Optimal Diffusion Auctions

TL;DR

This paper explores how to maximize seller revenue in diffusion auctions by designing optimal mechanisms tailored to specific social network structures, revealing the limitations of universal solutions.

Contribution

It introduces a class of optimal diffusion mechanisms for given network structures and demonstrates the non-existence of a universal optimal mechanism across all structures.

Findings

Optimal mechanisms can be designed for specific network structures.

A 'reserve structure' concept is introduced for mechanism design.

Universal optimal mechanisms across all networks do not exist.

Abstract

Diffusion auction design is a new trend in mechanism design for which the main goal is to incentivize existing buyers to invite new buyers, who are their neighbors on a social network, to join an auction even though they are competitors. With more buyers, a diffusion auction will be able to give a more efficient allocation and receive higher revenue. Existing studies have proposed many interesting diffusion auctions to attract more buyers, but the seller's revenue is not optimized. Hence, in this study, we investigate what optimal revenue the seller can achieve by attracting more buyers. Different from the traditional setting, the revenue that can be achieved in a diffusion auction highly relies on the structure of the network. Hence, we focus on optimal auctions with given classes of underlying networks. We propose a class of mechanisms, where for any given structure, an optimal diffusion mechanism can be found. We point out that it implies an idea of "reserve structure". Moreover, we show that an optimal mechanism that handles all structures does not exist. Therefore, we also propose mechanisms that have bounded approximations of the optimal revenue in all structures.