Partly Verifiable Signals (c.n.) Glazer and Rubinstein (ECMA 2004)

Glazer and Rubinstein persuasion game State space finite 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 Optimal mechanism solves

L-principle Assume Consider any three types forming ``L’’ 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

Examples Examples - Optimal deterministic mechanism - Optimal bubbling mechanism - Optimal stochastic mechanism We consider finite problems with uniform distributions Number of mistakes

Direct deterministic mechanism Let Number of independent L’s? Mechanism: Accept only if for at least one

No verification Let Number of independent L’s? Mechanism: reject regardless of message

Stochastic vs deterministic mechanism Let Consider three L’s Mechanism: Ask for two highest aspects, verify them with probability 0.5.

Definitions Direct mechanism Conservative direct mechanism Observation: Direct mechanism need not be truthful

Auxiliary result Consider a problem P1: There exist optimal mechanism for which vector solves C: is optimal iff implied solves Structure of the proof Byproduct: exists optimal mechanism that is direct and conservative.

Properties of

Proof

Proof