1. Pragmatics of Persuasion
L15
Glazer and Rubinstein (TE 2006)
A study in the pragmatics of persuasion : a game theoretic approach.

2. Setup Today Sender choses which verified fact to reveal
Sender has limited capacity to verify facts
Receiver choses their interpretation
Optimal interpretation rule depends on S incentives
Pragmatics: A field of linguistics
Interpretation of utterances depends on the context
Cooperative principle (Grice 1989) requires aligned preferences
Noncooperative approach Benz at al. (2006)

3. A persuasion game Finite state space Action space
Sender always prefers
Acceptance and rejection region
(Arbitrary) type dependent message structure
Persuasion rule
Rule is deterministic if
Rule is finite if

4. Optimal persuasion rule
For probability of acceptance
Let
Optimal mechanism solves
Relative to Glazer and Rubinstein (2006):
S controls which verified facts are revealed
Random decision rule
Abstract (possibly infinite) type dependent message space

5. Milgrom’s message structure
Assume
Cheap talk with type independent preferences
Trivial optimal rule
Variant of Milgrom’s persuasion game
In any PBN equilibrium unraveling of information
Trivial optimal persuasion rule:
Problem interesting when high types cannot verify that they are high
Example: Vectoric message structure

6. Example Let Acceptance region
Vectoric message structure, capacity two aspects
Rule 1: Accept if any two aspects are verified
Rule 2: Accept if any to neighboring aspects are verified

7. 3 sets of results Randomization is not needed
Optimal rule given by a solution to linear optimization problem
Credibility (ex post optimality)
Side product: which mechanism is better (GR 2004) or (GR 2006)?

8. Lemma 1 L: There exist an optimal persuasion rule that is finite
Proof: Claim 1: For any there exist finite such that

9. Randomization is not needed
P1: There exist an optimal persuasion rule that is deterministic.
For any type probability of a mistake is
Implications (vectoric message structure)
Deterministic mechanism (GR 2004) equivalent to deterministic rule (GR 2006)
Optimal mechanism (GR 2004) weakly dominates optimal rule (GR 2006)

10. Proof
Let be finite optimal mechanism with the smallest number of noninteger values.
Suppose

11. Generalization of L with Vectoric message structure
For abstract message structure

12. Characterization L: Fix . Sum of errors on any satisfies
Let be a solution to a linear programming problem
P: There exists optimal deterministic mechanism inducing
P: Any optimal mechanism is credible

13. Conclusions Ability to verify facts improves information transmission
Skepticism and selective reporting
Unraveling of information from the top (frictionless verifiability)
Frictions:
Uncertainty about verifiability
Costly verifiability
Capacity constraints