Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Meta-mechanisms for Combinatorial Auctions over Social Networks

Yuan Fang, Mengxiao Zhang, Jiamou Liu, Bakh Khoussainov

TL;DR

This paper introduces MetaMSN, a universal meta-mechanism that converts classical auction mechanisms into formats suitable for networks of bidders, preserving IC, IR, and ND under a non-sensitivity assumption. Building on MetaMSN, the authors develop MetaMSN-m to handle general monotone valuations and apply these frameworks to combinatorial auctions with single-minded buyers and with general valuations, including a recap of the DNS mechanism and its networked variant. The work provides theoretical guarantees (preservation of key properties and welfare bounds) and empirical evidence from real-world networks showing near-optimal social welfare and robust revenue gains through information propagation, thereby offering the first combinatorial-auction solutions over social networks. The proposed approach unifies disparate network-auction mechanisms, facilitates new market designs in networked settings, and highlights practical considerations and limitations for future scalability and broader valuation classes.

Abstract

Recently there has been a large amount of research designing mechanisms for auction scenarios where the bidders are connected in a social network. Different from the existing studies in this field that focus on specific auction scenarios e.g. single-unit auction and multi-unit auction, this paper considers the following question: is it possible to design a scheme that, given a classical auction scenario and a mechanism $\tilde{\mathcal{M}}$ suited for it, produces a mechanism in the network setting that preserves the key properties of $\tilde{\mathcal{M}}$? To answer this question, we design meta-mechanisms that provide a uniform way of transforming mechanisms from classical models to mechanisms over networks and prove that the desirable properties are preserved by our meta-mechanisms. Our meta-mechanisms provide solutions to combinatorial auction scenarios in the network setting: (1) combinatorial auction with single-minded buyers and (2) combinatorial auction with general monotone valuation. To the best of our knowledge, this is the first work that designs combinatorial auctions over a social network.

Meta-mechanisms for Combinatorial Auctions over Social Networks

TL;DR

This paper introduces MetaMSN, a universal meta-mechanism that converts classical auction mechanisms into formats suitable for networks of bidders, preserving IC, IR, and ND under a non-sensitivity assumption. Building on MetaMSN, the authors develop MetaMSN-m to handle general monotone valuations and apply these frameworks to combinatorial auctions with single-minded buyers and with general valuations, including a recap of the DNS mechanism and its networked variant. The work provides theoretical guarantees (preservation of key properties and welfare bounds) and empirical evidence from real-world networks showing near-optimal social welfare and robust revenue gains through information propagation, thereby offering the first combinatorial-auction solutions over social networks. The proposed approach unifies disparate network-auction mechanisms, facilitates new market designs in networked settings, and highlights practical considerations and limitations for future scalability and broader valuation classes.

Abstract

Recently there has been a large amount of research designing mechanisms for auction scenarios where the bidders are connected in a social network. Different from the existing studies in this field that focus on specific auction scenarios e.g. single-unit auction and multi-unit auction, this paper considers the following question: is it possible to design a scheme that, given a classical auction scenario and a mechanism suited for it, produces a mechanism in the network setting that preserves the key properties of ? To answer this question, we design meta-mechanisms that provide a uniform way of transforming mechanisms from classical models to mechanisms over networks and prove that the desirable properties are preserved by our meta-mechanisms. Our meta-mechanisms provide solutions to combinatorial auction scenarios in the network setting: (1) combinatorial auction with single-minded buyers and (2) combinatorial auction with general monotone valuation. To the best of our knowledge, this is the first work that designs combinatorial auctions over a social network.
Paper Structure (23 sections, 8 theorems, 3 equations, 4 figures, 3 tables, 2 algorithms)

This paper contains 23 sections, 8 theorems, 3 equations, 4 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Contributions.
  2. Related work.
  3. Preliminaries
  4. The classical model.
  5. Meta-Mechanism for Social Networks
  6. Method
  7. Analysis
  8. Combinatorial Auction with Single-minded Buyers
  9. Combinatorial Auction with General Valuation Buyers
  10. The DNS Mechanism: A Recap
  11. MetaMSN-m
  12. Limitation of MetaMSN-m.
  13. Experiment
  14. Dataset.
  15. Valuation.
  16. ...and 8 more sections

Key Result

Theorem 1

Suppose $\tilde{\mathcal{M}}$ is a mechanism for an auction scenario that satisfies the non-sensitivity property. Then the mechanism $\mathcal{M}$ obtained from $\tilde{\mathcal{M}}$ by applying MetaMSN is IC, IR, & ND, whenever $\tilde{\mathcal{M}}$ is IC, IR, & ND, respectively.

Figures (4)

  • Figure 1: A social network
  • Figure 2: Valuations of $a,b,c$
  • Figure 3: Social welfare and revenue of four mechanisms in three datasets for (i) combinatorial auction with single-minded buyers
  • Figure 4: Social welfare and revenue of four mechanisms in three datasets for (i) combinatorial auction with single-minded buyers under normally distributed valuations

Theorems & Definitions (16)

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