Probabilistic Mechanism Design in Diffusion Auctions

TL;DR

This paper introduces novel probabilistic mechanisms for diffusion auctions on social networks, achieving incentive compatibility, revenue, efficiency, and resistance to collusion and Sybil attacks, including extensions to multi-unit settings.

Contribution

The paper proposes the Probabilistic Diffusion Mechanism (PDM) for path graphs and extends it to general networks, addressing incentive compatibility, revenue, efficiency, and robustness against collusion and Sybil attacks.

Findings

PDM satisfies incentive compatibility, non-negative revenue, and approximate efficiency.

f-PDM preserves key properties and can be Sybil-proof under certain conditions.

MUPDM and SP-MUPDM effectively handle multi-unit auctions with robustness against attacks.

Abstract

A diffusion auction refers to a selling process conducted over a social network, where each participant submits a bid and may invite other potential buyers to join the auction. Although various mechanisms have been proposed, none of them can simultaneously achieve incentive compatibility, non-negative revenue, and approximate efficiency with a constant approximation bound. In this paper, we propose the Probabilistic Diffusion Mechanism (PDM), a novel mechanism tailored for path graphs, which satisfies all three desired properties. We further extend PDM to general network structures through a map $f$, resulting in the $f$-PDM mechanism, which preserves the key properties of the original design. Beyond these, when $f$ satisfies properties such as breadth-first order, $f$-PDM also ensures Sybil-proofness and provides approximate revenue. Furthermore, to address buyer collusion, we introduce a modified version of the mechanism that balances collusion-proofness with revenue approximation. Finally, we extend the design to multi-unit diffusion auctions -- a more challenging setting -- and propose a simple yet effective mechanism, Multi-Unit PDM (MUPDM), that achieves approximate efficiency while maintaining IC. Moreover, we design Sybil-Proof MUPDM (SP-MUPDM) to resist Sybil attacks in the multi-item scenario.