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Combinatorial Diffusion Auction Design

Xuanyu Li, Miao Li, Yuhan Cao, Dengji Zhao

TL;DR

A combinatorial diffusion auction framework which can use any desirable single-item diffusion auction to produce a combinatorial auction to satisfy incentive compatibility (IC), individual rationality (IR), and weak budget balance (WBB).

Abstract

Diffusion auction design for combinatorial settings is a long-standing challenge. One difficulty is that we cannot directly extend the solutions for simpler settings to combinatorial settings (like extending the Vickrey auction to VCG in the traditional settings). In this paper, we propose a different approach to leverage the diffusion auctions for single-item settings. We design a combinatorial diffusion auction framework which can use any desirable single-item diffusion auction to produce a combinatorial auction to satisfy incentive compatibility (IC), individual rationality (IR), and weak budget balance (WBB).

Combinatorial Diffusion Auction Design

TL;DR

A combinatorial diffusion auction framework which can use any desirable single-item diffusion auction to produce a combinatorial auction to satisfy incentive compatibility (IC), individual rationality (IR), and weak budget balance (WBB).

Abstract

Diffusion auction design for combinatorial settings is a long-standing challenge. One difficulty is that we cannot directly extend the solutions for simpler settings to combinatorial settings (like extending the Vickrey auction to VCG in the traditional settings). In this paper, we propose a different approach to leverage the diffusion auctions for single-item settings. We design a combinatorial diffusion auction framework which can use any desirable single-item diffusion auction to produce a combinatorial auction to satisfy incentive compatibility (IC), individual rationality (IR), and weak budget balance (WBB).

Paper Structure

This paper contains 15 sections, 6 theorems, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Combinatorial Auction
  4. Diffusion Auction
  5. The Model
  6. Diffusion Combinatorial Auction Framework
  7. Candidate Distributor Determination Process
  8. Bundle Division Process
  9. Diffusion Resale Process
  10. Diffusion Combinatorial Auction Framework
  11. Dealer Retail Mechanism
  12. Greedy BDP
  13. IDM DRP
  14. Dealer Retail Mechanism
  15. Conclusion

Key Result

Theorem 1

Suppose that a single-item mechanism $\mathcal{\tilde{M}}$ satisfies IC, IR, and revenue consistency, a $CDP$ satisfies candidate distributor consistency, a $BDP$ satisfies resale diffusion monotonicity. Then the corresponding mechanisms generated by applying $DCAF$ are IC, IR, and WBB.

Figures (2)

  • Figure 1: The Pipeline of Diffusion Combinatorial Auction Framework
  • Figure 2: An example of a combinatorial auction on the social network. $Rev(b)=max(v_i(b))_{i\in T_n}$,$Pr(b)$ is the second max $v_i(b)_{i\in T_n}$

Theorems & Definitions (24)

  • Definition 1: Auction Mechanism
  • Definition 2: Diffusion Auction Mechanism
  • Definition 3: Individual Rationality
  • Definition 4: Incentive Compatibility
  • Definition 5: Seller's Revenue
  • Definition 6: Weak Budget Balance
  • Definition 7: Candidate Distributor Determination Process
  • Definition 8: Pricing Function
  • Definition 9: Resale Revenue Function
  • Definition 10: Bundle Division Process
  • ...and 14 more