A Profit-Maximizing Data Marketplace with Differentially Private Federated Learning under Price Competition

The proliferation of machine learning (ML) applications has given rise to a new and popular data marketplace paradigm. These marketplaces facilitate ML model requesters in obtaining data from data owners to train their desired models. To mitigate the privacy concerns of data owners, federated learning (FL) has been introduced, enabling collaborative model training without raw data trading. Furthermore, researchers have incorporated differential privacy (DP) techniques into FL, resulting in differentially private federated learning (DPFL) to enhance privacy preservation. However, existing designs of DPFL-based data marketplaces consider a simplified but unrealistic scenario where the model requester holds dominant market power, and data owners cannot set their own prices. In this work, we propose a novel DPFL-based data marketplace that accommodates both price-taking and price-setting data owners. We model the interactions among the model requester and these two types of data owners as a three-stage Stackelberg game, focusing on maximizing the model requester's profit. We rigorously establish that the formulated game is a convex game with a unique subgame perfect equilibrium. Moreover, we devise iterative algorithms to determine the equilibrium strategies for the model requester and price-setting data owners. Notably, our algorithms allow data owners to operate without requiring complete information about the model requester or other data owners. Numerical experiments demonstrate the superiority of our proposed three-stage framework in terms of the model requester's profitability compared to scenarios where only price-taking data owners are involved. Furthermore, we reveal that price competition among price-setting data owners reduces equilibrium market prices.