Mergers Among Asymmetric Bidders: A Logit Second-Price Auction Model

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 relationship--higher-value firms win more frequently and at better prices than lower-value firms. Since the extreme value distribution is closed under the maximum function, the value of the merged coalition also has an extreme value distribution and thus lies on the same price/share curve. Consequently, merger price effects can be computed as a movement along the price/share curve, from the average pre-merger share to the post-merger aggregate share. The parameter determining how much winning prices change is the standard deviation of the extreme value component. Merger efficiency claims can be benchmarked against the marginal cost reductions necessary to offset merger price effects.