1. Partly Verifiable Signals (c.n.)
Glazer and Rubinstein (ECMA 2004)
Glazer and Rubinstein (TE 2006)

2. Persuasion game State space finite with aspect Action space
Sender always prefers
Acceptance and rejection region
Verification mechanism

3. Preferences over Verification Mechanism
Fix
Let
R preferences over verification mechanisms
Type one error Type two error
Optimal mechanism solves

4. Auxiliary result Consider a problem
P1: For any solution there exist optimal mechanism for which
C: is optimal iff implied solves
Optimal mechanism: direct, conservative with
Result holds for arbitrary objective function increasing in each component

5. Characterization Linear program has simple structure
Domain: Convex polytope
Set of extreme points is finite
At least one extreme point is a solution
With more than one extreme point, any convex combination is also a solution
Alon (2003): Any extreme point takes a form

6. Main Result Linear programming: strong structure with extreme points
``Fair coin’’ mechanism:
P2: There exist an optimal mechanism that uses fair coin randomization
Result dramatically simplifies search for an optimal mechanism
Number of checks

7. Intuition
Example
Glazer and Rubinstein give example with

8. Deterministic Mechanism
Definition:
Example 1: optimal mechanism is deterministic
Example 2: Deterministic mechanism is not optimal
General conditions under which deterministic mechanism is optimal?
Alternative interpretation of deterministic SR model.

9. Result Assume: with uniform distribution is monotonic
closed convex and non-empty
P: There exists an optimal mechanism that is direct and deterministic.

10. Heuristic proof
Deterministic mechanism characterized by ``persuasive facts’’
For mechanism accepts iff
Parametric class of deterministic mechanisms
Sketch of the proof
the mechanism exists (within the restricted class)
necessary conditions for
the mechanism attains lower bound given by L priciple

11. Heuristic proof
Necessary optimality conditions for thresholds

12. Geometry of errors
L-principle

13. Credibility So far we have assumed commitment
Outcome of can be implemented as PBN in a sequential SR game
Construction of equilibrium uses solution to a dual problem

14. Related questions How large is the set of optimal mechanisms?
What are Pareto undominated ones?
Consider objective function
How the set of optimal mechanisms changes with
Non-linear objective functions?