Procurement Auctions with Losses

To study first-price procurement auctions in the presence of losses, we introduce a new fixed point gradient flow algorithm to compute the Bayesian Nash Equilibrium. We use this efficient algorithm to compare optimal, first-price and VCG auctions. This allows us to numerically estimate the social cost of sub-optimality of the nodal pricing mechanism in wholesale electricity markets. We also derive a closed form expression of the optimal mechanism procurement cost when the types are uniformly distributed. Last we show how the algorithm adapts to more general grids.