due to lack of disclosure, the disclosure principle does not hold…Why?
    1. Manager info may not be verifiable
    2. Tensions between managers and traders discourage info release
    3. Direct or indirect cost to disclose
    4. Investors uncertain about presence of information
    5. Compensation could be independent of disclosures
  • Two deviations considered in the paper: (i) investors unaware whether manger has info, and (ii) release affects firm future earnings only through effect on compensation

Distinctions arise in the amount of information disclosed across markets, depends upon investors knowledge on information and relative proprietary/non-proprietary information splits. Princiapl agent problem also arises between shareholders and managers.

A

Dye (1985)

13
Q

[Reversed]

Costly persuasion menas concavification approach is not generally feasible since payoff not fully det. by posterior belief.

Model: introduce a family of cost functions compatible with concavification

  • Finite space of states, signal is a prob. dist over them
  • Signals are costly
  • Priors
  • Sender and Receiver as standard, commit to information design
  • Cost of a signal is proportional to expected reduction in uncertainty relative to some fixed reference belief eg. entropy or residual variance

Results: still concavification, except now it is a value function over the belief adjusted for the cost of inducing such a posterior

  • Example in Convict / Acquit setting where cost of investigation is entropy evaluated at 50/50 posterior being induced
  • Costs reduce the likelihood of conviction since proof of innocence has become prohibitvely costly.
  • Excessive costs –> Optimal to conduct uninformative investigation
  • Costts rising –> Lower sender payoff, but receivers payoff can go up or down
A

Gentzkow and Kamenica (2014) [AER]

14
Q

Gentzkow and Kamenica (2014) [AER]

A

Costly persuasion menas concavification approach is not generally feasible since payoff not fully det. by posterior belief.

Model: introduce a family of cost functions compatible with concavification

  • Finite space of states, signal is a prob. dist over them
  • Signals are costly
  • Priors
  • Sender and Receiver as standard, commit to information design
  • Cost of a signal is proportional to expected reduction in uncertainty relative to some fixed reference belief eg. entropy or residual variance

Results: still concavification, except now it is a value function over the belief adjusted for the cost of inducing such a posterior

  • Example in Convict / Acquit setting where cost of investigation is entropy evaluated at 50/50 posterior being induced
  • Costs reduce the likelihood of conviction since proof of innocence has become prohibitvely costly.
  • Excessive costs –> Optimal to conduct uninformative investigation
  • Costts rising –> Lower sender payoff, but receivers payoff can go up or down
15
Q

Shin (2003) [Etca]

A

Finanical market information strategic incentives between sender and receiver, usually sender has some vested interest.

  • Negative disclosures increase return variance –> Driving negative serial correlation of asset returns
  • Earnings season reports susceptible to influence, Whisper numbers circulate before that create expectations

Model: explains how uncertainty is resolved over time via public information disclosures from self interested disclosures

  • Interested party (Manager) and sophisticated traders in a game
  • M: well informed, wants to max. stock price, mandated reports which must contain verifiable evidence eg. accounts
  • T: discount reports given info asymmetry, places trades det. price
  • Binomial tree of up and down across many firm projects
  • Three dates: initial, interim, final –> some project outcomes realised at interim and some at final giving asymmetry in info at interim stage
  • Free to disclose some or all of what is known at any time with evidence - no false evidence allowed
  • Sequential eq*

Results: uncertainty increases during a crises, absence of news seen as bad news

  1. No full disclosure
  2. “Sanitization strategy” removing bad news –> similar intuition to pricing a compund lottery, option pricing
  3. Market responds putting all weight on bad outcomes when manager is well informed about all projects –> “Unravelling result”.
  4. Escape unravelling by imperfectly informed managers about projects
16
Q

Milgrom (1981)

A

Introduce monotonicity into informational economics models to help model “good news”

Results: in application games developed about security markets, incentivising effort, persuasion

  1. Good news about a firm future returns always increases price
  2. More favourable news increases manager bonuses –> High profits indicate high effort
  3. Any information witheld must be damaging –> Hence, best strategies feature full disclosure
  4. Low bids signal low value –> Winner’s curse
  • Monotonicity has a key role in many economic models
  • Propose general theorems and definitions of “(Strict) Monotone likelihood ratio property”
17
Q

Crawford and Sobel (1982) [Etca]

A

Cheap Talk: quadratic loss but model is more general

Sender faces trade off between including enough information to induce R’s response, but also holding back enough info to make R response as favourable as possible.

Model:

  • Privately informed sender, sends a signal to a receiver
  • Receiver takes action determining welfare
  • Some misalignment of incentives in payoffs - “bias”

Assumptions:

  1. No commitment here, R cannot pre-commit like in principal agent problems –> No revelation principle here.
  2. BNE is solution concept
  3. No such signalling costs as in Spence, “talk is cheap” –> R’s action rule creates some endogenous signal costs
  4. Learn types before signalling

Results:

  • Set of BNE is always a partitioned set, introducing noise into the signal
  • Welfare improves as more informative eq*, also as payoff wedge shrinks –> Quadratic loss, more informative means less large mistakes minimising variance
  • Babbling equilibrium always exists
  • There exists at least one equilibrium of all message sizes upto max N*(b)
  • Any bias ==> No perfect information equilibrium!
  • Unravelleing result, as soon as some high types get pooled with lower types they are better to reveal themselves.
  • Iterative change of bids +b, +2b, +3b for why a perfectly revelaing eq* cant exist when b > 0
  • More uncertainty on the high signal side (biased side), larger intervals by 4b
  • Threshold types are indifferent between messages either side
  • Different sender types generally prefer different K message eq*
  • Commitment to tell the truth would actually benefit S, not possible here due to enforcement issues
18
Q

[Reversed]

Cheap Talk: quadratic loss but model is more general

Sender faces trade off between including enough information to induce R’s response, but also holding back enough info to make R response as favourable as possible.

Model:

  • Privately informed sender, sends a signal to a receiver
  • Receiver takes action determining welfare
  • Some misalignment of incentives in payoffs - “bias”

Assumptions:

  1. No commitment here, R cannot pre-commit like in principal agent problems –> No revelation principle here.
  2. BNE is solution concept
  3. No such signalling costs as in Spence, “talk is cheap” –> R’s action rule creates some endogenous signal costs
  4. Learn types before signalling

Results:

  • Set of BNE is always a partitioned set, introducing noise into the signal
  • Welfare improves as more informative eq*, also as payoff wedge shrinks –> Quadratic loss, more informative means less large mistakes minimising variance
  • Babbling equilibrium always exists
  • There exists at least one equilibrium of all message sizes upto max N*(b)
  • Any bias ==> No perfect information equilibrium!
  • Unravelleing result, as soon as some high types get pooled with lower types they are better to reveal themselves.
  • Iterative change of bids +b, +2b, +3b for why a perfectly revelaing eq* cant exist when b > 0
  • More uncertainty on the high signal side (biased side), larger intervals by 4b
  • Threshold types are indifferent between messages either side
  • Different sender types generally prefer different K message eq*
  • Commitment to tell the truth would actually benefit S, not possible here due to enforcement issues
A

Crawford and Sobel (1982) [Etca]

19
Q

Kolotilin et. al (2017)

A

Costly Persuation: linear environments, can the sender benefit from designing a complex persuasion mechanism conditioning on receiver type reports?

Model:

  • Linear payoffs to both, dep. on state and R type
  • Private type receiver, choosing between two actions
  • Sender designs persuasion mechanism or experiment about payoff relevant state
    • Mechanism: condition info on R type report
    • Experiement: disclose info independent of R type

Assumptions:

  1. Sender uninformed about R preferences
  2. R knows type but unsure on world state
  3. S can only provide info, no transfers –> S can only ask R to report type
  4. S commits to a mechanism / experiment: report R type, returna stochastic message dep. on state and report
  5. State and type independent, both on real line

Results:

  • Equivalence: persuasion mechanism = experiment –> comes from linearity implying only posterior mean matters
  • Consider the set of IC mechanisms inducing truthful reporting
  • Experiment is just one sided message transmission S –> R
  • Mechanism = menu of experiments…but here menu is irrelevant!

Extensions:

  • Linearity - Can extend beyond linearity in type..linear in a transformation, but cannot extend beyond linearity in the state!
  • Binary actions - cannot extend exactly, obedience constraints impose additional conditions for implementability and more outcomes feasible under persuasion mechanisms but not experiments
20
Q

Grossman (1981)

Milgrom (1981)

A

Must tell the truth but no the whole truth

21
Q

Grossman (1981)

A

Good sellers trying to distinguish themselves from bad ones. Single seller context, only allowed to make truthful disclosures –> How much truth will they tell?

Case 1: ex-post verifiable, warranties eg. diamond weight

  • Less than full disclosure makes rational expectations belief worse possible trader

Case 2: ex-post non-verifiable, car quality…can see if it breaks down but not if the brake pads are dodgy!

  • Warranties less than full must signal consumer would be mistaken to purchase
  • Sharper conjectures than the signalling model, requiring consumers to have some information on warranty and quality relationship –> Consumers here cannot invert contract and find quality
  • Similar to optimal contracting, information rent story, “skim the cream” deviations etc.
  • No moral hazards on the consumer side is key assumption –> We dont tamper with the car as consumers

Struggle to extend to many type examples.

22
Q

[Reversed]

Attempt at interim Bayesian persuasion.

Model: not a sender committing before learning type, commit after learning type

  • Low and High types of sender, seeking validation by choosing an info system
  • Receiver only wants to validate High
  • Solution concept is PBE
  • Sender learns type –> Commit to info design –> Receiver learns and takes action

Results: WLOG to focus entirely on pooling equilibria. Three refinements get the set of eq* to high type optimal equilibria

  1. Version of undefeated eq* from signalling –> deviations interpreted as coming from a type that benefits under eq* of deviation
  2. Adaptation of the “core” –>
  3. Perfect sequential eq* strengthened
  • PBE weak if no perfect revelation
  • Any outcome can be supported as polling
  • Anyd eviation attractive to H will also be attractive to L,
A

Perez-Richet (2014)

23
Q

Perez-Richet (2014)

A

Attempt at interim Bayesian persuasion.

Model: not a sender committing before learning type, commit after learning type

  • Low and High types of sender, seeking validation by choosing an info system
  • Receiver only wants to validate High
  • Solution concept is PBE
  • Sender learns type –> Commit to info design –> Receiver learns and takes action

Results: WLOG to focus entirely on pooling equilibria. Three refinements get the set of eq* to high type optimal equilibria

  1. Version of undefeated eq* from signalling –> deviations interpreted as coming from a type that benefits under eq* of deviation
  2. Adaptation of the “core” –>
  3. Perfect sequential eq* strengthened
  • PBE weak if no perfect revelation
  • Any outcome can be supported as polling
  • Anyd eviation attractive to H will also be attractive to L,
24
Q

[Reversed]

Costly Persuation: linear environments, can the sender benefit from designing a complex persuasion mechanism conditioning on receiver type reports?

Model:

  • Linear payoffs to both, dep. on state and R type
  • Private type receiver, choosing between two actions
  • Sender designs persuasion mechanism or experiment about payoff relevant state
    • Mechanism: condition info on R type report
    • Experiement: disclose info independent of R type

Assumptions:

  1. Sender uninformed about R preferences
  2. R knows type but unsure on world state
  3. S can only provide info, no transfers –> S can only ask R to report type
  4. S commits to a mechanism / experiment: report R type, returna stochastic message dep. on state and report
  5. State and type independent, both on real line

Results:

  • Equivalence: persuasion mechanism = experiment –> comes from linearity implying only posterior mean matters
  • Consider the set of IC mechanisms inducing truthful reporting
  • Experiment is just one sided message transmission S –> R
  • Mechanism = menu of experiments…but here menu is irrelevant!

Extensions:

  • Linearity - Can extend beyond linearity in type..linear in a transformation, but cannot extend beyond linearity in the state!
  • Binary actions - cannot extend exactly, obedience constraints impose additional conditions for implementability and more outcomes feasible under persuasion mechanisms but not experiments
A

Kolotilin et. al (2017)

25
Q

Summary of Dan Topics:

A
  • Persuading one receiver –> No Type II errors
  • Persuading multiple receivers –> Type II errors useful
    • Private information can do better
  • Appel to Jensen’s inequality in Persuasion answers!
26
Q

[Reversed]

Introduce monotonicity into informational economics models to help model “good news”

Results: in application games developed about security markets, incentivising effort, persuasion

  1. Good news about a firm future returns always increases price
  2. More favourable news increases manager bonuses –> High profits indicate high effort
  3. Any information witheld must be damaging –> Hence, best strategies feature full disclosure
  4. Low bids signal low value –> Winner’s curse
  • Monotonicity has a key role in many economic models
  • Propose general theorems and definitions of “(Strict) Monotone likelihood ratio property”
A

Milgrom (1981)

27
Q

[Reversed]

Must tell the truth but no the whole truth

A

Grossman (1981)

Milgrom (1981)