Asymptotic Efficiency for Discriminatory Private Value Auctions

We consider discriminatory auctions for multiple identical units of a good. Players have private values, possibly for multiple units. None of the usual assumptions about symmetry of players' distributions over values or of their equilibrium play are made. Because of this, equilibria will typically involve inefficiency: objects may not end up in the hands of those who value them most. We show that, none the less, such auctions become arbitrarily close to efficient as the number of players, and possibly the number of objects, grows large.