L17 Information Design Literature Discussed papers Kamienica and Genzkow AER 2011 Bergmann and Morris 2017 Genzkow and Kamienica REStud 2017 Other important papers Bergmann and Morris ECMA 2013 TE 2016 ID: 633439
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Slide1
Information Design
Today: basic Bayesian Persuasion
L17Slide2
Information Design Literature
Discussed papers:
Kamienica and Genzkow (AER 2011)Bergmann and Morris (2017)Genzkow and Kamienica (REStud 2017)Other important papers:Bergmann and Morris (ECMA 2013, TE 2016)Mathavet Perego and Taneva (2016) Bergmann Heumann and Morris (JET 2015)Bergmann, Brooks, and Morris (2017)Kolotlin, Mylovanov and Zapechelnyuk
(2015)Slide3
Dynamic Information Design
Papers:
Ely (AER 2017)Ely Frankel and Kamienica (JPE 2015)Doval and Ely (2016)Slide4
Information Design
Economic lessons:
Conditions for (full or partial) information transmissionObfuscation of information (outcome manipulation)Less power to manipulate if R more informed (more precise prior)Many R: Private vs public signals Technical insights:Concavification of value functionTwo stage procedure (feasible outcome =correlated equilibrium)Slide5
Basic Bayesian Persuasion
Two agents: Sender (S) and Receiver (R)
Type space Action space . Message spacePreferences S sends message, , R responds with an actionMessage strategyRelative to cheap talk: S commits to. (no IC for S)Let Solution: strategy Slide6
Senders commitment
Sender
ex ante commits to message strategy to maximize his welfareS ``designs’’ information structure to motivate R (or R’s)Literal information designer (KG 2011):Legal mandate (a prosecutor and a judge)Coarse grading policies Rating agenciesPublic tests of the products (medical drug trials)Metaphorical information designer (mediator)Minimal revenue in auctions (BBM 2017)Maximal volatility of aggregate output (BHM 2017)Welfare outcomes (BBM 2017)Slide7
Example 1: Persuasion in a quadratic model
State space
Preferences:Fix Best response of R Ex ante welfare of SOptimal persuasion rule:Remarks:Relative to optimal rule for R?Problem more interesting with type independent preferencesSlide8
Example 2: KG example
Story: prosecutor S and judge R
Binary model PreferencesBeliefsExpected R utility given beliefsOptimal R choiceExpected utility as a function of beliefs (no persuasion)Slide9
Example 2: KG example
Value
funcionSlide10
Set of Bayes plausible (distributions of) posteriors
Aumann
and Mashler (1995) Messages split a prior into ``random’’ posteriors induces posteriors is Bayes plausible given if induced by some set of all Bayes plausible posteriorsP: if and only if Proof Equivalent optimization problem Slide11
Concavification
of value function
Value function of the persuasion programP: Value function coincides with concave closure of . on Implication: is concaveSlide12
Insight 1
Given prior , S benefits from transmission of information
iff Concave for all beliefs No transmission of information Example: Convex only at the degenerate beliefsFull transition of informationExampleExample