Convex elicitation of continuous properties Jessica Finocchiaro, - PowerPoint PPT Presentation

Introduction Main Result Summary Convex elicitation of continuous properties Jessica Finocchiaro, Rafael Frongillo University of Colorado- Boulder June 22, 2018

Introduction Main Result Summary Principal-agent problem You want to learn something from a reporter. Punish them based on their error. L ( r ✱ y ) r is the report. y is the observed outcome. Agent is seeking to minimize their expected loss.

Introduction Main Result Summary Definitions A property is a function of a probability distribution Γ : ∆ ( Y ) Ñ R A loss L : R ˆ Y Ñ R elicits a property Γ if for all p , t Γ ( p ) u = arg min r P R E Y „ p L ( r ✱ Y ) Here, Y is finite

Introduction Main Result Summary Problem at hand

Introduction Main Result Summary Problem at hand

Introduction Main Result Summary Problem at hand

Introduction Main Result Summary Main result Theorem (Informal) Let Γ be a real-valued, continuous property. Then Γ is elicitable ð ñ Γ is convex elicitable.

Introduction Main Result Summary Summary

Introduction Main Result Summary Summary

Introduction Main Result Summary What does this mean to EC? Scoring Rule Markets Axioms Tractable Trading Bounded Trader Budgets

Introduction Main Result Summary Thank you Questions?