Various Anonymity Properties in Diffusion Mechanism Design for Facility Location Games

Abstract

Diffusion mechanism design is a new research paradigm in the literature of mechanism design, which aims to incentivise agents to invite as many colleagues as possible to participate in a mechanism. An existing work on diffusion mechanism design for facility location games showed that there is no mechanism that satisfies strategy-proofness, Pareto efficiency and full anonymity, as well as proposed two naive mechanisms that satisfy strategy-proofness and Pareto efficiency by ignoring the full anonymity property. In this paper we aim to reveal to what extent strategy-proof and Pareto efficient mechanisms could be anonymous. We first define a class of anonymity properties by introducing a concept of partitions of the set of participating agents, and clarify a sufficient condition on partitions that guarantees the existence of mechanisms satisfying an anonymity property, as well as strategy-proofness and Pareto efficiency.