Truthful germs are contagious: a local to global characterization of truthfulness

We study the question of how to easily recognize whether a social unction f from an abstract type space to a set of outcomes is truthful, i.e. implementable by a truthful mechanism. In particular, if the restriction of f to every "simple" subset of the type space is truthful, does it imply that f is truthful? Saks and Yu proved one such theorem: when the set of outcomes is finite and the type space is convex, a function f is truthful if its restriction to every 2element subset of the type space is truthful, a condition called weak monotonicity. This characterization fails for infinite outcome sets. We provide a local-to-global characterization theorem for any set of outcomes (including infinite sets) and any convex space of types (including infinite-dimensional ones): a function f is truthful if its restriction to every sufficiently small 2-D neighborhood about each point is truthful. More precisely, f is truthful if and only if it satisfies local weak monotonicity and is vo...

• Type: Journal
• Year: 2008
• Where: SIGECOM
• Authors: Aaron Archer, Robert Kleinberg
• Keywords: ECommerce, SIGECOM 2008, Truthful, Truthful Mechanism, Type Space