Partly Verifiable Signals (c.n.)

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Presentation transcript:

Partly Verifiable Signals (c.n.) Glazer and Rubinstein (ECMA 2004) Glazer and Rubinstein (TE 2006)

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

Auxiliary result Consider a problem P1: For any solution there exist optimal mechanism for which C: is optimal iff implied solves Optimal mechanism: direct, conservative with Result holds for arbitrary objective function increasing in each component

Characterization Linear program has simple structure Domain: Convex polytope Set of extreme points is finite At least one extreme point is a solution With more than one extreme point, any convex combination is also a solution Alon (2003): Any extreme point takes a form

Main Result Linear programming: strong structure with extreme points ``Fair coin’’ mechanism: P2: There exist an optimal mechanism that uses fair coin randomization Result dramatically simplifies search for an optimal mechanism Number of checks

Intuition Example Glazer and Rubinstein give example with

Deterministic Mechanism Definition: Example 1: optimal mechanism is deterministic Example 2: Deterministic mechanism is not optimal General conditions under which deterministic mechanism is optimal? Alternative interpretation of deterministic SR model.

Result Assume: with uniform distribution is monotonic closed convex and non-empty P: There exists an optimal mechanism that is direct and deterministic.

Heuristic proof Deterministic mechanism characterized by ``persuasive facts’’ For mechanism accepts iff Parametric class of deterministic mechanisms Sketch of the proof the mechanism exists (within the restricted class) necessary conditions for the mechanism attains lower bound given by L priciple

Heuristic proof Necessary optimality conditions for thresholds

Geometry of errors L-principle

Credibility So far we have assumed commitment Outcome of can be implemented as PBN in a sequential SR game Construction of equilibrium uses solution to a dual problem

Related questions How large is the set of optimal mechanisms? What are Pareto undominated ones? Consider objective function How the set of optimal mechanisms changes with Non-linear objective functions?