1. Disclosure (Persuasion) games
Verifiable Signals
L11
Disclosure (Persuasion) games

2. Papers Milgrom (JEP 2007) Shin (ECMA 2002)
Glazer and Rubinstein (ECMA 2004), (TE 2006),
Dziuda (JET 2011)
Literature on market design

3. Information Transmission in Markets
Cheap Talk literature derives language endogenously (in equilibrium)
In markets
- meaning of messages already established (quality, emissions level etc.)
- conditional on a state, statements are either true and false
- legal/institutional framework prevents false statements
True reports need not be complete or detailed

4. Basic Persuasion Game One Sender and one Receiver
Timing and actions (no commitment):
Sender observes state , , sends message
Receiver observes messages , choses action
Preferences:
Sender: type independent
Receiver: supermodular
Exogenous language: message space
Verifiable signals (alternative interpretation)
Type dependent message space
Infinite cost of lying
Latter interpretation: a special case of signaling game (a’la Spence)

5. Example: A seller and a buyer
A drug seller (S) and a hospital (R).
quality of a drug (survival rate after treatment )
message space = statements ``survival rate is at least ’’
Hospital (R) demand is
Seller (S) maximizes quantity
If , seller goes to jail forever (and everyone knows it).

6. PBN Equilibrium Strategies: Sender Receiver Posterior
D: Equilibrium s.t. 1. 2. 3.

7. Bubbling equilibrium?

8. Refinements for signaling gAmes
Many refinements: Intuitive, Devine criterions
Weakest: Strict dominance criterion
For type message is dominated by if
for any type let
``Reasonable’’ (off equilibrium) beliefs satisfy
Set of refined PBN equilibria in signaling game set of PBN in a simplified game with state dependent strategy space
Persuasion game

9. Unraveling of information
Equilibrium is fully revealing if
P: Every dominance refined PBN is fully revealing
C: Every PBN equilibrium in a game with type dependent message space is fully revealing
Benchmark result

10. Proof

11. Proof

12. Unraveling of information
Multiplicity of (outcome equivalent) equilibria
Unraveling of information from the top
Extreme receiver ‘s skepticism
Normative implications:
Efficient outcome
No room for market regulation