[Paper Review] Fixed-price Diffusion Mechanism Design

Tianyi Zhang, Dengji Zhao+2 more|arXiv (Cornell University)|May 14, 2019

Auction Theory and ApplicationsDecision Sciences13 references3 citations

TL;DR

This paper proposes the Fixed-Price Diffusion Mechanism (FPDM), a novel mechanism that incentivizes buyers in a tree-structured social network to propagate sale information without revealing valuations, thereby increasing the seller’s revenue. It guarantees at least half of the optimal revenue under fixed pricing, using a computationally efficient, budget-balanced reward scheme based on distance from the winner.

ABSTRACT

We consider a fixed-price mechanism design setting where a seller sells one item via a social network, but the seller can only directly communicate with her neighbours initially. Each other node in the network is a potential buyer with a valuation derived from a common distribution. With a standard fixed-price mechanism, the seller can only sell the item among her neighbours. To improve her revenue, she needs more buyers to join in the sale. To achieve this, we propose the very first fixed-price mechanism to incentivize the seller's neighbours to inform their neighbours about the sale and to eventually inform all buyers in the network to improve seller's revenue. Compared with the existing mechanisms for the same purpose, our mechanism does not require the buyers to reveal their valuations and it is computationally easy. More importantly, it guarantees that the improved revenue is at least 1/2 of the optimal.

Motivation & Objective

• To design a fixed-price mechanism that enables a seller to expand buyer reach via social network diffusion without relying on valuation disclosures.
• To ensure the seller’s revenue is improved by at least half of the optimal revenue achievable under fixed pricing.
• To create a computationally efficient mechanism that does not require full knowledge of network structure or buyer valuations.
• To achieve incentive compatibility so buyers are motivated to truthfully propagate information to their neighbors.
• To extend the MIT Red Balloon Challenge’s reward model into a fixed-price mechanism for social network-based sales.

Proposed method

• The mechanism uses a distance-based reward scheme where buyers receive a fraction of the price difference based on their depth from the winner, scaled by (1/2)^d_i.
• It defines an optimal price p_j^opt(a') for each branch j, derived from the inverse of the root of (1 + k_{-j})^{1/k_{-j}}.
• The base price p_base is set as the minimum among all optimal prices, and rewards are computed as (p_j^opt - p_base) * α * (1/2)^d_i.
• The mechanism ensures that truthful diffusion maximizes utility for all buyer types, including winners, path participants, and others.
• It employs a tree-structured social network model where the seller is the root and buyers are leaf or internal nodes with independent valuations from [0,1].
• The mechanism is designed to be incentive-compatible by ensuring that diffusing to all neighbors always yields at least as high utility as any other action.

Experimental results

Research questions

• RQ1 Can a fixed-price mechanism be designed to incentivize buyers to propagate sale information in a social network without requiring valuation disclosures?
• RQ2 What is the maximum revenue improvement achievable through information diffusion under fixed pricing, and can it be bounded?
• RQ3 How can a mechanism be constructed to ensure truthful diffusion while maintaining computational efficiency and budget balance?
• RQ4 Can the mechanism guarantee at least half of the optimal revenue under fixed pricing, even without full network or valuation knowledge?
• RQ5 How does the structure of the social network (e.g., tree vs. general graph) affect the mechanism’s performance and design?

Key findings

• The Fixed-Price Diffusion Mechanism guarantees that the seller’s revenue is at least 1/2 of the optimal revenue achievable under fixed pricing.
• The mechanism is incentive-compatible: truthful diffusion to all neighbors maximizes each buyer’s utility, regardless of their position in the network.
• Buyers are rewarded based on their distance from the winner using a (1/2)^d_i decay factor, ensuring fairness and computational simplicity.
• The mechanism does not require buyers to reveal their valuations, preserving privacy and reducing information burden.
• The mechanism is computationally efficient, relying only on local network information and fixed pricing rules.
• The mechanism maintains budget balance and does not require advance payments to participants.