1. Intro to Information Design (and some Basic Bayesian Persuasion)L7

2. General information Design
Two agents: Sender (S) (designer) and Receivers (R)
Type space Action space Message space
Preferences
S message strategy
Relative to cheap talk: S
commits to information structure
objective: ex ante welfare of S
Players (R), strategies and payoffs, along with define Bayesian game
Each BN equilibrium generates unique decision rule
Let be a set of equilibrium decision rules in game
Solution concept

3. Remarks Problem can be easily accommodated
Adversarial (robust) approach
Harder, no revelation principle
Gains popularity recently
Alternative: receivers with private information
Bayesian persuasion problem is a (very) special case
One receiver
Max max criterion
S no private information
Type independent preferences of S

4. Big picture
Cheap talk: no commitment power, S and R maximizes ex post welfare
Mechanism design (Arbitration)
Single receiver (designer), potentially many senders
Commitment by R
R maximizes ex ante welfare, S welfare ex post
Information design (Bayesian Persuasion)
Single sender, potentially many receivers
Commitment by S
S maximizes ex ante welfare, R welfare ex post (with respect to posterior)
General mechanism design (Myerson 82)

5. Senders commitment
Sender ex ante commits to message strategy, maximizes ex ante welfare
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
Minimal revenue in auctions (BBM 2017)
Maximal volatility of aggregate output (BHM 2017)
Welfare outcomes (BBM 2017)

6. Main lessons Substantive Insights :
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)

7. 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)

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

9. Bayesian persuasion Two agents: Sender (S) and Receiver (R)
Type space Action space Message space
Preferences
Timing
(1) S commits to experiment
(2) S observes type, sends message according to distribution
(3) R observes message choses action
Let
Solution: strategy

10. Example 1: Persuasion in a quadratic model
State space
Preferences:
Fix
Best response of R
Ex ante welfare of S
Optimal persuasion rule:

11. Example 1: Persuasion in a quadratic model
Relative to cheap talk:
- No multiplicity of equilibria
- S could commit to ``bubbling’’ but in this example it is suboptimal
Relative to Arbitration (Mechanism Design)
- Commitment benefits more the side that cannot commit
Problem more interesting with type independent preferences of S

12. Example 2: KG example Story: prosecutor S and judge R Binary model
Preferences
Cheap talk prediction?

13. Beliefs and expected utility of S
Fix R beliefs over types
Expected R utility given beliefs
R best response given
Expected utility as a function of beliefs (no persuasion)
Think of S as manipulating ex post beliefs

14. Example 2: KG example
Value function

15. Information structures
Value function

16. Information structures
Value function