  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.
