Optimal Procurement Auction for Cooperative Production of Virtual Products: Vickrey-Clarke-Groves Meet Cremer-McLean

We set up a supply-side game-theoretic model for the cooperative production of virtual products. In our model, a group of producers collaboratively produce a virtual product by contributing costly input resources to a production coalition. Producers are capacitated, i.e., they cannot contribute more resources than their capacity limits. Our model is an abstraction of emerging internet-based business models such as federated learning and crowd computing. To maintain an efficient and stable production coalition, the coordinator should share with producers the income brought by the virtual product. Besides the demand-side information asymmetry, another two sources of supply-side information asymmetry intertwined in this problem: 1) the capacity limit of each producer and 2) the cost incurred to each producer. In this paper, we rigorously prove that a supply-side mechanism from the VCG family, PVCG, can overcome such multiple information asymmetry and guarantee truthfulness. Furthermore, with some reasonable assumptions, PVCG simultaneously attains truthfulness, ex-post allocative efficiency, ex-post individual rationality, and ex-post weak budget balancedness on the supply side, easing the well-known tension between these four objectives in the mechanism design literature.