1. Today: basic Bayesian Persuasion
Information Design
L17
Today: basic Bayesian Persuasion

2. 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)

3. Dynamic Information Design
Papers:
Ely (AER 2017)
Ely Frankel and Kamienica (JPE 2015)
Doval and Ely (2016)

4. Information Design Economic lessons:
Conditions for (full or partial) information transmission
Obfuscation 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 function
Two stage procedure (feasible outcome =correlated equilibrium)

5. Basic Bayesian Persuasion
Two agents: Sender (S) and Receiver (R)
Type space Action space Message space
Preferences
S sends message, , R responds with an action
Message strategy
Relative to cheap talk: S commits to (no IC for S)
Let
Solution: strategy

6. Senders commitment
Sender ex ante commits to message strategy to maximize his welfare
S ``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 agencies
Public 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)

7. Example 1: Persuasion in a quadratic model
State space
Preferences:
Fix
Best response of R
Ex ante welfare of S
Optimal persuasion rule:
Remarks:
Relative to optimal rule for R?
Problem more interesting with type independent preferences

8. Example 2: KG example Story: prosecutor S and judge R Binary model
Preferences
Beliefs
Expected R utility given beliefs
Optimal R choice
Expected utility as a function of beliefs (no persuasion)

9. Example 2: KG example
Value funcion

10. 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 posteriors
P: if and only if
Proof
Equivalent optimization problem

11. Concavification of value function
Value function of the persuasion program
P: Value function coincides with concave closure of on
Implication: is concave

12. 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 beliefs
Full transition of information
Example