Pragmatics of Persuasion
L15
Glazer and Rubinstein (TE 2006)
A study in the pragmatics of persuasion : a game theoretic approach.
Setup
• Today
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Sender choses which verified fact to reveal
-
Sender has limited capacity to verify facts
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Receiver choses their interpretation
• Optimal interpretation rule depends on S incentives
• Pragmatics: A field of linguistics
-
Interpretation of utterances depends on the context
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Cooperative principle (Grice 1989) requires aligned preferences
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Noncooperative approach Benz at al. (2006)
A persuasion game
• Finite state space
• Action space
• Sender always prefers
• Acceptance and rejection region
• (Arbitrary) type dependent message structure
• Persuasion rule
• Rule
• Rule
is deterministic if
is finite if
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
Milgrom’s message structure
• Assume
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Cheap talk with type independent preferences
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Trivial optimal rule
• Assume
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Variant of Milgrom’s persuasion game
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In any PBN equilibrium unraveling of information
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Trivial optimal persuasion rule:
• Problem interesting when high types cannot verify that they are high
• Example: Vectoric message structure
• Let
Example
• 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
3 sets of results
1.
Randomization is not needed
2.
Optimal rule given by a solution to linear optimization problem
3.
Credibility (ex post optimality)
4.
Side product: which mechanism is better (GR 2004) or (GR 2006)?
Lemma 1
L: There exist an optimal persuasion rule
Proof: Claim 1: For any
there exist finite.
that is finite
such that
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)
Proof
Let
be finite optimal mechanism with the smallest number of noninteger values.
Suppose
Generalization of
• L with Vectoric message structure
• For abstract message structure
Characterization
L: Fix
• Let
. Sum of errors on any
satisfies
be a solution to a linear programming problem
P: There exists optimal deterministic mechanism
P: Any optimal mechanism is credible
inducing
Conclusions
• Ability to verify facts improves information transmission
• Skepticism and selective reporting
• Unraveling of information from the top (frictionless verifiability)
• Frictions:
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Uncertainty about verifiability
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Costly verifiability
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Capacity constraints