CS364A: Algorithmic Game Theory Lecture #7: Multi-Parameter Mechanism Design and the VCG Mechanism

Previous lectures only considered single-parameter mechanism design problems, where each participant has just one piece of private information, its valuation per unit of stuff. In many problems, a participant has different private valuations for different items. Once we are unsure about whether a participant prefers item A to item B, for example, we are in the realm of multi-parameter mechanism design. Here are the ingredients of a general, multi-parameter mechanism design problem: