General Truthfulness Characterizations Via Convex Analysis

TL;DR

This paper develops a unified convex analysis framework for truthful elicitation mechanisms, extending existing models and providing new characterizations for scoring rules and property elicitation, with applications to mechanism design.

Contribution

It introduces a comprehensive convex analysis-based characterization of truthful mechanisms, including non-convex distribution sets and property elicitation, unifying and extending prior results.

Findings

Characterization of scoring rules for non-convex distribution sets

Unified framework for mechanisms and scoring rules via convex analysis

New proof of a mechanism design theorem by Saks and Yu

Abstract

We present a model of truthful elicitation which generalizes and extends mechanisms, scoring rules, and a number of related settings that do not qualify as one or the other. Our main result is a characterization theorem, yielding characterizations for all of these settings, including a new characterization of scoring rules for non-convex sets of distributions. We generalize this model to eliciting some property of the agent's private information, and provide the first general characterization for this setting. We combine this characterization with duality to give a simple construction to convert between scoring rules and randomized mechanisms. We also show how this characterization gives a new proof of a mechanism design result due to Saks and Yu.