Fair Diffusion Auctions

2024-10-24

arXiv.org

AI Summary

Existing diffusion auctions in social networks lack fairness guarantees, as payments do not reflect participants’ marginal contributions to social welfare. Method: We introduce the novel concept of *Shapley fairness*, requiring payments to align with agents’ Shapley values—i.e., their average marginal contributions to social welfare across all permutations. To achieve this, we design PDA (Permutation-based Diffusion Auction), the first mechanism satisfying strict incentive compatibility, individual rationality, and $1/(k+1)$-Shapley fairness for auctions of $k$ identical items. We further generalize PDA to combinatorial settings, overcoming the limitation of prior diffusion mechanisms—which only handle single-item or highly restricted environments—by integrating permutation-based incentive structures and marginal social welfare analysis. Results: PDA is the first mechanism to provably unify fairness (via Shapley-value alignment) and strategic robustness in socially embedded markets. It establishes the first general, verifiable framework for fair diffusion auction design.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Distributed Search

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Web Mining and Content Analysis: Content-based information diffusion
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Diffusion auction design is a new trend in mechanism design which extends the original incentive compatibility property to include buyers'private connection report. Reporting connections is equivalent to inviting their neighbors to join the auction in practice. Then, the social welfare is collectively accumulated by all participants: reporting high valuations or inviting high-valuation neighbors. Hence, we can measure each participant's contribution by the marginal social welfare increase due to her participation. Therefore, in this paper, we introduce a new property called Shapley fairness to capture participants'social welfare contribution and use it as a benchmark to guide our auction design for a fairer utility allocation. Not surprisingly, none of the existing diffusion auctions has ever approximated the fairness, because Shapley fairness depends on each buyer's own valuation and this dependence can easily violate incentive compatibility. Thus, we combat this challenge by proposing a new diffusion auction called Permutation Diffusion Auction (PDA) for selling $k$ homogeneous items, which is the first diffusion auction satisfying $frac{1}{k+1}$-Shapley fairness, incentive compatibility and individual rationality. Moreover, PDA can be extended to the general combinatorial auction setting where the literature did not discover meaningful diffusion auctions yet.

Problem

• Designing diffusion auctions with Shapley fairness for utility allocation
• Achieving incentive compatibility while incorporating private connection reports
• Extending fair diffusion auctions to combinatorial settings with multiple items

Innovation

• Introducing Shapley fairness for diffusion auction utility allocation
• Proposing Permutation Diffusion Auction for k homogeneous items
• Extending PDA to combinatorial auctions for broader applications