Fair Diffusion Auctions

TL;DR

This paper introduces a new diffusion auction model that incorporates Shapley fairness to fairly allocate social welfare contributions, achieving incentive compatibility and individual rationality, and extends to complex combinatorial settings.

Contribution

It proposes the Permutation Diffusion Auction (PDA), the first to satisfy Shapley fairness along with incentive compatibility and rationality, and extends diffusion auction design to combinatorial auctions.

Findings

PDA achieves 1/(k+1)-Shapley fairness.

PDA is incentive compatible and individually rational.

Extension to general combinatorial auctions demonstrated.

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.