Rank-Based Methods for the Analysis of Auctions
A new method is proposed for the analysis of first price and all pay auctions, where bidding functions are written not as functions of values but as functions of the rank or quantile of the bidder's value in the distribution from which it was drawn. This method gives new results in both symmetric and asymmetric cases with independent values. It is shown that under this new method if one bidder has a stochastically higher distribution of values then her bidding function in terms of rank will always be higher than her rival's. This is a clearer result under weaker conditions than using standard methods. We also look at auctions where one bidder has more precise information than the other.
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