On the Relationship between the VCG Mechanism and Market Clearing

We consider a social cost minimization problem with equality and inequality constraints in which a central coordinator allocates infinitely divisible goods to self-interested N firms under information asymmetry. We consider the Vickrey-Clarke-Groves (VCG) mechanism and study its connection to an alternative mechanism based on market clearing-price. Under the considered set up, we show that the VCG payments are equal to the path integrals of the vector field of the market clearing prices, indicating a close relationship between the VCG mechanism and the 'clearing-price' mechanism. We then discuss its implications for the electricity market design and also exploit this connection to analyze the budget balance of the VCG mechanism.