Approximate Revenue Maximization for Diffusion Auctions

Reserve prices are widely used in practice. The problem of designing revenue-optimal auctions based on reserve price has drawn much attention in the auction design community. Although they have been extensively studied, most developments rely on the significant assumption that the target audience of the sale is directly reachable by the auctioneer, while a large portion of bidders in the economic network unaware of the sale are omitted. This work follows the diffusion auction design, which aims to extend the target audience of optimal auction theory to all entities in economic networks. We investigate the design of simple and provably near-optimal network auctions via reserve price. Using Bayesian approximation analysis, we provide a simple and explicit form of the reserve price function tailored to the most representative network auction. We aim to balance setting a sufficiently high reserve price to induce high revenue in a successful sale, and attracting more buyers from the network to increase the probability of a successful sale. This reserve price function preserves incentive compatibility for network auctions, allowing the seller to extract additional revenue beyond that achieved by the Myerson optimal auction. Specifically, if the seller has $ρ$ direct neighbours in a network of size $n$, this reserve price guarantees a $1-{1 \over ρ}$ approximation to the theoretical upper bound, i.e., the maximum possible revenue from any network of size $n$. This result holds for any size and any structure of the networked market.