Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fair Diffusion Auctions

Zixin Gu, Yaoxin Ge, Yao Zhang, Dengji Zhao

TL;DR

This work addresses fair welfare-sharing in diffusion auctions by introducing $\epsilon$-Shapley fairness and designing the Permutation Diffusion Auction (PDA) for selling $k$ homogeneous items, which is incentive compatible, individually rational, and guarantees $\frac{1}{k+1}$-Shapley fairness. PDA randomizes an agent order and allocates items via irrevocable, per-step social-welfare maximizations, with payments equal to the marginal welfare gains to winners, yielding a close alignment between utilities and Shapley contributions. The authors extend the approach to combinatorial settings (CPDA), achieving at least $\frac{1}{n}$-Shapley fairness, thereby offering a principled fairness benchmark in diffusion auctions beyond single-item or purely revenue-focused designs. The results expose a revenue–fairness trade-off and open questions about non-deficit Shapley-fair mechanisms, highlighting practical implications for networks where broad participation and fairness are prioritized over maximal revenue.

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.

Fair Diffusion Auctions

TL;DR

This work addresses fair welfare-sharing in diffusion auctions by introducing -Shapley fairness and designing the Permutation Diffusion Auction (PDA) for selling homogeneous items, which is incentive compatible, individually rational, and guarantees -Shapley fairness. PDA randomizes an agent order and allocates items via irrevocable, per-step social-welfare maximizations, with payments equal to the marginal welfare gains to winners, yielding a close alignment between utilities and Shapley contributions. The authors extend the approach to combinatorial settings (CPDA), achieving at least -Shapley fairness, thereby offering a principled fairness benchmark in diffusion auctions beyond single-item or purely revenue-focused designs. The results expose a revenue–fairness trade-off and open questions about non-deficit Shapley-fair mechanisms, highlighting practical implications for networks where broad participation and fairness are prioritized over maximal revenue.

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 homogeneous items, which is the first diffusion auction satisfying -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.

Paper Structure

This paper contains 10 sections, 5 theorems, 22 equations, 4 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Related Work
  4. Preliminaries
  5. Permutation Diffusion Auction
  6. The Definition of PDA
  7. IC and IR Analysis
  8. Fairness Analysis
  9. Extension to Combinatorial Auctions
  10. Discussion

Key Result

Theorem 1

PDA is individually rational and incentive compatible.

Figures (4)

  • Figure 1: A network example of diffusion auctions. A single item is sold in this network. Each node represents one participant with her valuation in the circle ($s$ is the seller). The edges show the social relationships among them.
  • Figure 2: An example of PDA. (a)&(b) The dashed nodes represent buyers who have not joined yet, the blue nodes signify buyers who have joined but are not feasible, and the red nodes indicate feasible participants. Specifically, the triangles mark the newly joined buyers, and the filled nodes represent those who have become feasible due to the entry of the new buyers. (c) The expected utility in PDA (red) and the Shapley contribution (blue) of buyers.
  • Figure 3: An example of PDA that shows $\frac{1}{2}$ is a tight bound when selling a single item. The graph illustrates a single-chain network containing $s, A, B$; the table shows the utility and marginal contribution of $A$ and $B$ under different choices of orders, as well as their expected utilities and Shapley contribution. We can find that the expected utility is half of her Shapley contribution for buyer $B$.
  • Figure 4: The relationship between expected revenue and the allocation efficiency of Shapley fair diffusion auction mechanisms. The horizontal axis represents the efficiency of allocations and the vertical axis represents the expected revenue. The red parallelogram shows the space of $\epsilon$-Shapley fair mechanisms. Specially, for $1$-Shapley fair mechanisms, the space is an inclined line segment at the bottom.

Theorems & Definitions (15)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Example 1
  • Theorem 1
  • proof
  • Theorem 2
  • ...and 5 more