Partly Verifiable Signals
L12
Glazer and Rubinstein (ECMA 2004)
Information Transmission in Markets
• S-R setting with type independent preferences of S
• Benchmarks:
- Cheap Talk (only bubbling equilibrium)
- Perfectly (costlessly) verifiable types (only fully revealing equilibrum)
• Realistic Settings: fact checking is costly and verification is partial
• Questions:
- Uncertainty about verifiability
- Which party should verify information?
- Optimal verification effort?
- Does prior communication improve verification process?
- If yes, what is the optimal verification mechanism?
Partial verification
• State space
where
is an aspect and quality is
• Uncertainty about verification (Shin 2003)
-
Low types S strategically withhold negative information
-
Pooling at the bottom
-
Uncertainty mutes R’s skepticism
-
result in asymmetric return dynamics
• Unaware buyers (Milgrom and Roberts 1986)
-
R unaware which characteristics are relevant
-
S announce high but irrelevant test scores
-
Test scores ignored by R
-
With heterogenous buyers competition among S better than regulation
Costly verification
• Costly verification by a sender (Jovanovic 1982)
-
Excessive testing and selective reporting (data mining)
-
Welfare loss (as in the signaling literature)
• Costly verification by a receiver (Townsend 1979)
-
Insurance against wealth shocks
-
S informs about the wealth shock
-
R can verify the claim at some cost
-
Optimal contract: no verification until default
• Today: capacity constraint (can verify only one aspect)
Motivating example
• A candidate with two characteristics (talent, loyalty) and an employer
• Decision: hire, not hire
• Candidate (sender, speaker)
- strictly prefers action ``hire’’
- can send a message regarding his characteristics
• Employer (receiver, listener)
- wants to hire only if sum of characteristics above one
- has capacity to verify only one characteristic
• Questions:
1.
Can employer reduce probability of a mistake by talking to a candidate?
2.
If yes, how should he verify information obtained in the conversation?
Glazer and Rubinstein persuasion game
• State space
• Action space
• Sender always prefers
• Acceptance and rejection region
•
Verification mechanism
with aspect
Preferences over Verification Mechanism
• Fix
• Let
• R preferences over verification mechanisms
-
Type one error
-
mechanism
Type two error
is R-optimal if it solves
• Remarks:
-
We search for the best verification mechanism for R
-
Commitment (this assumption is relaxed)
-
More general loss function
and arbitrary prior
Important classes of Mechanisms
• Direct mechanism
• Deterministic mechanism
• Bubbling mechanism
Does conversation improve welfare?
• Consider candidate-employer problem
• Bubbling mechanism improves over no verification
• Conversation improves over a ``bubbling’’ mechanism
L-principle
• Assume
• Consider any three types
P: For any mechanism
forming ``L’’
the sum of mistake probabilities is
• ``Mass of independent ``Ls’’ gives a lower bound for the number of mistakes
• Easy check of mechanism optimality
Proof: L-principle
• Fix mechanism
and
. Let
be optimal for