The enduring value of the Vickrey-Clarke-Groves (VCG) mechanism has been highlighted due to its adoption by Facebook ad auctions. Our research delves into its utility in the collaborative virtual goods production (CVGP) game, which finds application in realms like federated learning and crowdsourcing, in which bidders take on the roles of suppliers rather than consumers. We introduce the Procurement-VCG (PVCG) sharing rule into existing VCG mechanisms such that they can handle capacity limits and the continuous strategy space characteristic of the reverse auction setting in CVGP games. Our main theoretical contribution provides mathematical proofs to show that PVCG is the first in the CVGP game context to simultaneously achieve truthfulness, Pareto efficiency, individual rationality, and weak budget balance. These properties suggest the potential for Pareto-efficient production in the digital planned economy. Moreover, to compute the PVCG payments in a noisy economic environment, we propose the Report-Interpolation-Maximization (RIM) method. RIM facilitates the learning of the optimal procurement level and PVCG payments through iterative interactions with suppliers.

翻译：Vickrey-Clarke-Groves（VCG）机制因其在Facebook广告拍卖中的应用而彰显其持久价值。本研究深入探讨了其在协作虚拟商品生产（CVGP）博弈中的效用，该博弈适用于联邦学习和众包等领域，其中投标人扮演供应商而非消费者的角色。我们将采购-VCG（PVCG）分配规则引入现有VCG机制，使其能够处理CVGP博弈中反向拍卖场景的容量限制和连续策略空间特征。我们的主要理论贡献提供了数学证明，表明PVCG在CVGP博弈背景下首次同时实现了真实性、帕累托效率、个体理性与弱预算平衡。这些特性暗示了数字计划经济中实现帕累托效率生产的潜力。此外，为在噪声经济环境中计算PVCG支付，我们提出了报告-插值-最大化（RIM）方法。RIM通过与供应商的迭代交互，促进最优采购水平与PVCG支付的学习。