Low and high types in asymmetric first-price auctions

We study first-price auctions with n bidders where bidders’ types (valuations for the object) are drawn independently according to heterogeneous distribution functions. We show a relation between the distributions of high types and their equilibrium bids. On the other hand, we show that there is no relation between the distributions of types and equilibrium bids of low types, i.e. the equilibrium bids of low types are invariable.