In this paper, we derive estimators of, and closed-form (non-integral) expressions for, the distribution of bids in an extreme value, asymmetric, second-price, private-values auction. In equilibrium, prices (winning bids) and shares (winning probabilities) have a simple monotonic...

In a private values, open auction, we show that bidder surplus can be expressed as a simple difference between unconditional moments of order statistics. The strength of the result is its simplicity and generality, as we dispense with the typical assumptions of independence and/or symmetry. We...