Partly Verifiable Signals 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: Can employer reduce probability of a mistake by talking to a candidate? If yes, how should he verify information obtained in the conversation?

Glazer and Rubinstein persuasion game State space with aspect Action space Sender always prefers Acceptance and rejection region Verification mechanism

Preferences over Verification Mechanism Fix Let R preferences over verification mechanisms Type one error Type two error mechanism 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 forming ``L’’ P: 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

Proof: L-principle Fix mechanism and . Let be optimal for