Fair Diffusion Auctions

Abstract: Diffusion auction design is a new trend in mechanism design which extended 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. The social welfare of a diffusion auction is collectively accumulated by all participants: reporting high valuations or inviting high-valuation neighbors. Because of this, 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 \textit{Shapley fairness} to capture their social welfare contribution and to 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 \textit{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. Furthermore, PDA can be extended to the general combinatorial auction setting where the literature did not discover meaningful diffusion auctions yet.