A study in the pragmatics of persuasion a game theoretic approach L15 Glazer and Rubinstein TE 2006 Setup Today Sender choses which verified fact to reveal Sender has limited capacity to verify facts ID: 594655
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Pragmatics of Persuasion
A study in the pragmatics of persuasion : a game theoretic approach.
L15Glazer and Rubinstein (TE 2006) Slide2
Setup
Today
Sender choses which verified fact to revealSender has limited capacity to verify factsReceiver choses their interpretationOptimal interpretation rule depends on S incentivesPragmatics: A field of linguisticsInterpretation of utterances depends on the context Cooperative principle (Grice 1989) requires aligned preferencesNoncooperative approach Benz at al. (2006) Slide3
A persuasion game
Finite state space
Action space Sender always prefers Acceptance and rejection region(Arbitrary) type dependent message structurePersuasion ruleRule is deterministic if Rule is finite if Slide4
Optimal persuasion rule
For probability of acceptance
LetOptimal mechanism solvesRelative to Glazer and Rubinstein (2006):S controls which verified facts are revealedRandom decision ruleAbstract (possibly infinite) type dependent message space Slide5
Milgrom’s
message structure
Assume Cheap talk with type independent preferencesTrivial optimal rule AssumeVariant of Milgrom’s persuasion gameIn any PBN equilibrium unraveling of informationTrivial optimal persuasion rule:Problem interesting when high types cannot verify that they are highExample: Vectoric message structure Slide6
Example
Let
Acceptance regionVectoric message structure, capacity two aspectsRule 1: Accept if any two aspects are verifiedRule 2: Accept if any to neighboring aspects are verifiedSlide7
3 sets of results
Randomization is not needed
Optimal rule given by a solution to linear optimization problemCredibility (ex post optimality)Side product: which mechanism is better (GR 2004) or (GR 2006)? Slide8
Lemma 1
L: There exist an optimal persuasion rule that is finite
Proof: Claim 1: For any there exist finite. such that Slide9
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)Slide10
Proof
Let be finite optimal mechanism with the smallest number of
noninteger values.SupposeSlide11
Generalization of
L with
Vectoric message structure For abstract message structure Slide12
Characterization
L: Fix . Sum of errors on any satisfies
Let be a solution to a linear programming problem P: There exists optimal deterministic mechanism inducingP: Any optimal mechanism is credible Slide13
Conclusions
Ability to verify facts improves information transmission
Skepticism and selective reporting Unraveling of information from the top (frictionless verifiability)Frictions:Uncertainty about verifiabilityCostly verifiabilityCapacity constraints