A Small-Scale Restricted Double Auction Mechanism Based on Local Differential Privacy

Auctions have been widely applied in resource allocation due to their fairness and efficiency. For instance, platforms receive requests from service requesters and utilize auction theory to select suitable service providers. Existing studies typically assume that winners are determined based on bidders’ true valuations by allowing arbitrary transactions between requesters and providers, which can lead to serious valuation privacy leakage issues and limitations in application scenarios. Although some research has addressed these concerns using differential privacy techniques, they mostly rely on a trusted platform, and the introduction of noise results in utility loss, making them unsuitable for restricted auction contexts. To overcome these limitations, we propose a restricted double auction mechanism based on local differential privacy. Specifically, we extract the characteristics of the valuation data and constrain the noise addition probability density function based on the data features. Then we design a novel exponential selection mechanism that ensures that the relative positions of the obfuscated bids remain unchanged compared to the original valuations, while satisfying ε-local differential privacy. Furthermore, we develop an auction matching mechanism that maintains properties such as truthfulness under restricted allocation. The simulation results demonstrate that the proposed bid obfuscation mechanism ensures that the relative positions of the interfered bids remain unchanged while incurring low time overhead. Compared to existing mechanisms, our restrictive auction mechanism can generate greater social welfare while reducing the risk of valuation privacy leakage.