[Paper Review] Incentive-Compatible Diffusion Auctions

Bin Li, Dong Hao+1 more|arXiv (Cornell University)|Jan 20, 2020

Auction Theory and Applications14 references4 citations

TL;DR

This paper establishes a sufficient and necessary condition for dominant-strategy incentive-compatible (DSIC) diffusion auctions, proving that monotonic allocation policies can be implemented in such mechanisms. It derives the optimal payment policy that maximizes seller revenue for any monotonic allocation, providing a general framework for designing efficient, revenue-maximizing diffusion auctions with truthful reporting incentives.

ABSTRACT

Diffusion auction is a new model in auction design. It can incentivize the buyers who have already joined in the auction to further diffuse the sale information to others via social relations, whereby both the seller's revenue and the social welfare can be improved. Diffusion auctions are essentially non-typical multidimensional mechanism design problems and agents' social relations are complicatedly involved with their bids. In such auctions, incentive-compatibility (IC) means it is best for every agent to honestly report her valuation and fully diffuse the sale information to all her neighbors. Existing work identified some specific mechanisms for diffusion auctions, while a general theory characterizing all incentive-compatible diffusion auctions is still missing. In this work, we identify a sufficient and necessary condition for all dominant-strategy incentive-compatible (DSIC) diffusion auctions. We formulate the monotonic allocation policies in such multidimensional problems and show that any monotonic allocation policy can be implemented in a DSIC diffusion auction mechanism. Moreover, given any monotonic allocation policy, we obtain the optimal payment policy to maximize the seller's revenue.

Motivation & Objective

• To close the gap in the literature by providing a general characterization of incentive-compatible diffusion auctions.
• To identify a sufficient and necessary condition for dominant-strategy incentive compatibility (DSIC) in diffusion auctions with multidimensional agent types.
• To formulate monotonic allocation policies that are implementable in DSIC diffusion auctions.
• To derive the optimal payment policy that maximizes seller revenue for any given monotonic allocation policy.
• To show that existing mechanisms like VCG and IDM are special cases of this general framework.

Proposed method

• The authors model diffusion auctions as multidimensional mechanism design problems where agents report both their valuations and their diffusion strategies (i.e., which neighbors to inform).
• They define a monotonic allocation policy as one where increasing a buyer’s reported valuation or diffusion set does not decrease her chance of winning.
• They prove that monotonicity is both necessary and sufficient for DSIC in this setting, extending classical value monotonicity to the diffusion context.
• They derive a general payment policy form: buyers pay a base amount based on the welfare without them and a reduction based on their reported diffusion set.
• The optimal payment policy is shown to be the one that maximizes seller revenue, derived by solving a constrained optimization problem over the payment structure.
• They validate their framework by showing that the VCG mechanism and the Information Diffusion Mechanism (IDM) both satisfy the derived conditions and payment forms.

Experimental results

Research questions

• RQ1 What is the general condition that ensures dominant-strategy incentive compatibility in diffusion auctions?
• RQ2 Can all monotonic allocation policies be implemented in a DSIC diffusion auction?
• RQ3 What is the optimal payment policy that maximizes seller revenue for a given monotonic allocation?
• RQ4 How do existing diffusion mechanisms like VCG and IDM fit into this general framework?
• RQ5 Is it possible to design an efficient, incentive-compatible, and budget-balanced diffusion auction?

Key findings

• A sufficient and necessary condition for dominant-strategy incentive compatibility in diffusion auctions is monotonicity of the allocation policy.
• Any monotonic allocation policy can be implemented in a DSIC diffusion auction mechanism.
• The optimal payment policy that maximizes seller revenue is derived as a function of the welfare without a buyer and the welfare under their reported diffusion strategy.
• The VCG mechanism, despite being efficient, is not budget-balanced and thus cannot be weakly budget-balanced in diffusion auctions.
• The Information Diffusion Mechanism (IDM) is a special case of the general framework, with a payment policy that matches the derived optimal form.
• There exists no individually rational and incentive-compatible diffusion auction that is both efficient and weakly budget-balanced.