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

2. Glazer and Rubinstein 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. L-principle Assume Consider any three types forming ``L’’
For any mechanism the sum of mistake probabilities is
``Mass of independent ``Ls’’ gives a lower bound for the number of mistakes
Easy check of mechanism optimality

5. Examples Examples - Optimal deterministic mechanism
- Optimal bubbling mechanism
- Optimal stochastic mechanism
We consider finite problems with uniform distributions
Number of mistakes

6. Direct deterministic mechanism
Let
Number of independent L’s?
Mechanism: Accept only if for at least one

7. No verification Let Number of independent L’s?
Mechanism: reject regardless of message

8. Stochastic vs deterministic mechanism
Let
Consider three L’s
Mechanism: Ask for two highest aspects, verify them with probability 0.5.

9. Definitions Direct mechanism Conservative direct mechanism
Observation: Direct mechanism need not be truthful

10. Auxiliary result Consider a problem
P1: There exist optimal mechanism for which vector solves
C: is optimal iff implied solves
Structure of the proof
Byproduct: exists optimal mechanism that is direct and conservative.

11. Properties of

12. Proof

13. Proof